# 11.8: Sums of Integers with Different Signs

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

**Practice**Sums of Integers with Different Signs

Callie continued to work on her sweater throughout the evening. For some reason, once she changed the thread, the stitches did look even.

"What is wrong with this?" She commented in frustration.

Callie's Mom came over to look at her work.

"What's the matter?" her Mom asked.

"These stitches don't look right. I made 14 and then took out 4 before adding 8 more and it still looks funny," Callie said showing her Mom the sweater.

"You have the wrong size needle. If you change to a smaller needle, the stitches will look a lot better," her Mom instructed.

Callie was relieved and went to the sewing box to get a new needle.

Callie's stitches present a situation where you could demonstrate adding positive and negative numbers.

Do you know how to write this expression? How many stitches did Callie sew?

**This Concept is all about adding integers with different signs. By the end of the Concept, you will know how to answer these two questions.**

### Guidance

You now know how to add integers with the same sign. What about when two integers have different signs? We started working on this when we used a number line for adding earlier in this Concept. But if you don’t have a number line, you can still add integers with different sign. Let’s learn how to do this now.

**How do we add integers with different signs?**

**We can add integers with different signs by ignoring the sign and by finding the difference between the two values. Then the sign of the greater loss or gain becomes the sign of the answer.**

8 + -3 = ____

**First, ignore the sign and find the difference between 8 and 3. Difference means to subtract. We subtract 8 and 3 and get 5.**

**8 - 3 = 5**

**Next, think about losses and gains. The gain is greater than the loss. So our sign is positive.**

8 + -3 = 5

**The answer is positive 5.**

**We can check our work by using a number line.**

**We start with positive 8.**

**We add a negative three to that, so we move three units towards the negative side of the number line.**

**The answer is 5, so our answer checks out.**

Let's try another one.

-9 + 4 = ____

**First, ignore the signs and find the difference between the two values.**

**9 - 4 = 5**

**Next, think about losses and gains. Here the loss is negative nine. That is a big loss. The loss is greater than the gain. A loss of nine is greater than a gain of four, so our sign in negative.**

-9 + 4 = -5

**The answer is negative five.**

Now it’s time for you to try a few on your own. Figure out each sum.

#### Example A

**7 + -13 = ____**

**Solution: -6**

#### Example B

**-22 + 10 = ____**

**Solution: -12**

#### Example C

**-1 + 16 = ____**

**Solution: 15**

Now back to Callie and the sweater. Here is the original problem once again.

Callie continued to work on her sweater throughout the evening. For some reason, once she changed the thread, the stitches did look even.

"What is wrong with this?" She commented in frustration.

Callie's Mom came over to look at her work.

"What's the matter?" her Mom asked.

"These stitches don't look right. I made 14 and then took out 4 before adding 8 more and it still looks funny," Callie said showing her Mom the sweater.

"You have the wrong size needle. If you change to a smaller needle, the stitches will look a lot better," her Mom instructed.

Callie was relieved and went to the sewing box to get a new needle.

Callie's stitches present a situation where you could demonstrate adding positive and negative numbers.

Do you know how to write this expression? How many stitches did Callie sew?

To write this expression, we begin by writing the stitches. A positive value is when Callie added a stitch and a negative value is when she took one out.

\begin{align*}14 + -4 + 8\end{align*}

Next, we add them together. We add the first two values and then add the third to that sum.

\begin{align*}10 + 8 = 18\end{align*}

**Callie added 18 stitches in all.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Integer
- the set of whole numbers and their opposites. Positive and negative whole numbers are integers.

- Absolute Value
- the number of units that an integer is from zero. The sign does not make a difference.

### Guided Practice

-2 + 8 = _____

**First, ignore the signs and find the difference between the two values.**

**8 - 2 = 6**

**Next, think about losses and gains. This problem starts with a loss of 2, that’s the negative two, and then there is a gain of 8. That is a sum of positive 6. Since the gain is greater than the loss, the answer is positive.**

**The answer is positive six.**

### Video Review

Here are videos for review.

Khan Academy, Adding Integers with Different Signs

James Sousa, Example of Adding Integers

### Practice

Directions: Add the following pairs of integers.

1. \begin{align*}12 + -4\end{align*}

2. \begin{align*}-24 + 14\end{align*}

3. \begin{align*}32 + -4\end{align*}

4. \begin{align*}-52 + 14\end{align*}

5. \begin{align*}67 + -64\end{align*}

6. \begin{align*}55 + -64\end{align*}

7. \begin{align*}78 + -84\end{align*}

8. \begin{align*}99 + -104\end{align*}

9. \begin{align*}-112 + 114\end{align*}

10. \begin{align*}-19 + -4 + 12\end{align*}

11. \begin{align*}-32 + -24 + 65\end{align*}

12. \begin{align*}98 + -12 + -34\end{align*}

13. \begin{align*}70 + -34 + 23\end{align*}

14. \begin{align*}82 + -54 + 27\end{align*}

15. \begin{align*}98 + -34 + -18\end{align*}

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Absolute Value

The absolute value of a number is the distance the number is from zero. Absolute values are never negative.Integer

The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., -3, -2, -1, 0, 1, 2, 3...### Image Attributions

Here you'll learn to add integers with different signs.