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4.2: Absolute Value of Integers

Difficulty Level: At Grade Created by: CK-12

Victor's grandparents live in Moscow, Russia. They told him that in the winters the high temperatures average around 10C\begin{align*}-10^\circ C\end{align*} while in the summers the high temperatures average around 23C\begin{align*}23^\circ C\end{align*}. In science class Victor learned that in Celsius, water freezes at 0C\begin{align*}0^\circ C\end{align*}. How could Victor use absolute value to determine which temperature is closer to the freezing point of water, 0C\begin{align*}0^\circ C\end{align*}?

In this concept, you will learn how to find the absolute value of an integer and you will learn how to find the opposite of an integer.

Absolute Value

The absolute value of a number is its distance from zero on the number line. The symbol for absolute value is | |\begin{align*}| \ |\end{align*} .

Let's look at an example.

|3|\begin{align*}|-3|\end{align*}

This is read as “the absolute value of -3”. To figure out the absolute value of -3, think about how far the number -3 is from zero. -3 is 3 units from zero on the number line. This means the absolute value of -3 is 3.

The answer is |3|=3\begin{align*}|-3| = 3\end{align*}.

Let's look at another example.

|3|\begin{align*}|3|\end{align*}

This is read as “the absolute value of 3”. 3 is 3 units from zero on the number line. This means the absolute value of 3 is 3.

The answer is |3|=3\begin{align*}|3| = 3\end{align*}.

Notice that both |3|\begin{align*}|-3|\end{align*} and |3|\begin{align*}|3|\end{align*} are equal to 3. This is because both -3 and 3 are 3 units from zero on the number line.

Keep in mind that the absolute value of a number will always be a positive value. This is because all numbers will always be a positive number of units away from zero on the number line.

In general, any positive integer and its opposite will have the same absolute value. To find the opposite of an integer, just change its sign either from positive to negative or from negative to positive.

Let's look at an example.

Find the opposite of -16.

-16 is a negative integer. To find its opposite, change the negative sign to a positive sign.

The answer is that the opposite of -16 is +16 or 16.

Let's look at another example.

Find the opposite of 900.

900 is a positive integer. It's the same as +900. To find its opposite, change the positive sign to a negative sign.

The answer is that the opposite of 900 is -900.

Examples

Example 1

Earlier, you were given a problem about Victor who has grandparents in Moscow. The winter temperature there is around 10C\begin{align*}-10^\circ C\end{align*} while the summer temperature is around 23C\begin{align*}23^\circ C\end{align*}. Victor wondered which of these temperatures is closer to the freezing point of water, 0C\begin{align*}0^\circ C\end{align*}.

First, consider the winter temperature of 10C\begin{align*}-10^\circ C\end{align*}.

|10|=10\begin{align*}|-10| = 10\end{align*}.

This means that 10°C\begin{align*}-10°C\end{align*} is 10 degrees away from the freezing point of water.

Next, consider the summer temperature of 23°C\begin{align*}23°C\end{align*}.

|23|=23\begin{align*}|23| = 23\end{align*}

This means that 23C\begin{align*}23^\circ C\end{align*} is 23 degrees away from the freezing point of water.

The answer is that because |10|\begin{align*}|-10|\end{align*} is less than |23|\begin{align*}|23|\end{align*}, the winter temperature is closer to the freezing point of water.

Example 2

Find the absolute value.

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

First, read the expression. This expression is read as “the absolute value of -234”.

Next, you should think about how far the integer -234 is from zero on the number line. -234 is 234 units from zero on the number line. This means that the absolute value of -234 is 234.

Remember that in general, the absolute value of a number will always be positive.

Example 3

Find the absolute value.

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

First, read the expression. This expression is read as “the absolute value of 22”.

Next, you should think about how far the integer 22 is from zero on the number line. 22 is 22 units from zero on the number line. This means that the absolute value of 22 is 22.

Notice that our sign didn't change. The absolute value of a number will always be positive.

Example 4

Find the absolute value.

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

First, read the expression. This expression is read as “the absolute value of -222”.

Next, you should think about how far the integer -222 is from zero on the number line. -222 is 222 units from zero on the number line. This means that the absolute value of -222 is 222.

Remember that the absolute value of a number will always be positive.

Example 5

Find the opposite of -18.

First, notice that -18 is a negative integer. To find its opposite, change the negative sign to a positive sign.

Review

Write the opposite of each integer.

1. 20

2. -7

3. 22

4. -34

5. 0

6. -9

7. 14

8. 25

Find the absolute value of each integer.

9. |13|\begin{align*}|13|\end{align*}

10. |11|\begin{align*}|-11|\end{align*}

11. |5|\begin{align*}|-5|\end{align*}

12. |17|\begin{align*}|17|\end{align*}

13. |9|\begin{align*}|-9|\end{align*}

To see the Review answers, open this PDF file and look for section 4.2.

1. [1]^ License: CC BY-NC 3.0
2. [2]^ License: CC BY-NC 3.0

Date Created:

Dec 02, 2015

Dec 02, 2015
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