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Types of Numbers
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Types of Numbers Examples
Integers and Absolute Value
Integers Think of the distance from one integer to another as being one step. If you start at zero and take two steps to the right, you get to 2. If you start at 0 and take two steps to the l...
Equivalent Fractions
There are infinitely many different ways to represent the same fraction. Since we see no reason to abandon our brownie analogy, let's stick with it  half of that pan of brownies can be represented...
Mixed Numbers
Until now, we have seen a bunch of examples of fractions. Fractions whose numerator is smaller than the denominator are called proper fractions. The point of proper fraction is that if y...
Reducing Fractions
There are many ways to represent any one fraction. How do we choose which to use? It will depend on the problem, but it's often helpful to simplify or reduce the fraction. We know that if we star...
Least Common Denominator
This process of cutting numbers down to size in order to get the pieces we want is referred to as finding the " lowest (or least) common denominator (LCD)." Yes, the "L" can stand for either "lowe...
Multiplication of Fractions
You may generally think of multiplication as being a slightly more complex process than that of addition, but when it comes to fractions it's actually not as big a pain in the neck. That's because...
Equivalent Fractions and Multiplication by 1
Multiplication by 1. We bet you like the sound of that. And well you should. It's as simple as it sounds.Mathematicians call 1 the multiplicative identity, meaning that any number multiplied by 1...
Multiplication by Clever Form of 1
This super handy trick lets you simplify an expression without changing its value. Which is good, because fractions should not be subject to inflation.Sample ProblemHere's a horrible fraction. A re...
Multiplicative Inverses
Every fraction with a nonzero numerator has a multiplicative inverse, which is simply the number we can multiply our fraction by to get 1. You'll find that we are very often striving to get...
Division of Fractions
In the world of fractions, division is really just another way of saying "multiplication by the reciprocal."The phrase a divided by b means "a multiplied by the reciprocal of b."For examp...
Multiplication and Division with Mixed Numbers
In order to multiply or divide with mixed numbers, turn the mixed numbers into fractions first. Just wave your wand over the top of them, whisper the magic incantation, and poof! Or, you can conver...
Converting Fractions into Decimals
To change a fraction into a decimal, divide the denominator into the numerator using long division. That's it? That's it.
Converting Decimals into Fractions
Since a decimal is an abbreviation for a fraction whose denominator is a power of 10, we already know how to do this. We don't even have to dig deep to recall the process. We can dig prett...
Comparing Decimals
A couple of equivalent fractions for 4/10 are 40/100 and 400/1000. Converting these into decimals, we see that 0.4 is equivalent to 0.40 and 0.400. To summarize: adding extra zeros to the end of a...
Adding and Subtracting Decimals
To add decimals, remember that decimals are abbreviations for fractions. 0.3 + 0.04 + 0.001 translates to . Since and , this means that . Is this paragraph making you dizzy?...
Multiplication and Division by Powers of 10
When you're multiplying or dividing a decimal by a power of 10, there are some nice shortcuts.First we'll show you how to solve one of these problems without the shortcut. That should heighten your...
Multiplying Decimals
When multiplying a decimal number by another decimal number, it again helps to be reminded what they'd look like in fraction form.Sample ProblemAs with addition and subtraction, converting decimals...
Dividing Decimals
To divide one decimal by another decimal, we use long division. Don't you just love making use of existing skill sets? First, a quick refresher on the names for the different parts of a...
Infinite Decimals
So far, all the decimal arithmetic we've done has involved decimal numbers with a finite number of decimal places. However, sometimes decimal numbers are infinite. Make sure you don't confuse "infi...
Percents
A percent is an abbreviation for a fraction where the denominator is 100. "%" means "over 100." So that 64% you got on your history pop quiz last week? Yeah  that wasn't actually out of...
Things to Do with Real Numbers
Compare ThemWhen comparing real numbers, it can help to think of the number line. Ah, how fondly we remember it. Our favorite line of all the lines. The numbers on a number line get bigger as we go...
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