Algebraic fractions look incredibly difficult at first, and can seem daunting to tackle for the untrained student. With a mixture of variables, numbers, and even exponents, it is hard to know where to begin.


Math is hard. It's easy to forget even core concepts when you are trying to remember dozens of different principles and methods. Here's your refresher on two methods to reduce fractions.


Renaming a mixed number as an improper fraction means to convert it to an equivalent fraction. If you need to write the fraction in its simplest form, you need to complete the added step of simplifying, or reducing it.


Traditionally, a radical or irrational number cannot be left in the denominator (the bottom) of a fraction. When a radical does appear in the denominator, you need to multiply the fraction by a term or set of terms that can remove that radical expression.


While it's easy to order whole numbers like 1, 3, and 8 by size, fractions can be hard to measure at a glance. If each lower number, or denominator, is the same, you can order them like whole numbers, for instance 1/5, 3/5, and 8/5.


Multiplying fractions with whole numbers is simple once you know how to put the whole number in fraction form. If you want to know how to multiply fractions with whole numbers, just follow these 4 very easy steps.


In order to add or subtract fractions with different denominators (the bottom number of the fraction), you must first find the least common denominator shared between them.


Multiplying fractions is one of the basic skills anyone who deals with fractions should know. To multiply fractions, you just have to multiply their numerators and the denominators, and then simplify your answer if you can.


As you begin to subtract bigger and bigger numbers, the rules of subtraction stay the same; however, the calculations can become trickier because often you will need to regroup, or borrow, several times.


Reciprocals are helpful in all sorts of algebraic equations. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd.


Addition is one of the few things we learn in school that we're actually asked to put into use every day of our lives. Luckily, it's easy to learn how to add.


To add and subtract square roots, you need to combine square roots with the same radical term. This means that you add or subtract 2√3 and 4√3, but not 2√3 and 2√5.


Dividing decimals can be a bit trickier than dividing whole numbers. But if you know how to master a few tricks, you'll be able to divide decimals in no time.


Dividing double digits is a lot like single-digit long division, but it does take a little longer and some practice. Since most of us haven't memorized our 47 times tables, this can take a little guesswork, but there's a handy trick you can learn to make it faster.


The binary number system works similarly to the base 10 decimal system we are used to using, except that it is a base 2 system consisting of only two digits, 1 and 0.


You might think of  integers  as just ordinary numbers, like 3, -12, 17, 0, 7000, or -582 but many people do confuse them as whole numbers. Integers are a lot like whole numbers but they also contain their additive inverse and zero. (


Bet someone you can add five consecutive integers faster than they can. You can use this as a  bar trick , with your friends, or (if you are a student) impress your teacher!


Dividing expressions that have exponents is easier than it looks. As long as you're working with the same base, all you have to do is subtract the values of the exponents from each other and keep the base the same.


Cross multiplying is a way to solve an equation that involves a variable as part of two fractions set equal to each other. The variable is a placeholder for an unknown number or quantity, and cross-multiplying reduces the proportion to one simple equation, allowing you to solve for the variable in question.


Binary division problems can be solved using long division, which is a useful method for teaching the process to yourself or writing a simple computer program.


Determine the Number of Divisors of an Integer

A divisor, or factor, is a number that divides evenly into a larger integer.  [1]   It is easy to determine how many divisors a small integer (such as 6) has by simply listing out all the different ways you can multiply two numbers together to get to that integer.


Teach the Multiplication Tables to Your Child

Many children struggle with learning their times tables--as their parent, you may feel like it's your duty to help. After all, they'll need quick multiplication skills to help them throughout high school, college, and life.


Being able to multiple with your fingers is a valuable skill to have, and people have been doing it since at least the 15th century. We may have cellphone calculators, but in many cases it is actually easier to keep your phone in your pocket and multiply with your fingers.


You've probably already noticed a pattern with some multiples of 11. The two digit numbers are easy to recognize: 11, 22, 33, 44, and so on. But once you get to larger numbers, it's difficult to recognize them at a glance.


Multiplication is one of the four basic operations in elementary arithmetic and can be considered repeated  addition . It's the mathematical operation of scaling one number by another number.


Calculate Divisibility By Single Digit Numbers

Many times in math, you find yourself wondering whether a big number is divisible by a single digit. While this is easy enough to determine using a calculator, you might not always have access to one, or you might want a shortcut to help you determine divisibility before going through the trouble of calculating.


Dividing by a decimal number can look difficult at first. After all, no one taught you the "0.7 times tables." The secret is to change the division problem into a format that only uses whole numbers.


Solve the Wave Equation in One Dimension

The wave equation is one of the most important partial differential equations, as it describes waves of all kinds as encountered in physics. In this article, we use Fourier analysis to solve the wave equation in one dimension.


Create a Times Table to Memorize in Excel

In this article, you'll learn to create a Times Table or Multiplication Table in Microsoft Excel, which can be adapted to being a Division Table and saved separately.


Exact differential equations are a subset of first-order ordinary differential equations. An equation of the form        P  (  x  ,  y  )    d    x  +  Q  (  x  ,  y  )    d    y  =  0    {\displaystyle P(x,y){\mathrm {d} }x+Q(x,y){\mathrm {d} }y=0}       is considered to be exact if the following condition holds.


The series RLC circuit is a circuit that contains a resistor, inductor, and a capacitor hooked up in series. The governing differential equation of this system is very similar to that of a damped harmonic oscillator encountered in classical mechanics.


Solve Differential Equations Using Laplace Transforms

The  Laplace transform  is an integral transform that is widely used to solve linear differential equations with constant coefficients. When such a differential equation is transformed into Laplace space, the result is an algebraic equation, which is much easier to solve.


Solve Poisson's Equation Using Fourier Transforms

Poisson’s equation is an important partial differential equation that has broad applications in physics and engineering. This article will deal with electrostatic potentials, though the techniques outlined here can be applied in general.


Solve a Separable Ordinary Differential Equation

Separation of variables is one of the most important techniques in solving differential equations. In this article, we show how to apply this to ordinary differential equations.


Determine Convergence of Infinite Series

Infinite series can be daunting, as they are quite hard to visualize. By inspection, it can be difficult to see whether a series will converge or not.


Solve Linear Differential Equations Using the Method of Undetermined Coefficients

The method of solving linear differential equations with constant coefficients is a very simple and straightforward process of solving equations of the form below, where        Q  (  x  )  =  0.


Derive the BAC‐CAB Identity Using Index Notation

The vector triple product involves taking two cross products. Because this can often be tedious to calculate, we often use BAC-CAB, a useful mnemonic that simplifies vector calculations by converting a problem requiring computation of cross products into one that computes dot products.


Solve Laplace's Equation in Spherical Coordinates

Laplace's equation         ∇    2    f  =  0    {\displaystyle \nabla ^{2}f=0}       is a second-order partial differential equation (PDE) widely encountered in the physical sciences.


Calculate the Laplace Transform of the Natural Logarithm

The  Laplace transform  is an integral transform widely used to solve differential equations with constant coefficients. The transforms are typically very straightforward, but there are functions whose Laplace transforms cannot easily be found using elementary methods.


Solve Homogeneous Linear Differential Equations with Constant Coefficients

A linear ordinary differential equation is one of the form below.


In complex analysis, a holomorphic function is a function that is complex differentiable in a neighborhood of every point in its domain (i.e., analytic).


Differentiating a polynomial function can help track the change of its slope. To differentiate a polynomial function, all you have to do is multiply the coefficients of each variable by their corresponding exponents, lower each exponent by one degree, and remove any constants.


Calculating square root is easy if you have a whole number. If you don’t, there’s a logical process you can follow to systematically figure out the square root of any number, even if you don’t use a calculator.


Logarithms may look difficult to use, but just like exponents or polynomials, you just need to learn the correct techniques. You only need to know a couple basic properties to divide two logarithms of the same base, or to expand a logarithm that contains a quotient.


An exponent, also called a power or index,  [1]   is a number that tells you how much to multiply a base number. To solve an addition sentence that includes exponents, you must know how to find the value of the individual exponential expressions, either by hand or by using a calculator.


In calculus, the multiple integral generalizes the definite integral to functions of more than one variable. Multiple integration is straightforward and similar to single-variable integration, though techniques to simplify calculations become more important.


Calculate the Fourier Transform of a Function

The Fourier transform is an integral transform widely used in physics and engineering. They are widely used in signal analysis and are well-equipped to solve certain partial differential equations.


In multivariable calculus, the gradient generalizes the partial derivative to multiple dimensions. Calculating the gradient is thus a straightforward application of partial derivatives, with many applications in the physical sciences.


Surface integrals are a generalization of line integrals. While the line integral depends on a curve defined by one parameter, a two-dimensional surface depends on two parameters.


With the use of calculators, finding the cube root of any number may be just buttons away. But perhaps you don't have a calculator, or you want to impress your friends with the ability to calculate a cube root by hand.


Memorizing perfect squares in math can be tough to do, but you will be glad once you did. Knowing your perfect squares can make it easier to compute larger numbers without using a calculator and save you valuable time on tests and quizzes.


In the days before calculators, students and professors alike had to calculate square roots by hand. Several different methods have evolved for tackling this daunting process, some giving a rough approximation, others giving an exact value.


Figure out 10 to the Power of Any Positive Integer

Figuring out 10 to the power of any positive integer is easier than it looks. All you have to do is know that the exponent above the number 10 simply indicates the number of times that you have to multiply 10 by itself.


