# Understanding Integers

Integers are numbers, specically, they are whole numbers (not fractions or decimals) above or below 0.

To put it more concisely, **integers are positive and negative whole numbers**.

Integers can be as high ($32$ or $32,000,009,876$) or low ($-12$ or $-765,987,322,000$) as you can imagine (both positive and negative numbers go on infinitely). But, remember integers do not include any numbers with decimals ($3.45$ or $-.98$) or fractions ($5\dfrac{8}{9}$ or $-\dfrac{3}{89}$).

It's important to understand that as positive numbers get more positive and negative numbers get more negative, they move **AWAY** from 0. The more negative a number is, the lower it is. Let's look at a number line:

$\overleftrightarrow{-8 \quad -7 \quad -6 \quad -5 \quad -4 \quad -3 \quad -2\quad -1 \quad 0 \quad 1\quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8}$

Think about a game in which you can gain or lose power. -10 power is far worse than 0 power. But, -3 power is a little better than -4 power. Ovbviously 10 power is better than 2 power. And, any positive power is better than any negative power.

Whenever you're ordering integers, the lowest number (the largest negative) should be the farthest to the left. The highest number should be the farthest to the right.

Whenever you think about positive and negative numbers, thinking of a number line will help. Here's why:

*Example:*

*Which number is greater 33 or 56?*

$33<56$ so $56$ is greater than $33$.

*Which number is greater -33 or -56?*

$-33>-56$ so although $-56$ is more negative, $-33$ is farther to the right on the number line, so it is the "greater" number.

Bottom line, when working with integers, remember the lowest numbers go to the left (these are the most negative numbers) and the highest numbers go to the right -- these are the most positive (or least negative!) numbers.

#### Practice Problems:

## Understanding Integers

Use a number line to put the numbers in order from least to greatest:

1. 5, 7, 10, -2, 9, -4, -17

2. -2, 8, 15, -4, 4, 7

3. -32, 5, 3, 27, -9

4. -334, 9, 2, 18, -27

5. -17, -18, -16, -20, -2

6. -8, -9, -10, -22

Use a greater than (>) or less than (<) sign to show which of the following integers is greater:

7. $64\bigcirc 78$

8. $-90\bigcirc-99$

9. $-2\bigcirc-200$

10 $-56\bigcirc56$

11. $-9\bigcirc0$

12. $-3\bigcirc-4$

#### Answer Key: