# 11.2: Opposites of Given Integers

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

**Practice**Opposites of Given Integers

Have you ever thought about sea level? Is the town where you live close to or above sea level?

Well, Mrs. Harris' students have been learning about New Zealand so that they can better understand the place where their pen pals live. Charles looked up Auckland on the computer and brought in this information the next day.

"Did you know that Auckland is 196 meters above sea level?" he shared with the class.

Mrs. Harris wrote \begin{align*}+196\end{align*} on the board.

This is a situation where a positive integer was written on the board. Do you know how to write the opposite of this integer?

**This Concept is all about opposites of given integers. We will return to this dilemma at the end of the Concept.**

### Guidance

An ** integer** is the set of whole numbers and its opposites. This means that every integer has an opposite integer.

Here is what the set looks like.

**....-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...**

**You see that each integer has an opposite value and the three dots at each end means that the set of whole numbers continues indefinitely in both a positive and negative direction.**

**How do we write opposites of given integers?**

Well, it is actually very simple. Change the sign! Let's look at one.

Write the opposite of -15.

**The answer would be +15 or 15.**

Here is another one.

Write the opposite of -15.

**The answer would be +15 or 15.**

Write the opposite of each given integer.

#### Example A

A loss of 34.

**Solution: \begin{align*}+34\end{align*}**

#### Example B

998

**Solution: \begin{align*}-998\end{align*}**

#### Example C

67 feet above sea level

**Solution: \begin{align*}-67\end{align*}**

Now back to the dilemma from the beginning of the Concept.

Have you ever thought about sea level? Is the town where you live close to or above sea level?

Well, Mrs. Harris' students have been learning about New Zealand so that they can better understand the place where their pen pals live. Charles looked up Auckland on the computer and brought in this information the next day.

"Did you know that Auckland is 196 meters above sea level?" he shared with the class.

Mrs. Harris wrote \begin{align*}+196\end{align*} on the board.

This is a situation where a positive integer was written on the board. Do you know how to write the opposite of this integer?

To write this as an opposite we simply change the sign and use the same number.

\begin{align*}+196\end{align*} becomes \begin{align*}-196\end{align*}

**This is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Integers
- the set of whole numbers and their opposites

- Negative Numbers
- numbers that are less than zero

- Positive Numbers
- numbers that are greater than zero

- Zero
- is a part of the set of integers, but is neither positive or negative

### Guided Practice

Here is one for you to try on your own.

On day one, the stock market rose 25 points. If the opposite happened on day three, what integer could we write to represent this situation?

**Answer**

To complete this problem, first let's write the integer from day one.

A rise of 25 points is a positive integer.

\begin{align*}+25\end{align*}

The opposite on day three would indicate a negative integer.

\begin{align*}-25\end{align*}

**This is our answer.**

### Video Review

Here are videos for review.

James Sousa, Introduction to Integers

James Sousa, Example of Determining the Opposite of Integers

### Practice

Directions: Write the opposite of each integer described or written.

1. A loss of 18

2. A gain of 22

3. -78

4. 999

5. -87

6. 30 feet below the surface of the ocean

7. A rise of 15 feet

8. 25 feet below sea level

9. 80 feet above ground

10. 100 feet deep

11. A profit of ten dollars

12. The hill had a grade of 15%

13. -987

14. 65

15. -1,298

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
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Term | Definition |
---|---|

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... |

Negative Numbers |
Negative numbers are numbers that are less than zero. |

Zero |
Zero is a part of the set of integers, but is neither positive or negative. |

### Image Attributions

Here you'll learn to identify opposites of given integers.