Confused by the logarithms? Don't worry! A logarithm (log for short) is actually just an  exponent  in a different form.


Doubling large numbers can seem intimidating at first, but the task becomes easier with practice. There are multiple methods you can use to double a number.


A flexagon is a polygon folded out of paper in such a way that there are three patterned faces.  [1]   To make a flexagon you only need some paper, a template, scissors, and glue.


Children are often confused and mystified by the need to carry numbers in addition and multiplication. It's up to you to unveil the secrets and make it simple.


A circle is a two-dimensional shape made by drawing a curve. In trigonometry and other areas of mathematics, a circle is understood to be a particular kind of line: one that forms a closed loop, with each point on the line equidistant from the fixed point in the center.


Finding the third angle of a triangle when you know the measurements of the other two angles is easy. All you've got to do is subtract the other angle measurements from 180° to get the measurement of the third angle.


The radius of a sphere (abbreviated as the variable  r  or  R ) is the distance from the exact center of the sphere to a point on the outside edge of that sphere.


The perimeter of a rectangle is the sum total length of all of its sides.  [1]   A rectangle is defined as a quadrilateral, or a geometric shape with four sides.


A trapezoid is defined as a quadrilateral with two parallel sides. As with any polygon, to find the perimeter of a trapezoid you need to add all four of its sides together.


In geometry, the term "perimeter" usually refers to the  total distance around the outside of a polygon , a 2-dimensional shape of 3 or more sides and angles.


A rhombus is a parallelogram with four congruent sides.  [1]   These properties allow for numerous methods for finding the perimeter. Since all four sides of a rhombus are of equal length, finding the perimeter is possible when one side length is known.


To calculate the area of a triangle you need to know its height. If this information is not given to you, you can easily calculate it based on what you do know!


A prism is a three-dimensional solid with two parallel bases, or faces, that are congruent.  [1]   The shape of the base determines what type of prism you have, such as a rectangular or triangular prism.


To many readers, "Calculating a growth rate" may sound like an intimidating mathematical process. In actuality, growth rate calculation can be remarkably simple.


Inflation is a key concept in economics that represents the increase in the price of consumer products over a period of time.  [1]   It can also be used to calculate deflation, or a drop in prices.


Finding the center of a circle can help you perform basic geometric tasks like finding the circumference or area. There are several ways to find the center point!


Politicians love to tell their constituents that every life is priceless, worth saving at any cost. Any who say otherwise can expect to be accused of "supporting death panels," "putting corporate profits ahead of children's lives," or "wanting arsenic in your water supply" in their next election campaign.


In statistics, absolute frequency refers to the number of times a particular value appears in a data set. Cumulative frequency is different: it is the sum (or running total) of all the frequencies up to the current point in the data set.


Covariance is a statistical calculation that helps you understand how two sets of data are related to each other. For example, suppose anthropologists are studying the heights and weights of a population of people in some culture.


The general way to find the perimeter of any shape is to add up the length of all its sides. For certain shapes, such as rectangles and circles, there are specific formulas you can use to simplify the process.


Calculate Expected Opportunity Loss (EOL)

Expected opportunity loss (EOL) is a statistical calculation used primarily in the business field to help determine optimal courses of action. Doing business is full of decision making.


As prices increase on many of the things you use in your day-to-day life, it may become necessary for you to calculate that increase for forecasting or accounting purposes.


Do you need to calculate the average age? It's easy to do. All you need to do is use a simple three-step process, and you should be able to figure it out.


A confidence interval is an indicator of your measurement's precision. It is also an indicator of how stable your estimate is, which is the measure of how close your measurement will be to the original estimate if you repeat your experiment.


Are you planning to write up a math-related article or document but lost when it comes to the symbols? Learn how to type mathematical symbols using the Keyboard Viewer in Macintosh System OS X.


Protractors are a tool used in mathematics to measure angles in degrees. You might need a protractor to work on homework or make construction plans, so learning how to make your own can come in handy.


If you or your kids are struggling with math, you're likely looking for ways to make it easier. When working on math, each concept builds on the one before, so you need to start with the basics, especially with young kids.


Pascal's Triangle is an arrangement of multiple numbers that have been found to relate to many areas of math and science. This article will explain how you can form it.


Pie charts capture your data and present it graphically at a glance!! They are simple and quick to make in Excel.


Make a Parabolic Growth Chart with Semiannual Dieoffs

You will learn to make a Growth Chart of a parabolic growth rate with 2 annual severe die-offs of the population (one in winter and one due to overfishing), as is probably typical for many fish species.


A mathematical model is a description of a system using mathematical language. Mathematical models are used not only in the natural sciences and engineering disciplines but they are also used in biology, economics and sociology.


Mathematics is disliked by most students. They condemn this subject which often causes that red mark on the report card. Being good at Math is a skill, which means that it can be developed.


Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. After discussing ways to be a good math student, this article will teach you the basic progression of math courses and will give you the basic elements that you'll need to learn in each course.


Want to play a clever trick on your friends? How about proving to them that one is the same thing as zero! Using this method, you will ask your friends questions that will lead them inevitably to this conclusion (or any other conclusion you want) whether they like it or not.


Two fractions are equivalent if they have the same value. Knowing how to convert a fraction into an equivalent one is an essential math skill that's necessary for everything from basic algebra to advanced calculus.


Estimating (or making an educated guess) can be very helpful when it comes to fractions. If you're trying to figure out certain proportions without having the data or time to come to a precise answer, making a proper estimation will set you on the right track.


A mixed number, or mixed fraction, is a number that combines a whole number and a fraction.  [1]   It is possible to divide mixed numbers; however, doing so requires converting them to improper fractions first.


Dividing fractions by a whole number isn't as hard as it looks. To divide a fraction by a whole number, all you have to do is to convert the whole number into a fraction, find the reciprocal of that fraction, and multiply the result by the first fraction.


When dividing a whole number by a fraction, you are finding how many groups of the fraction you can fit in the whole. The standard way of dividing a whole number by a fraction is to multiply the whole number by the reciprocal of the fraction.


Convert a Whole Number to an Improper Fraction

You can easily convert a whole number to a fraction by putting it over one, right? You can, however, convert it to an unreduced fraction. It's not difficult at all!


Comparing fractions means looking at two fractions and figuring out which one is greater. To compare fractions, all you have to do is to make it so that they have the same denominator and then see which fraction has the greater numerator -- this will tell you which fraction is greater.


A repeating decimal, also known as a recurring decimal, is a decimal number that has a digit or digits that infinitely repeat at regular intervals. Repeating decimals can be tricky to work with, but they can also be converted into a fraction.


An improper fraction is a fraction with a larger numerator than denominator. You can convert an improper fraction to a percent the same way that you would convert any fraction to a percent.


Convert Improper Fractions Into Mixed Numbers

In math, improper fractions are fractions where the numerator (the top half) is a number that is bigger than or equal to the denominator (the bottom half).


Divide a Fractional Algebraic Expression by a Fractional Algebraic Expression (Using the Fractional Bar Form)

A fraction containing a fraction in the numerator and denominator is a called a complex fraction. These types of expressions can be daunting, especially when they are algebraic expressions including variables.


To calculate the volume of a pyramid, use the formula        V  =    1  3    l  w  h    {\displaystyle V={\frac {1}{3}}lwh}      , where  l  and  w  are the length and width of the base, and  h  is the height.


A cube is a three-dimensional shape that has equal width, height, and length measurements. A cube has six square faces, all of which have sides of equal length and all of which meet at right angles.


Basic fraction classification identifies individual fractions by their type according to certain characteristics. Beyond the basics, you can also classify fractions based on how they relate to other fractions within a group or set.


A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. This wikiHow will teach you how to calculate the volume of a cylinder.


The Pythagorean Theorem describes the lengths of the sides of a right triangle in a way that is so elegant and practical that the theorem is still widely used today.


Decimals are a way to write fractions and mixed numbers without using a numerator and denominator. Because the denominator isn’t written, it may be difficult at first to compare the values of two or more decimals, particularly when they have a different number of digits after the decimal point.


An object's density is defined as its mass per unit of volume. Density is used in geology, metallurgy and other physical sciences as an identifying property of rocks, minerals and metals and in calculations for an object's buoyancy in a given liquid to determine if it will float in that liquid.


Whether you need to to mail a package or pass you next test, finding the volume of a box is easy. Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box.


Cubic yards (abbreviated "yd 3 " or "cu yd")are a unit of volume measurement equal to the volume of a cube whose sides are exactly one yard in length or about 764.5 liters (202.0 US gal).


A sphere is a perfectly round geometrical object that is three dimensional, with every point on its surface equidistant from its center. Many commonly-used objects such as balls or globes are spheres.


Calculate the Volume of a Square Pyramid

A square pyramid is a three-dimensional solid characterized by a square base and sloping triangular sides that meet at a single point above the base.


Calculate the Volume of an Irregular Object

Perhaps you already know how to calculate the volume of a cube or a cone, by taking a few measurements and performing the right calculations. But how much space does a fork take up, or a toy car?


Calculate the Volume of a Regular Tetrahedron

In this article, you will learn how to calculate the volume of regular tetrahedron. It isn't hard once you memorize the formula.


CBM  stands for “cubic meters.” When abbreviated in this manner, this measurement typically refers to the total number of cubic meters required to pack and ship packages.


Calculate the Volume of a Rectangular Prism

Calculating the volume of a rectangular prism is easy once you know its width, length, and height. Read this wikiHow to learn how.


