Sums of Integers with the Same Sign

Add positive values with positive and negative values with negative.

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Sums of Integers with the Same Sign

Credit: Steven Depolo Source: https://farm4.staticflickr.com/3449/3706276774_7e60155bd3.jpg License: CC BY-NC 3.0 [Figure1]

Callie tore a small hole in the right sleeve of her favorite sweater. But her mother had just taught her how to darn a sweater. So she picked a thread that she thought matched the color of her sweater. She sewed fourteen stitches lengthwise across the hole and then added another ten over that, side to side. But when she looked at the sweater in the light, she realized the thread really didn't match. So Callie took out the 10 stitches, and then she took out the 14 stitches. How many did she take out altogether?

In this concept, you will learn how to add integers with the same sign.

Adding Integers with the Same Sign

positive number is a number greater than zero. It can be written with or without a + symbol in front of it. A gain in something is written with a positive number.

negative number is a number that is less than zero. It is always written with a - symbol in front of it. A loss is written with a negative number.

An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa.

When you add integers with the same sign, you think in terms of gains or in terms of losses, but not both at once.

Here is an example.

5 + 9 = ____

These two integers are both positive. The sum of two positive numbers is always positive. Five plus nine is fourteen.

5 + 9 = 14

Here is another example.

-9 + -8 = ____

A negative integer is a loss. A loss plus another loss is more loss. As before, the sign stays the same when you add two integers that have the same sign.

A negative nine plus a negative eight is a negative seventeen.

-9 + -8 = -17

The main thing to notice when you add two integers of the same sign is that the final answer also has the same sign. A gain and a gain is more gain. A loss and a loss is more loss.

Examples

Example 1

Earlier, you were given a problem about Callie and her torn sweater.

After mending it, she discovered that her thread didn't match. She had to take out the ten side to side stitches she'd sewn, and then the fourteen lengthwise stitches. How many stitches did she have to take out? And how many would she need to put back in with the right thread?

First, note that she was taking out stitches.

"Taking out" means a loss, so these are negative.

Next, re-write them as integers.

They are -10 and -14, respectively.

\begin{align*}-10 + -14 = -24\end{align*}

-24 is the answer. She will have to remove 24 stitches and then put in 24 more with the right color.

Example 2

-7 + -12 + -36 = ____

First, note that all three numbers are negative. That means, the final answer will be negative.

7 + 12 + 36 = 55

Then, make sure that the answer has the right sign.

In this example, the answer is -55.

Example 3

-9 + -11 = ____

First, note that both integers are negative, so the final answer will be negative.

9 + 11 = 20

Then, make sure that the answer has the correct sign.

Example 4

-8 + -13 = ____

First, note that both integers are negative, so the final answer will be negative.

8 + 13 = 21

Then, make sure that the answer has the correct sign.

Example 5

17 + 12 = ____

First, note that both integers are positive, so the final answer will be positive.

17 + 12 = 29

Then, make sure that the answer has the correct sign.

Review

1. \begin{align*}6 + 9\end{align*}
2. \begin{align*}-6 + -9\end{align*}
3. \begin{align*}-16 + -9\end{align*}
4. \begin{align*}16 + 19\end{align*}
5. \begin{align*}23 + 90\end{align*}
6. \begin{align*}86 + 99\end{align*}
7. \begin{align*}-96 + -9\end{align*}
8. \begin{align*}-76 + -29\end{align*}
9. \begin{align*}-336 + -9\end{align*}
10. \begin{align*}206 + 89\end{align*}
11. \begin{align*}-6 + -9 + -17\end{align*}
12. \begin{align*}-34 + -9 + -12\end{align*}
13. \begin{align*}-96 + -19+ -8\end{align*}
14. \begin{align*}-76 + -29 + -11\end{align*}
15. \begin{align*}-36 + -89 + -33\end{align*}

To see the Review answers, open this PDF file and look for section 11.7.

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Vocabulary Language: English

TermDefinition
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...