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Algebra
How to Add and Subtract Fractions in Algebra (Video)
In algebra, adding and subtracting fractions is easy when you find the common denominator. This video shows you how to convert fractions for the common denominator. After you determine the common denominator, you can add and subtract fractions, including story problems, with ease. [more…]
Calculus
How to Find the Volume of a Solid with a Circular Cross-Section (Video)
Calculus allows you to calculate the volume of conical objects by dividing the object into an infinite number of circular cross-sections - geometrical shapes resembling pancakes or washers - and adding up the volume of all those cross-sections through integration. This video tutorial shows you how. [more…]
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Geometry
Mastering the Formal Geometry Proof
Suppose you need to solve a crime mystery. You survey the crime scene, gather the facts, and write them down in your memo pad. To solve the crime, you take the known facts and, step by step, show who committed [more…]
Geometry
Sizing Up the Area of a Polygon
Not only can polygons be classified by the number of sides they have and by their angles, but they can also be grouped according to some of their qualities. Polygons can have three personality characteristics [more…]
Geometry
Simple and Easy Geometry Tips and Tools
The first rule of life? Life (as well as geometry) can be difficult. But why make it more difficult than it has to be? Do you need help with geometry? Here are 11 tried-and-true tips to make your forays [more…]
Geometry
Measuring and Making Angles
On a map, you trace your route and come to a fork in the road. Two diverging roads split from a common point and form an angle. The point at which the roads diverge is the [more…]
Geometry
Classifying Three Types of Triangles
Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves. That is, a triangle has [more…]
How to Convert from Percents to Fractions
Converting percents to fractions is fairly straightforward. Remember that the word percent means “out of 100.” So changing percents to fractions naturally involves the number 100. [more…]
How to Split Up a Pizza into Unequal Amounts
You may have to add or subtract fractions in word problems that involve splitting up part of a whole into unequal amounts. For example, consider the following pizza problem: [more…]
Calculate Addition and Subtraction Problems Using Decimals
You frequently work with decimals when dealing with money, metric measurements, and food sold by the pound. The following problem requires you to add and subtract decimals. Even though the decimals may [more…]
Calculate Percentages Using Addition and Subtraction
Many real-life problems involve adding and subtracting percents. For example, percents can represent answers in polls, votes in an election, or portions of a budget, and the total often has to add up to [more…]
Multiply Decimals and Percents in Word Problems
The word of in a word problem usually means multiplication. This idea is also true in word problems involving decimals and percents. The method for solving these two types of problems is similar, as you’ll [more…]
How to Determine a Salary Increase Based on a Percentage
If you need to calculate someone’s salary increaseor raise based on the percentage of the raise, you can do this using the distributive property. Here’s an example: [more…]
How to Calculate Interest on Top of Interest
When you receive interest from the bank, you get more money. And when you earn interest on the interest you earned earlier, this makes the dollar amounts grow even faster. Here’s an example: [more…]
How to Calculate a Percentage Discount
You can use subtraction to calculate a percentage discount. In fact, when you hear the words discount or sale price, you should automatically think of subtraction. Here’s an example: [more…]
How to Simplify Numbers Using Scientific Notation
When working with extremely large or small numbers, you can save on time and space — and make calculations easier — by using scientific notation. As you will see, it uses both decimals and exponents to [more…]
How to Estimate Metric Amounts
One reason people sometimes feel uncomfortable using the metric system is that when you’re not familiar with it, estimating amounts in practical terms is hard. For example, if your friend invites you to [more…]
How to Determine Likelihoods Using Basic Probability
Probability is the mathematics of deciding how likely an event is to occur. It has a wide variety of applications in insurance, weather prediction, biological sciences, and even physics. For example, [more…]
How to Recognize Different Types of Sets
To work with sets, you need to understand terms such as elements and cardinality. You also need to know how to recognize equal sets, subsets, and empty sets, and how they relate to each other. [more…]
Find the Union, Intersection, Relative Complement, and Complement of Sets
Set theory has four important operations: union, intersection, relative complement, and complement. These operations let you compare sets to determine how they relate to each other. [more…]
How to Find the Mean and Median in Quantitative Data
Quantitative data assigns a numerical value to each member of a statistical sample. You can use this information to find the mean and median values.
The following sample — which is purely fictional — uses [more…]
How to Convert Fractions into Percents
Converting a fraction to a percent is a simple two-step process. The first example below shows how to convert a simple fraction, and the second example shows how to convert a more complex fraction using [more…]
How to Solve Percent Problems
A lot of percent problems turn out to be easy to solve when you give them a little thought. In many cases, just remember the connection between percents and fractions and you’re halfway home: [more…]
How to Use the English System of Measurement
The English system of measurement is most commonly used in the United States (but, ironically, not in England). Although you’re probably familiar with most of the English units of measurement, in the following [more…]
How to Work with Qualitative Data
In statistics, qualitative datadivides a data set (the pool of data that you’ve gathered) into discrete chunks based on a specific attribute. You can then find information such as percentage amounts and [more…]
How to Subtract Fractions with Different Denominators
When you want to subtract fractions with different denominators, you have a choice of methods: the easy way, the quick trick, and the traditional way.
The easy way always works, and you should use this [more…]
How to Add Mixed Numbers
Whether mixed numbers have the same denominators or different denominators, adding them is a lot like adding whole numbers: you stack them up one on top of the other, draw a line, and add. For this reason [more…]
How to Create Your Own Multiplication Table
If you have trouble multiplying numbers, then you should get to know the multiplication table. There are two multiplication tables you can use: the cumbersome old table, and the newer, easy-to-use short [more…]
How to Do Long Division by One Number
In the olden days, knowing how to divide large numbers was important. Basic long division is still good to know, so the following examples will show you how to divide a one-digit divisor into another number [more…]
How to Convert a Basic Word Problem into an Equation
Word problems help you understand the logic behind setting up equations in real-life situations. The skill you need most when working with word problems is understanding how to turn the situation you’re [more…]
How to Find the Greatest Common Factor
The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all those numbers. For example, the GCF of the numbers 4 and 6 is 2 because 2 is the greatest number that’s [more…]
How to Recognize Types of Fractions
To work with fractions, you need to know the different forms they take — reciprocal fractions, mixed numbers, proper and improper fractions — as well as the parts they’re made up of — denominators, numerators [more…]