The volume of a shape is the measure of how much three-dimensional space that shape takes up.  [1]   You can also think of the volume of a shape as how much water (or air, or sand, etc.)


A prism is a solid geometric figure with two identical ends and all flat sides. The prism is named after the shape of its base, so a prism with a triangular base is called a "triangular prism."


Calculate the Volume of a Regular Dodecahedron

Regular dodecahedron is a 3D figure that has 12 sides.  Each side is made up of one regular pentagon.  Once you memorize the formula, calculating the volume of it is very easy.


You can calculate the volume of a cone easily once you know its height and radius and can plug those measurements into the formula for finding the volume of a cone.


Calculate the Volume of a Triangular Prism

In math, a triangular prism is a three-sided polyhedron with two parallel triangular bases and three rectangular faces. It should not be confused with a  pyramid.


Calculate the Volume of a Regular Octahedron

In this article, you will learn about how to calculate the volume of a regular octahedron, a polyhedron with eight faces.


Use Distance Formula to Find the Length of a Line

You can measure the length of a vertical or horizontal line on a coordinate plane by simply counting coordinates; however, measuring the length of a diagonal line is trickier.


A vector is a graphic representation of some physical force. It could represent motion, such as a plane traveling in a northeasterly direction at 400 mph (640 km/h).


A part of basic arithmetic, long division is a method of solving and finding the remainder for division problems that involve numbers with at least two digits.


Learn the Different Equations for a Line

You will learn the 3 basic Forms for the Equation of a Line: 1) the Point-Slope Form; 2) the Standard Form; and 3) the Slope-Intercept Form in the Cartesian Plane.


A vector is a geometric object that has direction and magnitude. It may be represented as a line segment with an initial point (starting point) on one end and an arrow on the other end, such that the length of the line segment is the magnitude of the vector and the arrow indicates the direction of the vector.


Polar functions are functions of the form r = f(θ). While you can make some really cool graphs with them, they are really quite tricky to work with.


In order to graph points on the coordinate plane, you have to understand the organization of the coordinate plane and know what to do with those (x, y) coordinates.


Quickly Determine the Equation of a Straight Line in a Graph

Often, determining the equations of lines on a graph can take a lot of calculation. But with simple straight lines, you need barely any calculations.


A rational function is an equation that takes the form  y  = N( x )/D( x ) where N and D are polynomials. Attempting to sketch an accurate graph of one by hand can be a comprehensive review of many of the most important high school math topics from basic algebra to differential calculus.


Calculate a Basic Derivative of a Function

This is intended as a guide to assist those who must occasionally calculate derivatives in generally non-mathematical courses such as economics, and can also be used as a guide for those just starting to learn calculus.


A pendulum is an object consisting of a mass suspended from a pivot so that it can swing freely. The mathematics of pendulums are governed by the differential equation


Integration is the inverse operation of differentiation. It is typically harder to integrate elementary functions than to find their derivatives. The reason is because a derivative is only concerned with the behavior of a function at a point, while an integral requires  global  knowledge of a function.


Calculating a limit can take a while to get a hang of. Below is a simple explanation of basic limit problems solved using different methods. With these easy steps, you can take on any limit problem.


A differential equation is an equation that relates a function with one or more of its derivatives. In most applications, the functions represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between them.


A logistic function is an S-shaped function commonly used to model population growth. Population growth is constrained by limited resources, so to account for this, we introduce a carrying capacity of the system        L  ,    {\displaystyle L,}       for which the population asymptotically tends towards.


Solve a Second Order Partial Differential Equation

Second order partial differential equations can be daunting, but by following these steps, it shouldn't be too hard.


Contour integration is integration along a path in the complex plane. The process of contour integration is very similar to  calculating line integrals  in multivariable calculus.


Integration by parts is a technique used to evaluate integrals where the integrand is a product of two functions.


When integrating functions involving polynomials in the denominator, partial fractions can be used to simplify integration. New students of calculus will find it handy to learn how to decompose functions into partial fractions not just for integration, but for more advanced studies as well.


Jacobian change of variables is a technique that can be used to solve integration problems that would otherwise be difficult using normal techniques.


The Gaussian function        f  (  x  )  =   e   −    x   2        {\displaystyle f(x)=e^{-x^{2}}}       is one of the most important functions in mathematics and the sciences.


Calculus is primarily the mathematical study of how things change. One specific problem type is determining how the rates of two related items change at the same time.


In calculus, an inflection point is a point on a curve where the curvature changes sign. It is used in various disciplines, including engineering, economics, and statistics, to determine fundamental shifts in data.


In vector calculus, Stokes' theorem relates the flux of the curl of a vector field          F      {\displaystyle {\mathbf {F} }}       through surface        S    {\displaystyle S}       to the circulation of          F      {\displaystyle {\mathbf {F} }}       along the boundary of        S  .


Integration is the inverse operation of differentiation. It is commonly said that differentiation is a science, while integration is an art. The reason is because integration is simply a harder task to do - while a derivative is only concerned with the behavior of a function at a point, an integral, being a glorified sum, requires  global  knowledge of the function.


Exponential functions are a special category of functions that involve exponents that are variables or functions. Using some of the basic rules of calculus, you can begin by finding the derivative of a basic functions like         a   x      {\displaystyle a^{x}}      .


The perimeter is the length of the entire outside boundary of a polygon, and the area is the measure of the space that fills the polygon boundary.  [1]   The area and perimeter are extremely useful measurements that can be used in household projects, construction, DIY projects, and in the estimation of materials you might use.


Estimate Distances (by Using Your Thumb and Eyes)

Hikers, photographers, hunters, golfers, home astronomers, and nature lovers, if you have ever wondered how far away you are from a given object, estimating that distance may be easier than you realized.


Parallel lines are two lines in a plane that will never intersect (meaning they will continue on forever without ever touching).  [1]   A key feature of parallel lines is that they have identical slopes.


Drawing perpendicular lines is quite easy to do, and you have probably accidentally done it before. All you need is a piece of paper and a pencil. If you don't know what this is, I will teach you how to do it.


An equilateral triangle has three sides of equal length, connected by three angles of equal width. It can be challenging to draw a perfectly equilateral triangle by hand.


Do you want to draw a polygon? Polygons are figures consisting of line segments in a closed chain. There are many different types of polygons, but they all have edges (or sides) and vertices (or corners).


A parallelogram is a quadrilateral that has two sets of parallel sides. Each pair of opposite sides are parallel to each other, and each pair of opposite sides are the same length as each other.


A hexagon is a six-sided polygon. A regular hexagon is one that has six equal side lengths. Because it has six axes of symmetry, it is possible to divide a regular hexagon into a number of smaller equal areas, or parts, using the center point and the vertices as reference points.


There are a number of different ways to divide circle into equal parts. If you are using a pencil and paper, you will need a compass to divide the circle accurately into six equal pieces.


Expected value (EV) is a concept employed in statistics to help decide how beneficial or harmful an action might be. Knowing how to calculate expected value can be useful in numerical statistics, in gambling or other situations of probability, in stock market investing, or in many other situations that have a variety of outcomes.


Planar geometric figures bounded by straight lines are called polygons. If a polygon has four sides of equal length, it is known as a square. Dividing a square into eight equal parts may sound confusing at first, but the process is a simple one and can actually be done in multiple ways.


Calculate 95% Confidence Interval for a Test's Sensitivity

The  sensitivity  of a test is the percentage of individuals with a particular disease or characteristic correctly identified as positive by the test.


Pie charts are a form of an area chart that are easy to understand with a quick look. They show the part of the total (percentage) in an easy-to-understand way.


Once you have collected all your qualitative data, it's easy to be overwhelmed with the amount of content your methods have created. Qualitative analysis is time consuming, but benefits from a considered, methodical approach.


Typing π on your keyboard can be almost as challenging as using π in an equation. But typing the π symbol isn't as hard as it seems, whether you have a Mac or a PC.


Calculate Spearman's Rank Correlation Coefficient

Spearman's rank correlation coefficient allows you to identify whether two variables relate in a monotonic function (i.e., that when one number increases, so does the other, or vice versa).


Relative risk is a statistical term used to describe the risk of a certain event happening in one group versus another. It is commonly used in epidemiology and evidenced based medicine, where relative risk helps identify the risk of developing a disease after an exposure (i.e. a drug/treatment or an environmental exposure) versus the risk of developing a disease in absence of the exposure.


A line plot is a graph that shows the frequency of data occurring along a number line. Line plots provide a quick and easy way to organize data and are best used when comparing fewer than 25 different numbers.


Probability is the measure of how likely an event is to occur out of the number of possible outcomes. This wikiHow will show you how to calculate different types of probabilities.


Calculate Mean, Standard Deviation, and Standard Error

After collecting data, often times the first thing you need to do is analyze it. This usually entails finding the mean, the standard deviation, and the standard error of the data.


Find the Surface Area and Volume of a Cube

A cube is defined as a solid (three-dimensional) figure consisting of six identical, square sides. Here's how to calculate the surface area and the volume of a cube.


Line graphs provide a visual representation of the relationship between variables and how that relationship changes. For example, you might make a line graph to show how an animal's growth rate varies over time, or how a city's average high temperature varies from month to month.


There are numerous ways to find a missing dimension of a rectangle, and the method you use will depend on what information you already have. As long as you know the area or perimeter, as well as the length of one side of the rectangle (or the relationship between the length and width), you can find a missing dimension.


