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Types of Numbers Examples


Integers and Absolute Value

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 left, you get...

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 r...

Mixed Numbers

We've seen a bunch of examples of fractions so far, but what happens when we mix them up with whole numbers? As a quick reminder, a fraction whose numerator is smaller than its denominator is c...

Reducing Fractions

There are tons of ways to represent any one fraction. How do we choose which to use? It'll depend on the problem, but it's often helpful to simplify or reduce the fraction. We know that if we sta...

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 "lo...

Multiplication of Fractions

You might think of multiplication as a slightly more complex process than addition, but when it comes to fractions, it's actually not as big a pain in the neck. That's because we don't need to co...

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...

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. Basically, we're striving to get back to 1 or to "achi...

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 example:...

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 co...

Converting Fractions into Decimals

To change a fraction into a decimal, divide the numerator by the denominator 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 pretty shal...

Comparing Decimals

When comparing decimal numbers to see which is bigger, first we look at the numbers before the decimal point. If one is greater than the other, we're done. Stick a fork in us. For example, 4.6248...

Adding and Subtracting Decimals

To add decimals, remember that decimals are abbreviations for fractions. For example, 0.3 + 0.04 + 0.001 translates to .Since and , this means that . Is this paragraph making you...

Multiplication and Division by Powers of 10

When you're multiplying or dividing a decimal by a power of 10, there are some sweet, sweet shortcuts.First we'll show you how to solve one of these problems without the shortcut. That should he...

Multiplying Decimals

When multiplying a decimal number by another decimal number, it always helps to be reminded what they'd look like in fraction form.Sample ProblemJust like with addition and subtraction, converting...

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 divisi...

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 "i...

Percents

A percent is an abbreviation for a fraction where the denominator is 100. That fancy "%" sign means "over 100." So that 64% you got on your history pop quiz last week? Yeah, that wasn't actuall...

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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