# 4.2: Absolute Value of Integers

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

Do you live where it snows? How much snow has ever accumulated in 24 hours where you live?

Cameron is amazed at the record snowfall in Alaska. One time, the day began without any snow on the ground. Then it began to snow and within 24 hours there was 62 inches of snow.

We can use an integer to write the increase in snowfall, and we can use absolute value to show the distance between the depth of snow and the bare ground.

Do you know how to do this?

**Understanding absolute value is the goal of this Concept. Pay attention and we will revisit this situation at the end of it.**

### Guidance

Sometimes, when we look at an integer, we aren’t concerned with whether it is positive or negative, but we are interested in how far that number is from zero. Think about water. You might not be concerned about whether the depth of a treasure chest is positive or negative simply how far it is from the surface.

This is where absolute value comes in.

**What is absolute value?**

**The** *absolute value***of a number is its distance from zero on the number line.**

We can use symbols to represent the absolute value of a number. For example, we can write the absolute value of 3 as \begin{align*}|3|\end{align*}.

Writing an absolute value is very simple you just leave off the positive or negative sign and simply count the number of units that an integer is from zero.

Find the absolute value of 3. Then determine what other integer has an absolute value equal to \begin{align*}|3|\end{align*}.

**Look at the positive integer, 3, on the number line. It is 3 units from zero on the number line, so it has an absolute value of 3.**

**Now that you have found the absolute value of 3, we can find another integer with the same absolute value. Remember that with absolute value you are concerned with the distance an integer is from zero and not with the sign.**

Here is how we find another integer that is exactly 3 units from 0 on the number line. The negative integer, -3, is also 3 units from zero on the number line, so it has an absolute value of 3 also.

**So,** \begin{align*}|3|=|-3|=3\end{align*}.

**This example shows that the positive integer, 3, and its opposite, -3, have the same absolute value. On a number line, opposites are found on opposite sides of zero. They are each the same distance from zero on the number line. Because of this, any integer and its opposite will always have the same absolute value. To find the opposite of an integer, change the sign of the integer.**

**Just like we can find the absolute value of a number, we can also find the opposite of a number.**

Find the opposite of each of these numbers: -16 and 900.

**-16 is a negative integer. We can change the negative sign to a positive sign to find its opposite. The opposite of -16 is +16 or 16.**

**900 is the same thing as +900. We can change the positive sign to a negative sign to find its opposite. So, the opposite of 900 is -900.**

Find the absolute value of each number.

#### Example A

\begin{align*}|22|\end{align*}

**Solution: \begin{align*}22\end{align*}**

#### Example B

\begin{align*}|-222|\end{align*}

**Solution:\begin{align*}222\end{align*}**

#### Example C

Find the opposite of -18.

**Solution:\begin{align*}18\end{align*}**

Here is the original problem once again.

Do you live where it snows? How much snow has ever accumulated in 24 hours where you live?

Cameron is amazed at the record snowfall in Alaska. One time, the day began without any snow on the ground. Then it began to snow and within 24 hours there was 62 inches of snow.

We can use an integer to write the increase in snowfall, and we can use absolute value to show the distance between the depth of snow and the bare ground.

Do you know how to do this?

To express both of these values using integers and absolute value, we can begin with the increase in snowfall. Because it is an increase in snowfall, we use a positive integer to express this amount.

\begin{align*}+62\end{align*} inches

To express the difference in snowfall accumulation and the bare ground, we use an absolute value.

\begin{align*}|62|\end{align*}

The absolute value of 62 is 62.

**This is how we can express this situation using integers.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Whole Numbers
- the positive counting numbers including 0.

- Fraction
- a part of a whole written with a numerator and denominator.

- Integers
- positive whole numbers and their opposites. Positive and negative numbers

- Opposites
- for a negative number, it has a positive partner. For a positive number, it has a negative partner.

- Absolute Value
- the distance that a number is from zero.

### Guided Practice

Here is one for you to try on your own.

\begin{align*}|-234|\end{align*}

**Answer**

To identify the absolute value of this number, we have to think about the number of units it is from zero. Remember that absolute value does not concern positive or negative, but the distance that a value is from zero.

\begin{align*}|-234| = 234\end{align*}

**This is our answer.**

### Video Review

Here is a video for review.

- This James Sousa video is an introduction to integers includes absolute value.

### Practice

Directions: Write the opposite of each integer.

7. 20

8. -7

9. 22

10. -34

11. 0

12. -9

13. 14

14. 25

Directions: Find the absolute value of each number.

15. \begin{align*}|13|\end{align*}

16. \begin{align*}|-11|\end{align*}

17. \begin{align*}|-5|\end{align*}

18. \begin{align*}|17|\end{align*}

19. \begin{align*}|-9|\end{align*}

### Image Attributions

Here you'll learn to identify absolute value and opposites of given integers, recognizing zero as neither positive nor negative.