Find the Circumference and Area of a Circle

A circle is a two-dimensional line that forms a closed loop, where every point on that loop is an equal distance from the center.  [1]   The circumference (C) of a circle is its perimeter, or the distance around it.


Density is the amount of mass an object has per unit volume (amount of space that object occupies).  [1]   The metric units of density are grams per milliliter (g/mL).


A regular polygon is a 2-dimensional convex figure with congruent sides and angles equal in measure. Many polygons, such as  quadrilaterals  or  triangles  have simple formulas for finding their areas, but if you're working with a polygon that has more than four sides, then your best bet may be to use a formula that uses the shape's apothem and perimeter.


An isosceles triangle is a triangle with two sides of the same length. These two equal sides always join at the same angle to the base (the third side), and meet directly above the midpoint of the base.


There are a variety of methods to determine if your current weight, and where you carry that weight, is healthy for you. Your waist-to-height ratio provides information on whether your weight is appropriate for your height and whether or not you're at increased risk for chronic diseases like heart disease.


A semi-circle is half of a circle. Therefore, to find the area of a semi-circle, you just have to  find the area of a full circle  and then divide it by two.


Finding the area of a square is easy as long as you know the length of its side, perimeter, or diagonal. Here's how to do it.


Easy steps on how to get a day of a certain date. These 2 tables of keys below must be given in calculating what day is a certain date.


Linear interpolation, also called simply interpolation or “lerping,”  [1]   is the ability to deduce a value between two values explicitly stated in a table or on a line graph.


Eventually, you'll find yourself in a situation where you'll have to solve a math problem without a calculator. Even if you're good at math, mental math can be incredibly difficult to do.


Roman numerals are the numerical system used in ancient Rome. They use combinations of letters from the Latin alphabet to represent different values.


Know the Day of the Week for Any Day of Any Year

You want to know the day of the week on which certain event, like birth, or a future event will take place, happened, just use the chart.


When a quantity is dimensionless it means it is a bare number, without any physical dimension applicable to it. Basically, it doesn't have a unit next to it.


The surface area of a shape is the sum of the area of all of its faces. To find the area of a cylinder, you need to find the area of its bases and add that to the area of its outer wall.


Rectangular prisms are 3-dimentianal model that have six rectangular faces, with three sets of two congruent sides. To illustrate the concept in more concrete terms, you can make a simple model of a rectangular prism using construction paper or cubic blocks.


The surface area of a cone is the sum of the lateral surface area and the base surface area. If you know the radius of the base and the slant height of the cone, you can easily find the total surface area using a standard formula.


The surface area of a sphere is the number of units (cm, inches, feet -- whatever your measurement) that are covering the outside of a spherical object.


The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six.


Finding the surface area of a box is easy as long as you know the length of the sides. Once you know how long the sides are, you simply have to plug them into a basic equation to get your answer.


Surface area is the total amount of space that all of the surfaces of an object take up. It is the sum of the area of all the surfaces of that object.


A parallelogram is defined as a simple quadrilateral with two pairs of parallel sides. If you need to find the area of a parallelogram, it's easily done with a simple formula.


Find the Area of a Trapezium with No Parallel Sides

In this article, you will learn how to find the area of a quadrilateral with no parallel sides – a trapezium in American English, but a trapezoid in British English.


Square meters are a measurement of  area , usually used to measure a two-dimensional space such as a field or floor. For example, you might measure the footprint of a couch in square meters, then measure your living room in square meters to see if it will fit.


In geometry, a prism is a three-dimensional shape with the same polygon at its ends. The sides are usually rectangles or parallelograms, though cylinders and other shapes can also be considered prisms.


Drawing an ellipse is often thought of as just drawing a major and minor axis and then winging the 4 curves. This is good enough for rough drawings; however, this process can be more finely tuned by using concentric circles.


Find the Area of the Region Bounded by Rectangular Grid

In math competitions such as AMCs, you may encounter problems requiring you to find the area of the region bounded by rectangular grid with irregular polygons that can challenge you.


Find the Volume of a Cube from Its Surface Area

The volume of a three-dimensional shape is a measurement of the space inside the shape and is determined by multiplying the length, width, and height.


There are many different shapes and many reasons why you might want to know their area! Whether you're doing your homework or trying to figure out how much paint you'll need to refurbish that living room, wikiHow has your back!


Most of us encourage our kids to begin reading and writing at an early age, but are less keen to encourage an interest in math. Despite this, math plays a fundamental role in virtually everything we do, and almost every single occupation uses math in some way.


The y-intercept of an equation is a point where the graph of the equation intersects the Y-axis. There are several ways to find the y-intercept of an equation, depending on the starting information you have.


Want a run-down on how graphs work? Here's a quick read to explain the basics.


There are multiple mathematical functions that use vertices. Polyhedrons have vertices, systems of inequalities can have one vertex or multiple vertices, and parabolas or quadratic equations can have a vertex, as well.


Change Mixed Numbers to Improper Fractions

A mixed number is one that contains both a whole number and a proper fraction (a fraction where the numerator is smaller than the denominator). For instance, if you’re baking a cake and need 2 ½ cups of flour, that’s an example of a mixed number.


Math isn't easy for everyone. Some of the main concepts are quite difficult. If you need to know how to change a fraction to a decimal, it can get confusing depending on the fraction.


Current ratio is a measurement of a company’s ability to pay back its short-term obligations and liabilities. It is crucial for determining a company’s financial health.


Ever struggle with those confusing math problems? A very difficult area for many people is fractions, especially when you begin adding. This can become even more complex when the fractions have different denominators, or bottom numbers.


An arithmetic sequence is a series of numbers in which each term increases by a constant amount. To sum the numbers in an arithmetic sequence, you can manually add up all of the numbers.


Fractions are comprised of a numerator and denominator, and when two fractions have the same number for a denominator, it is known as a common, or like, denominator.


Cancelling fractions is also called simplifying fractions.  [1]   Basically, a fraction can be made simpler by dividing the top and bottom by the same number.


The surface area of any pyramid can be found by adding the surface area of the base to the surface area of the lateral faces. When working with regular pyramids, you can find the surface area using a formula, as long as you know how to find the area of the base of the pyramid.


Once you understand the concept of fractions, you can start performing simple operations with them. You can add fractions just like you can add other types of numbers.


Adding fractions is a very handy skill to know. Not only is it an important part of school — from elementary school all the way up to high school — it's also a really practical skill to know.


A lot of times you will add fractions when putting parts of two things together. You might sometimes multiply fractions if you need to find a portion of a fraction.


Graphing equations  is a much simpler process that most people realize. You don't have to be a math genius or straight-A student to learn the basics of graphing without using a calculator.


The vertex of a  quadratic equation  or parabola is the highest or lowest point of that equation. It lies on the plane of symmetry of the entire parabola as well; whatever lies on the left of the parabola is a complete mirror image of whatever is on the right.


A parabola is a two-dimensional, mirror-symmetrical curve that is shaped like an arch. Any point on the parabola is equidistant from a fixed point (the focus) and a fixed straight line (the directrix).


Find Vertical Asymptotes of a Rational Function

A rational function is a mathematical function (equation) that contains a ratio between two polynomials.  [1]   That is, there must be some form of a fraction, involving more than just the coefficients.


Find the Slope of a Line Using Two Points

Finding the slope of a line is an essential skill in coordinate geometry, and is often used to draw a line on graph, or to determine the x- and y-intercepts of a line.


Find the Perpendicular Bisector of Two Points

A perpendicular bisector is a line that cuts a line segment connected by two points exactly in half by a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.


A vector is a geometrical object that has both a magnitude and direction.  [1]   The magnitude is the length of the vector, while the direction is the way it’s pointing.


Lines are everywhere in English, whether you are taking Algebra I, Geometry, or Algebra II. If you know how to find the slope of a line, many things become clearer to you, like whether two lines are parallel or perpendicular, where they will intersect, and many other concepts.


Construct an Angle Congruent to a Given Angle

The earliest mathematicians did not have the benefit of plastic protractors to measure and copy angles. In true geometry constructions, you are allowed only a straight edge and a compass.


Create the Star of David Using a Pencil, Ruler and Compass

The Star of David has interesting geometrical properties apart from being the symbol appearing on the flag of Israel. It is essentially a fractal with the exception that open vertices are closed by straight lines.


Construct a Triangle when Its Three Sides Are Given (SSS Criterion)

This article teaches you how to construct a triangle when the lengths of all three of its sides are known.


Find the Length of the Hypotenuse, Adjacent and Opposite Side of a Right Triangle

This article aims at helping you to fully understand the concept of how to find the length of any side of a right triangle. It will take you through the necessary steps to be taken when finding the hypotenuse, opposite or adjacent side of a right triangle.


Construct a Triangle when Two Sides and the Included Angle are Given (SAS Criterion)

Construction is an ancient method of duplicating a geometric figure using only a straightedge and a compass. If you begin with any chosen triangle, you can construct a congruent copy of it if you match any two sides and the angle between them.


A square is a quadrilateral with four right angles and four congruent sides. Easy to draw, right? Not so fast. Drawing a perfect square requires more than just a steady hand.


Construct a Perpendicular Line to a Given Line Through Point on the Line

Perpendicular lines are lines that form right angles. These types of lines are used often in geometry, so it is important to know how to construct them.


Construct a Perpendicular Line to a Given Line Through Point Outside the Line

Using a simple point completely above a horizontal line, it is possible to construct a perpendicular line using a compass (not a protractor). This article will help you construct this perpendicular line using a compass.


