# 11.9: Differences of Integers Using a Number Line

**At Grade**Created by: CK-12

**Practice**Differences of Integers Using a Number Line

Have you ever had an job after school? Jamie wrote to his pen pal all about his job cutting grass. He also told his pen pal about a situation where he owed money that he had borrowed from his brother. Take a look.

Jamie earned ten dollars cutting grass. He owes his brother twelve dollars from a movie that they went to. Does Jamie still owe his brother money if he gives him the whole ten dollars he made? How much does he still owe?

**This is a situation where we can find differences of integers by using a number line. Pay attention and this Concept will teach you what you need to know.**

### Guidance

In our last few Concepts, you learned how to add integers using a number line. This Concept focuses on finding the ** differences** of integers. The word

**is a word that you have seen before. It is a key word that means**

*difference***. When you see the word difference, you know that you will be subtracting values.**

*subtract*One of the best ways to learn about finding the differences of integers is to use a number line. We can subtract values using a number line.

-6 – 2 = ____

Here we have the value of negative six and we are subtracting two from it. Let’s use a number line to figure this out.

We start at the first value, which is negative six.

Next, we subtract two from this value. If we subtract two, we move further into the negatives. Think of it as another loss. We start at negative six and move two units to the left into the negatives.

-6 – 2 = -8

We start with a loss and we have more loss, so our answer is a greater loss.

**The answer is negative eight.**

Let’s look at another one.

2 – 9 = ____

Here we have two minus nine. We start at positive two.

We have a loss of nine. We subtract nine from the two where we started.

The answer is negative 7.

2 – 9 = -7

**The answer is negative seven.**

Practice a few of these on your own. Use a number line to work through the problem.

#### Example A

**4 – 10 = ____**

**Solution: -6**

#### Example B

**-9 – 3 = ____**

**Solution: -12**

#### Example C

**-12 – 4 = ____**

**Solution: -16**

Now back to Jamie. Here is the original problem from the beginning of the Concept.

Have you ever had an job after school? Jamie wrote to his pen pal all about his job cutting grass. He also told his pen pal about a situation where he owed money that he had borrowed from his brother. Take a look.

Jamie earned ten dollars cutting grass. He owes his brother twelve dollars from a movie that they went to. Does Jamie still owe his brother money if he gives him the whole ten dollars he made? How much does he still owe?

Let’s start by writing a number sentence to represent this problem.

Jamie earned $10.00. He owes his brother $12.00.

10 - 12 = ____

Let’s use a number line to figure out if Jamie still owes his brother money.

We start at positive ten and then subtract 12. This means that we move twelve units toward the negative side of the number line.

10 – 12 = -2

**The answer is yes-he still owes more money. Jamie owes his brother $2.00.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Sum
- the result of an addition problem.

- Difference
- the result of a subtraction problem.

### Guided Practice

Here is one for you to try on your own.

Write a number sentence for this situation and then solve it.

Marcy lost 12 gems from a small jewel bag. Then she lost another four gems. How many did she lose?

**Answer**

To write this expression, you simply have to use negative numbers for losses.

\begin{align*}-12\end{align*}

Marcy lost 12 gems.

\begin{align*}-4\end{align*}

Then she lost another four gems.

\begin{align*}-12 - 4 = -16\end{align*}

**Marcy lost \begin{align*}-16\end{align*} −16 gems.**

### Video Review

Here is a video for review.

James Sousa, Subtracting Integers: The Basics

### Practice

Directions: Find each difference by using a number line.

1. \begin{align*}-5 - 2\end{align*}

2. \begin{align*}7 - 12\end{align*}

3. \begin{align*}-5 - 12\end{align*}

4. \begin{align*}-25 - 42\end{align*}

5. \begin{align*}5 - 32\end{align*}

6. \begin{align*}-15 - 12\end{align*}

7. \begin{align*}18 - 2\end{align*}

8. \begin{align*}25 - 22\end{align*}

9. \begin{align*}-45 - 32\end{align*}

10. \begin{align*}-35 - 37\end{align*}

11. \begin{align*}14 - 32\end{align*}

12. \begin{align*}15 - 44\end{align*}

13. \begin{align*}-41 - 12\end{align*}

14. \begin{align*}-18 - 13\end{align*}

15. \begin{align*}7 - 92\end{align*}

### Image Attributions

Here you'll learn to find differences of integers on a number line.