Construct a Line Parallel to a Given Line Through a Given Point

Parallel lines are lines that are equidistant at all points and would never touch if they went on forever.  [1]   Sometimes you may be presented with one line and need to create another line parallel to it through a given point.


Adobe InDesign offers a great suite of tools to be able to create illustrations for books, magazines, brochures, and the like. With InDesign you can create and manipulate different shapes.


Determine if Three Side Lengths Are a Triangle

Determining if three side lengths can make a triangle is easier than it looks. All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side.


Determine a Square and Circle of Equal Perimeter

A perimeter is generally thought of as the sum of all the side lengths of a shape. Like all two-dimensional shapes, a circle has a perimeter (usually called the circumference), but since a circle does not have sides its perimeter is calculated differently than that of other polygons.


You can bisect an angle just as you can bisect a line. To bisect means to divide something into two equal parts. There are two methods for bisecting an angle.


In single-variable calculus, finding the extrema of a function is quite easy. You simply set the derivative to 0 to find critical points, and use the second derivative test to judge whether those points are maxima or minima.


Cut a Equilateral Triangle from a Square of Paper

To cut a right-angled triangle from a square piece of paper is not difficult. To cut an Equilateral triangle is a little more of a challenge, though.


A line tangent to a circle touches the circle at exactly one point. The tangent line is perpendicular to the radius of the circle.


The Consumer Price Index (CPI) is a measure of changes in product costs over a specific time period, and it is used as both an indicator of the cost of living and economic growth.


Calculate Mean Deviation About Mean (for Ungrouped Data)

In working with data, there are several different ways to measure how closely grouped your data values are. The most common is the mean. Most people learn early in school to calculate the mean by finding the sum of a group of data values and then dividing by the number of values in the set.


So you've been assigned homework that requires you to find the area of a quadrilateral ... but you don't even know what a quadrilateral is. Don't worry—help is here!


A pentagon is a polygon with five straight sides. Almost all problems you'll find in math class will cover regular pentagons, with five equal sides.


A kite is a type of a quadrilateral that has two pairs of equal, adjacent sides.  [1]   Kites can take the traditional look of a flying kite, but a kite can also be a rhombus or a square.


Find the Area and Perimeter of a Rectangle

A rectangle is a plane, a quadrilateral that has 4 right angles. The sides that are parallel to each other are identical in length.  [1]   If the rectangle has four equal sides, it is called a square.


A prism is a three-dimensional shape with two parallel, congruent bases.  [1]   In a triangular prism, the bases are triangles. A triangular prism also has three lateral sides.


Find Perpendicular Vectors in 2 Dimensions

A vector is a mathematical tool for representing the direction and magnitude of some force. You may occasionally need to find a vector that is perpendicular, in two-dimensional space, to a given vector.


Average atomic mass is not a direct measurement of a single atom. Instead, it is the average mass per atom for a typical sample of a given element. If you could measure the mass of billions of individual atoms, you could calculate this value the same way you would find any average.


The range of a function is the set of numbers that the function can produce. In other words, it is the set of y-values that you get when you plug all of the possible x-values into the function.


Area is a measurement of the amount of space inside a two-dimensional figure. Sometimes, finding area can be as simple as simply multiplying two numbers, but often times it can be more complicated.


Finding the midpoint of a line segment is easy as long as you know the coordinates of the two endpoints. The most common way to do this is to use the midpoint formula, but there's another way to find the midpoint of a line segment if it's vertical or horizontal.


Find the Surface Area of a Rectangular Prism

A rectangular prism is a name for a 6-sided 3-dimensional figure that is very familiar to everybody—a box. Think of a brick, or a shoebox, and you know exactly what a rectangular prism is.


Find the Minimum and Maximum Points Using a Graphing Calculator

Big math test coming up? Need to find local minimums or maximums? Not to fret! Easily find the minimum or maximum point of any non-linear equation using a graphing calculator.


Perimeter is a measure of the area or distance around a two-dimensional shape. On a rectangle, for instance, the perimeter is the total length of the rectangle’s outline, including the two widthwise borders and the two lengthwise borders.


Find the Nth Term for an Arithmetic Sequence of High Order

An arithmetic sequence of high order is a sequence of numbers where the difference of terms get larger and forms an arithmetic sequence of their own.


Determine Equal Cube and Sphere Surfaces

The formula for the surface area of a cube is 6s^2 where s=side, and the formula for a sphere's surface is 4πr^2 where r=radius, By equating the two formulas, we can determine a constant factor for the relation between r and s.


Find the Measurement of the Diagonal Inside a Rectangle

A diagonal is a straight line that connects one corner of a rectangle to the opposite corner.  [1]   A rectangle has two diagonals, and each is the same length.


Unlike a straight line, a curve's slope constantly changes as you move along the graph. Calculus introduces students to the idea that each point on this graph could be described with a slope, or an "instantaneous rate of change."


Find the Longest Internal Diagonal of a Cube

This article will demonstrate that the lowest to highest and opposing corners diagonal of a cube is equal to the side times the square root of 3.


In order to find the equation of a line, you need  two things : a) a point on the line; and b) the slope (sometimes called the gradient) of the line.


Find the Least Common Multiple of Two Numbers

A multiple is the result of multiplying a number by an integer. The least common multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers.


All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite or the right angle, or the longest side of the right triangle.


Squaring fractions is one of the simplest operations you can perform on fractions. It is very similar to squaring whole numbers in that you simply multiply both the numerator and the denominator by itself.


Dividing a fraction by a fraction might seem confusing at first, but it is really very simple. All you need to do is flip, multiply and reduce! This article will guide you through the process and show you that dividing fractions by fractions is really a breeze.


Find the Equations of the Asymptotes of a Hyperbola

Asymptotes of a hyperbola are the lines that pass through center of the hyperbola. The hyperbola gets closer and closer to the asymptotes, but can never reach them.


Teach Food Fractions for First Grade Math

Basic math is typically taught to children while they are still toddlers. Toward the end of kindergarten, they should be ready to count by 10's, know basic mathematics relating to money, and understand estimation.


If you are a mathematician or graphics programmer, you may need to find the angle between two given vectors. This wikiHow will show you how to do that.


A graph is a diagram (as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.


Construct a 60 Degrees Angle Using Compass and Ruler

Often you are required to construct some angles without using a protractor. This article teaches you how to draw a 60 degrees angle using a compass and a ruler.


Calculate the Cross Product of Two Vectors

The cross product is a type of vector multiplication only defined in three and seven dimensions that outputs another vector. This operation, used in almost exclusively three dimensions, is useful for applications in physics and engineering.


Bisect a Line With a Compass and Straightedge

Bisecting a line (dividing a line in half) is easy enough if you know the length of the line, or can measure the line. But if you don’t know the length of the line, you can still bisect it using a straightedge and compass.


The familiar rectangular grid is an easy system to learn, but it is not convenient in all situations. What if you want to plot the spokes on a wheel, or the movement of water down a drain?


Many common physical quantities are often vectors or scalars. Vectors are akin to arrows and consist of a positive magnitude (length) and importantly a direction.


Construct a 90 Degrees Angle Using Compass and Ruler

Often you are required to construct some angles without using a protractor. This article teaches you how to draw a 90 degrees angle using a compass and a ruler.


Construct a 30 Degrees Angle Using Compass and Straightedge

Learn to construct a 30 o  angle using compass and straightedge by different methods.


A polygon is any closed figure with sides made from straight lines. At each vertex of a polygon, there is both an interior and exterior angle, corresponding to the angles on the inside and outside of the closed figure.


The perimeter of a two-dimensional shape is the total distance around the shape, or the sum of the length of its sides.  [1]   By definition, a square is a four-sided shape with four straight sides of equal length, and four right (90°) angles.


The radius of a circle is the distance from the center of the circle to any point on its circumference.  [1]   The easiest way to find the radius is by dividing the diameter in half.


The diagonal of a square is the line stretching from one corner of the square to the opposite corner. To find the diagonal of a square, you can use the formula        d  =  s    2      {\displaystyle d=s{\sqrt {2}}}      , where        s    {\displaystyle s}       equals one side length of the square.


In geometry, an angle is the space between two rays or line segments with the same endpoint, or vertex. The most common way to measure angles is in degrees, with a full circle measuring 360 degrees.


Geometry is the study of shapes and angles and can be challenging for many students. Many of the concepts are totally new and this can lead to anxiety about the subject.


A circle is defined by any three non-collinear points.  [1]   This means that, given any three points that are not on the same line, you can draw a circle that passes through them.


Loosely-defined, a hexagon is any polygon with six sides, but a regular hexagon features six equal sides and six equal angles. Look at pictures of hexagons to get a better idea of what you're drawing.


In simple terms, a sphere is a solid round ball. To calculate the mass of a sphere, you must know the size (volume) of the sphere and its density. You might calculate volume using the sphere’s radius, circumference or diameter.


Calculate the Center of Gravity of a Triangle

The center of gravity, or centroid, is the point at which a triangle’s mass will balance. To help visualize this, imagine you have a triangular tile suspended over the tip of a pencil.


"Case cube" is a measurement used in wholesale purchasing and shipping. The case cube denotes how much volume, or 3-dimensional space, a case of any given item will take up in your warehouse.


Sometimes you might need to determine the area under an arc, or the area of a sector. A sector is a part of a circle that is shaped like a piece of pizza or pie.


An ellipse is a two-dimensional shape that looks like a flat circle. The area equation for an ellipse will look familiar if you've studied circles before.


A trapezoid (also known as a trapezium in British English) is a quadrilateral with two parallel sides of different lengths. This means that both of these sides can be called a base, and that the trapezoid is unique in having two bases.


A rhombus is a parallelogram with four congruent sides. It does not have to have right angles. There are three formulas for finding the area of a rhombus.


A parallelogram is a quadrilateral, or four-sided shape, with two sets of parallel sides. Squares, rectangles, and rhombuses are special types of parallelograms, though most people think of a "slanted" rectangle, with two diagonal sides and two flat sides, when they think of the parallelogram.


A common problem in geometry class is to have you calculate the area of a circle based on provided information. You need to know the formula for finding the area of a circle,        A  =  π    r   2      {\displaystyle A=\pi r^{2}}      .


The domain of a function is the set of numbers that can go in to a given function. In other words, it is the set of x-values that you can put in to any given equation.


Find the Circumference of a Circle Using Its Area

You may need to calculate the circumference of a circle. You can do that by using its area.


Find the Area of a Square Using the Length of its Diagonal

The most common formula for the area of a square is simple: it's the length of the side squared, or s 2 . But sometimes you only know the length of the square's diagonal, running between opposite vertices.


A rectangle is a quadrilateral with two sides of equal length and two sides of equal width that contains four right angles. To find the area of a rectangle, all you have to do is multiply its length with its width.


Every function contains two types of variables: independent variables and dependent variables, whose values literally “depend” on the independent variables.


Find the Diagonal of a Square Using Its Area

A diagonal is a straight line that runs between opposite corners of a square.  [1]   A diagonal divides a square into two right triangles. This property, as well as the fact that a square has four equal side lengths, makes it possible to find the length of a square’s diagonal using the area.


How to find the mode, median, mean and range. Be sure to arrange the numbers by their numerical value. The order should range from low to high or high to low.


Find the Area of a Rectangle Using the Diagonal

You will learn how, in a few steps, to find the area of a rectangle by knowing that its diagonal is the hypotenuse of the rectangle's width and height.


Find the Area of a Circle Using Its Circumference

Finding the area of a circle is a straightforward calculation if you know the length of the circle’s radius. If you don’t know the radius, however, you can still calculate the area if you are given the length of the circle’s circumference, or perimeter.


Mean, median, and mode are values that are commonly used in basic statistics and in everyday math. Though you can find each value pretty easily, it's also easy to mix them up.


The scale factor, or linear scale factor, is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are different sizes.


Whether you're doing craft work, putting fencing around your hot tub, or just solving a math problem for school, knowing how to find the circumference of a circle will come in handy in a variety of circle-related problems.


Calculating the area of a polygon can be as simple as finding the area of a regular triangle or as complicated as finding the area of an irregular eleven-sided shape.


A hexagon is a polygon that has six sides and angles. Regular hexagons have six equal sides and angles and are composed of six equilateral triangles.


Finding the area of an object is easy as long as you understand the technique and formulas involved. If you have the right knowledge, you can find the area and surface area of any given object.


Finding how many factors are in a number is as easy a 1 2 3 if you know how to do it. But for larger numbers, you can't just count one by one. This is a nice trick to find how many factors are in an integer.


One of the most important parts of planning an upcoming construction or home improvement project is to determine how much material is needed. For many projects, this means finding the linear feet of material you need. (


The most common way to find the area of a triangle is to take half of the base times the height. Numerous other formulas exist, however, for finding the area of a triangle, depending on what information you know.


When deciding where to order a pizza, you likely want to consider value. One way to consider the value of a pizza is to determine how much the pizza costs per square inch.


The average rate of change is a function that represents the average rate at which one thing is changing with respect to something else that is changing.


An arc is any portion of the circumference of a circle.  [1]   Arc length is the distance from one endpoint of the arc to the other. Finding an arc length requires knowing a bit about the geometry of a circle.


Are you burdened by the evil of memorizing a sequence of random and intangible numbers simply to perform a simple operation like calculating the  area of a circle ?


The Koch snowflake is one of the earliest fractal curves to have been described. It has an infinitely long perimeter, thus drawing the entire Koch snowflake will take an infinite amount of time.


A Venn Diagram is a type of graphic organizer that uses overlapping circles to illustrate logical relationships. Typically, Venn Diagrams are employed mathematically to illustrate principles of inclusion, exclusion, and intersection between data sets; however, Venn Diagrams can also be adapted to reflect these types relationships for a host of other topics and projects.


When evaluating an expression, you need to give some operations precedence. If you complete the operations in no particular order, your answer will have no particular significance, and two people solving the same expression will come up with different answers.


A Möbius strip is a surface that has one side and one edge. It is easy to make one with a piece of paper and some scissors. The interesting part is what happens when you start manipulating it.


Find How Many Diagonals Are in a Polygon

Finding diagonals in a polygon is a necessary skill to develop in math. It may seem difficult at first, but is pretty simple once you learn the basic formula.


Maybe you are looking to make a 250 USAMO index this year. Or maybe you just want to qualify for the AIME. Whatever your motivation, math contests can be an obsession when you get deeply involved in them and achieving the highest scores possible becomes a wonderful challenge.


Express a Huge Number in the Form of Scientific Notation

Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians and engineers.


Dot plots are great for solving basic math problems from anything to advanced math problems. They are used to count data in the form of dots on a plots, which is where its name (Dot Plot) comes from.


A Pythagorean Tree is a fractal that is created out of squares. The process of creating one is very simple, but when it's complete it looks pretty cool!


The chunking method is an alternative to long division. It is also another way to do partial quotients. By breaking apart a dividend into easily calculated value chunks, you can solve complex division problems.


A percentage is a special way of representing a portion of something. A percentage is a number that indicates a fraction made up of 100 parts. Thus, 100% means the whole thing (whatever is being measured), while 50% means one half.


There is some simple algebra involved in Neutral Operations. Learn to do the algebraic sub-steps in this article. Neutral Operations are important for several reasons: they can be symmetrical (which is a hot topic in math these days!),


Use a Graphing Calculator to Solve a Systems of Equations

Solving a systems of equations can become messy after a while. This is especially true when you have three or more equations to be solved. Try using your graphing calculator instead by following these easy steps.


The determinant is a unique number associated with a square matrix - that is, a matrix with the same number of rows as columns. The determinant of a matrix has several uses; for one, it immediately tells you if the matrix has an inverse or not (see tips).


Cramer's rule is used to find the values of three variables in a given set of equations. It's a simple method which requires you to find three matrices to get the values of the variables.


In linear algebra, matrix equations are very similar to normal algebraic equations, in that we manipulate the equation using operations to isolate our variable.


The determinant of a matrix is frequently used in calculus, linear algebra, and higher level geometry. Outside the academic world, engineers and computer graphics programmers use matrices and their determinants all the time.


To solve systems of three or more linear equations, one typically converts the problem into an augmented matrix and row reduces from there. However, this is slow and woefully inefficient with more equations.


If you’ve ever taken an algebra course in middle or high school, you’ve probably encountered a problem like this one: solve for        x    {\displaystyle x}       and        y  .


The null space of a matrix        A    {\displaystyle A}       is the set of vectors that satisfy the homogeneous equation        A    x    =  0.    {\displaystyle A{\mathbf {x} }=0.}


Matrix algebra is a foundation element for modern computer graphics and engineering. In the same way that ordinary algebra deals with real numbers, matrix algebra provides tools and methods for manipulating vectors and simultaneous sets of equations.


The determinant of a square matrix is an important number associated with that matrix. From the determinant, many important properties can be found about the matrix.


You will learn how to algebraically solve sqrt(a) + sqrt(b) = sqrt(a) * sqrt(b)=c, sqrt(a) - sqrt(b) = sqrt(a) * sqrt(b)=c, sqrt(a) + sqrt(b) = sqrt(a) / sqrt(b)=c and sqrt(a) - sqrt(b) = sqrt(a) / sqrt(b)=c (whereby two operators are held neutral to each other between constants, rendering a "tipping point") and to graph the final a and b as x and y. You will also learn goal seeking to 2π for each above equation.


The article on  solving differential equations  goes over different types of differential equations and how to solve them. However, it only covers single equations.


The mathematical process has many components. These components help you to organize your thoughts, solve problems effectively, and communicate your understanding.


Inverse operations are commonly used in algebra to simplify what otherwise might be difficult. For example, if a problem requires you to divide by a fraction, you can more easily multiply by its reciprocal.


The matrix equation        A    x    =    b      {\displaystyle A{\mathbf {x} }={\mathbf {b} }}       involves a matrix acting on a vector to produce another vector.


The row-echelon form of a matrix is highly useful for many applications. For example, it can be used to geometrically interpret different vectors, solve systems of linear equations, and find out properties such as the determinant of the matrix.


Balance Chemical Equations Using Linear Algebra

Balancing chemical equations is typically done by first identifying uncommon elements in compounds and working your way towards hydrogen and oxygen.


Trying to figure out if a circuit is an Euler Circuit or has Euler paths? Do you need help in understanding how to Eulerize a graph? Here are some theorems, algorithms, and ideas to help you do Euler Circuits.


Cost-Volume-Profit Analysis is an important tool from Cost Accounting to help managers decide how many units to sell, answer questions about the product mix, set profit targets reasonably -- all in accord with a given product's cost behavior given certain assumptions.


Do a Short Goalseeking Neutral Operations Problem in Excel

One of the more useful tools of Excels in Goal seeking. Here is how to apply it to quickly solve a problem involving Neutral Operations between two circle areas.


Economic order quantity (EOQ) analysis offers a business a key advantage -- ordering just the right amount of stock at the right price right on time.


Creating a factor tree is one simple way to find all of the prime number factors of a number. Once you know how to do factor trees, it becomes easier to perform more advanced tasks, like finding the greatest common factor or the least common multiple.


Find Least‐Squares Solutions Using Linear Algebra

In data analysis, it is often a goal to find correlations for observed data, called trendlines. However, real life observations almost always yield inconsistent solutions to the matrix equation        X   β    =    y    ,    {\displaystyle X{\boldsymbol {\beta }}={\mathbf {y} },}       where          y      {\displaystyle {\mathbf {y} }}       is called the observation vector,        X    {\displaystyle X}       is called the        m  ×   n    {\displaystyle m\times n}       design matrix, and we are looking for values of         β    ,    {\displaystyle {\boldsymbol {\beta }},}       the parameter vector.


Have you ever had to look up a value in a table only to find that the conditions you have are found in between those that are listed? What did you do when this happened?


Do a Simple Rate Distance Time Problem with Neutral Operations

Neutral Operations has been shown thus far to be capable in the realm of computer graphics (see top Related wikiHow). Now apply it to a simple problem of Rate = Distance/Time = Distance - Time, as one begins to delve into its applicability in the realm of Space-Time problems.


With this article, you can learn how to fully sort simultaneously by writing a macro three columns of disconnected but similar data. In other words, you can use this when you want the results to be ordered in the same selection area as the original data was given, and the results are  not  to be sorted column by column.


We know how to divide, by paper. Or, we can just try to solve the problem using the calculator. Now, can you divide in Excel? Well, multiplication is the opposite of division, and it does not mean you enter =PRODUCT(number1-number2).


Polynomials can be divided the same as numeric constants, either by factoring or by long division. The method you use depends upon how complex the polynomial dividend and divisor are.


Negative numbers represent numbers that have a value of less than zero. These numbers are found when working with the numbers on the left side of the number line.


Determine Whether Two Variables Are Directly Proportional

When two variables are directly proportional, they change at the same rate. The rate is shown by the constant        k    {\displaystyle k}       in the equation        y  =  k  x    {\displaystyle y=kx}      .


Determining the square inches (also written as in 2 ) in any two-dimensional area is usually a fairly straightforward process. In the simplest cases, when the area in question is in the shape of a square or rectangle, the area in square inches is given by the equation  width × length.


Determine the Mean Proportion or Square Root Geometrically

In case you ever find yourself in the woods with a compass, straightedge, pencil and paper, and a 10 cm ruler, here is how to find the square root or mean proportion.


It’s easy to get distracted when trying to complete math homework. One way to try to focus your attention is by giving yourself a time limit to get your work done.


Disable Useless Services That Cause a Slow Computer

Do you know there are many useless services can cause a slow computer? They not only take memory resource but also can be used by spyware. Technically, service is known as a process to run various process which does not requires user's intervention.


There are several methods for disabling the on-board audio using the PC platform running any version of the Windows operating system. The on-board sound device can be disabled in the system BIOS prior to start up or by utilizing the device manager in Windows.


Determine the Geometric Version of the Golden Mean (Ratio or Proportion)

Euclid's "Elements", Book II Proposition 11, gives a method for determining the geometric Golden Mean (or Golden Ratio or Golden Proportion). Via Microsoft Excel, an {X,Y} chart is designed and explained how it arrives at one of the roots of the Golden Mean(-1), 0.618033988749895, and its square.


Chkdsk appears in the start up and you want to disable it. Just follow these few easy steps to do so:


Design and Build a Laser Cut Computer Case With Plywood

The most extreme computer-builders create computer cases entirely from the ground up. Using templates from their own parts and the internet, they use a variety of household materials to craft a case, such as aluminum sheets, acrylic or plywood.


Determine the Area of a Polygon in OpenLayers

Polygons are a great way to represent the approximate area of land on a map, and it's often helpful to know the area of the polygon you have defined.


Disable Shell Extensions with ShellExView

ShellExView is a free utility that allows for easier manipulation of shell extensions that are installed on your computer. You can use this application to disable and enable certain shortcuts or commands available from the programs in your computer.


If you own a Dell product, you may be asked for a 5 to 7 character Dell Service Tag in certain situations. A Service Tag is required for phone support, updating drivers on Dell's website, or checking your warranty status.


This article will show you how to decode binary numbers into alphabetical or numerical characters.


Delete Items on Your Computer That You Don't Want to Part With

Do you have many items on your computer that it's hard to find what you're looking for? Are many useless, old files that you don't want to part with slowing down your computer?


Deny a Country Access to Your PC with PeerBlock

I know it maybe a tad bit extreme, but I was interested in this just to see if this could be done. How much it would cost and if blocking an entire country would be worth it.


Decline a Phone Call with a Text Message

Imagine that you are in a meeting, and your phone goes off. You can take the call and run the risk of annoying your colleagues, or you can reject the call and run the risk of offending someone.


Determine a Line = to Square Root of 3 Geometrically

For a cube, the long internal diagonal from bottom to top diagonally cross-corner to cross-corner = side times the square root of 3, which is related to the formula for the diagonal for a square, side times the square root of 2.


The practice of decomposing numbers allows young students to understand the patterns and relationships between digits within a larger number and between numbers within an equation.


On the Google Chrome Web Store, there are plenty of apps to try out, but what if you don't like them? Here are some simple steps to delete an app on your Google laptop.


Determine a Cube and Sphere of Equal Volume

In this article r1 is used to represent the side of the cube and r2 to represent the radius of the sphere. The formula for the volume V of a cube c is s^3  where s = side (but here r is used for s) so r1^3 = V(c), and the volume of a sphere s is 4/3 πr^3, so in this example 4/3πr2^3 = V(s).


Datamine for Primes Using a Spirallic Dataset

This article will demonstrate how to datamine the spirallic dataset for prime numbers by extending it along probable lines. There has been added some good editorial criticism, for the determining process has never been held to be perfect, only a prospective method.


Euclid, in his treatise of geometry, "Elements", gave in Book I Proposition XLVI, the method "On a given line (AB) to describe a square." You will learn in this article to make a Euclidean square.


Define, Add, and Subtract Matrices in MATLAB

MATLAB is a very powerful program. With it, you can perform everything from basic mathematical operations to high-end programming. However, if you're an inexperienced user, you may need to know some basics to get you started.


Create Bifurcation Theory Catastrophe Curves in XL

You will learn to create catastrophe curves, which come from a branch of Bifurcation Theory in math. These are great curves to have in your portfolio in the realm of graphics.


Create Spheroidal Asymptotes and Skewed Sphere Ring

It is unusual in math, usually, to find patterned asymptotes. In this article, you'll learn to make spheroidal asymptotes as pictured below and a skewed sphere-ring.


Create Higher Exponential Powers Geometrically

This method of multiplication was used by Descartes and is from Euclid's "Elements", Book VI, Proposition 12. It is based on similar triangles. It may very well be the way Mother Nature accomplishes Multiplication!


You can graph a linear or quadratic inequality similarly to how you would graph an equation. The difference is that, since an inequality shows a set of values greater than or less than, your graph will show more than just a dot on a number line or a line on a coordinate plane.


Evaluating an algebraic expression means to calculate the expression given a certain variable. Sometimes a problem will ask you to do this; most of the time, however, you will want to evaluate an expression to check your own algebra work.


The Fibonacci sequence is a pattern of numbers generated by summing the previous two numbers in the sequence. The numbers in the sequence are frequently seen in nature and in art, represented by spirals and the golden ratio.


Frequency, also called wave frequency, is a measurement of the total number of vibrations or oscillations made within a certain amount of time. There are a few different ways to calculate frequency based on the information you have available to you.


Complex numbers can be written in the polar form        z  =  r   e   i  θ     ,    {\displaystyle z=re^{i\theta },}       where        r    {\displaystyle r}       is the magnitude of the complex number and        θ     {\displaystyle \theta }       is the argument, or phase.


Here is that funny long division-like method for finding square and cube roots generalized to nth roots. These are all really extensions of the Binomial Theorem.


Advanced reverse distributing is one way of solving a second degree equation. The prominent feature of the equation will be when it's formatted as (x + ?)(


Static electricity does more than shock you when you go to open a door, or attract dust to your furniture and clothes. It can actually bend a stream of water.


A graph of a function is a visual representation of a function's behavior on an x-y plane. Graphs help us understand different aspects of the function, which would be difficult to understand by just looking at the function itself.


Algebra is a branch of mathematics that studies numbers by representing unknown quantities with letter variables, as well as the mathematical operations applied to them.


Polynomials are mathematical structures with strands of terms made up of numerical constants and variables. There are certain ways that polynomials must be multiplied based on how many terms are contained within each one.


A system of an equation is a set of two or more equations, which have a shared set of unknowns and therefore a common solution. For linear equations, which graph as straight lines, the common solution to a system is the point where the lines intersect.


A radical expression is an algebraic expression that includes a square root (or cube or higher order roots). Often such expressions can describe the same number even if they appear very different (ie, 1/(sqrt(2) - 1) = sqrt(2)+1).


Binomials are small mathematical expressions made up of a variable term (x, a, 3x, 4t, 1090y) added or subtracted by a constant term (1, 3, 110, etc.).


Graphing a function is not as simple as creating a table and plotting those points. Functions can get very complex and go through transformations, such as flips, shifts, stretching and shrinking, making the usual graphing techniques difficult.


Did you ever think that you could use a vegetable as a battery? Batteries produce electricity by passing electrons back and forth between two metal plates.


Batteries are an essential part of everyday life. They allow you to carry electronic devices on the go without having to plug them into a wall outlet.


Experimentation is the method by which scientists test natural phenomena in the hopes of gaining new knowledge. Good experiments follow a logical design to isolate and test specific, precisely-defined variables.


Popsicle stick towers are a common engineering project to be assigned in school.  [1]   Your assignment may have various criteria for height, weight, and number of popsicles, but this guide will give you a general idea of how to construct a sturdy tower out of just popsicle sticks and wood glue.


Looking for a sure and fun way to never forget what a DNA strand looks like? What better way to embed an image of DNA in your head that you'll never forget, than by building an edible one.


Pendulums are a lot of fun and easy to make! A pendulum is basically an object that hangs down from a fixed point which swings backwards and forwards under the action of gravity.


Matter exists in three basic states: solid, liquid, or gas. Try this science project to see how it is possible to change the state of a particular solution or compound using several methods, from very simple to extremely complicated.


Plants move nutrients and water throughout their systems through specialized tiny tubes called the xylem.  [1]   All plants, from the mighty tree to the humble celery stalk, have this tube system in common.


If you'd like to keep track of how much rainfall you're getting, you can buy a rain gauge, or you can make one for yourself. Simply get an empty soda bottle, cut off the top, use it as a funnel, and calculate exactly how much rain has fallen.


A hydrometer is a simple device that allows you to measure the density of various liquids relative to water. Hydrometers are used for a myriad of different purposes: they are used to measure the fat content of milk, the alcohol content of beer, wine, and spirits, and even the water content of urine to test for dehydration.


Balloon-powered boats are a fun science experiment that can teach kids about motion. They also make great toys for bathtubs and pools. All you need is something that can float, a balloon, a piece of plastic tubing, and a few extra supplies.


A pair of  lemons  and a trip to the hardware store is all you need to convert natural chemical energy into electrical power. A common  lemon  can provide acid to make this work.


With water, dish soap, and a bit of spinning, you can make a tornado in a bottle! This can be a great way to learn how tornados work.  [1]   For a basic experiment, try making a tornado in a single bottle.


Capacitors are a modern way to store electric charges. While some modern capacitors are complex and difficult to build, its predecessor, the Leyden jar, is simpler to construct.


How do hot air balloons work? You can make a very small hot air balloon and watch how it works with just a teabag and a lighter. This article explains how you can make your very own hot air balloon at home!


Making a solar system model is a fun educational activity. Sometimes school science courses will require this as a project. There are many ways to make a solar system model, but this wikiHow will show you one of the simplest and easiest.


Chemical reactions make lots of fun experiments and enjoyment. Use carbon dioxide, baking soda, and lemon juice to create reaction by funneling the gas through a drinking bottle and into your balloon.


Experiments at home are a fun way to learn some basic science and create a few interesting things. The experiments suggested here are provided for their ease of creation and their huge fun factor.


Making fake ice can be a creative, fun project to do if you're for up a little bit of experiment, or if you like staging and taking photographs. It isn't too difficult to make and only requires a few tools to make realistic, real-looking ice cubes.


Kids and grown ups alike are often fascinated by science and chemistry. One great way to keep an audience entertained in a classroom or at home is to make your own hydrogen.


Baffled as to where to begin with a physics problem? There is a very simply and logical flow process to solving any physics problem.


Prove That Light Travels in a Straight Path

Light is an essential part of your day. It allows you to see objects, shapes, and colors. In fact, the pupils in your eyes filter in light to help you see everything around you.


Glow sticks are a type of light source that contains two chemicals and a dye called sensitizer or fluorophosphate.   [1]   This creates an endothermic reaction and causes the glow sticks to glow.


If you've just finished an experiment in your physics class, you might have to write a report about it. This may sound intimidating, but it's actually a simple process that helps you explain your experiment and your results to your teacher and anyone else who is interested in learning about it.


Verify the Uncertainty Principle for a Quantum Harmonic Oscillator

The quantum harmonic oscillator is the quantum analogue to the classical simple harmonic oscillator. Using the ground state solution, we take the position and momentum expectation values and verify the uncertainty principle using them.


Work out the Critical Angle of a Substance

The critical angle of a substance when passing a light ray from that substance to vacuum is very important as you must use it to determine whether total internal reflection will occur.


Solve a Basic Heat Transfer Problem in Thermodynamics

Thermodynamics is a difficult subject for anyone. This instructions manual hopes to help instruct Thermodynamics students in the basics of ideal gas law and heat transfer.


Quantum physics (AKA quantum theory or quantum mechanics) is a branch of physics providing a description of the behaviour and interaction of matter and energy on the scale of subatomic particles, photons and certain materials at very low temperature.


Study the Spin Concept in Quantum Theory

This article discusses the quantum mechanical concept of the spin. In this article, the concept of the spin is discussed, and in particular the electron spin due to its importance to the understanding of the theory of chemical bond and spectroscopic information of atoms and molecules.


A pendulum consists of a weight suspended from a rod or string that swings back and forth. Pendulums are found in timekeeping devices such as metronomes, grandfather clocks, seismometers, and swinging incense burners, and can be used to illustrate complex physics problems.


Specific gravity, also referred to as relative density, is used to relate the weight or density of liquids to that of water. Specific gravity is a unitless measurement that is derived as a ratio of either the weight of another liquid or the density of another liquid divided by the weight or density of water.


Use an Energy Balance to Solve Complex Steam Turbine Problems

Many academic and real-world engineering problems revolve around steam turbines. In order to solve them, you must utilize an energy balance and various other engineering concepts.


Metaphysics is a branch of philosophy investigating the fundamental nature of reality and being. Simply, it answers two basic questions: "What is there?"


Study the Quantum Mechanical Equation of Schroedinger

In the world of physics and quantum mechanics, the Schrödinger equation is an important one. According to quantum physicists, the equation provides a mechanism for modelling systems ranging from that which can be observed to the subatomic and from the simple to the most complex.


Fog in a bottle is a fun science experiment you can do in your own home. Fog is created when water vapor condenses, forming a haze of tiny water droplets in the air.


Atomic energy holds the promise of reducing the greenhouse gas emissions that cause global climate change. Though the technology has been around for decades now, it is little understood how atomic energy is actually produced and harnessed to the benefit of mankind.


Viscosity can be defined as the measurement of a liquid's resistance to flow. Consider water and molasses. Water flows relatively freely, while molasses is less fluid.


Physics exams can be hard to pass at the best of times, but fortunately, they can be easily beaten with these simple steps.


In the physical universe, locations in spacetime are called events; an event is specified a location in three-dimensional space and a point in time.


Although invisible ink and secret messages seem the stuff of spy stories and wizarding schools, anyone can make invisible ink at home with everyday household ingredients.


Mixing colored lights to create new colors is very different than mixing paint or food coloring. The three primary colors of light are red, blue, and green, unlike the primary colors of paint which are red, blue, and yellow.


Thomas Young's  double slit experiment was extremely important in the area of  wave theory . His experiment proves that light exhibits wavelike properties.


We all have been students still or have been in some time. We all know how important to have guidance for the studies from seniors. This article is very helpful for students in order to understand how to prepare a lab report for their chemistry, physics or other science lab experiments.


While this thermometer won't tell you if you have a fever or not, it can tell you how hot and cold your surroundings are -- you could even calibrate your thermometer or work out your own scale if you wanted!


Carbon dioxide (CO 2 ) is colorless and odorless, so you can't detect it through direct observation. You'll need to collect an air sample (or a CO 2  sample), then run one of several simple tests to identify the presence of the gas.


Contrary to popular belief, special relativity is able to deal with acceleration and accelerating reference frames (though these only apply locally - see tips).


Win First Place in Your School Science Fair

Science fairs are important and fun parts of many people’s educational experience. While some people approach their science fair project as just something to get through, other people are more committed to creating a project that is potentially award winning.


Scientists have long observed differences in the way insects interact with different colors. Several hypotheses exist as to why insects seem to have “favorite colors.”


The Newton’s Cradle is a device that doubles as a desk ornament and a tool for explaining the basic foundations of physics. It is constructed by mounting a series of balls on strings to a common bar.


"Without knowing it, we utilize hundreds of products each day that owe their origin to wild animals and plants. Indeed our welfare is intimately tied up with the welfare of wildlife.


Show Oxygen Is a By Product of Photosynthesis

This simple version of a traditional science experiment makes a great class project to demonstrate that oxygen is a by-product of photosynthesis. This project is best started in the morning of a sunny day.


Osmosis is a biological and chemical process that describes the movement of water from one concentration to another. During osmosis, water molecules move through a semi-permeable membrane to create an equal distribution of water on both sides.


Think of Fourth Grade Science Project Ideas

Many children look forward to the day that they get to participate in a science fair or develop their own science project. One of the trickiest steps teachers face when developing a science project is deciding on a topic.


When harmful gases contained in air pollution react with moisture in the air, acid rain can result. Ordinary rain is naturally acidic, with a pH between 5.0 and 5.5.


Simplify and Explain the Scientific Method for Kids

The scientific method is a series of steps used by scientists to determine whether a hypothesis is true or not. It can also be used to solve everyday problems in any topic or area.