Learn how to find the absolute value of a number and how to solve math problems containing absolute values and integers.

## Related Topics

- How to Add and Subtract Integers
- How to Multiply and Divide Integers
- How to Use Order of Operations
- How to Order Integers and Numbers

## Step by step guide to solve integers and absolute value problems

- To find the absolute value of a number, just find its distance from \(0\) on a number line! For example, the distance of \(12\) and \(- \ 12\) from zero on number line is \(12\)!

### Integers and Absolute Value – Example 1:

Solve. \(|8 \ – \ 2| \ × \ \frac{ |- \ 4 \ × \ 6|}{3}=\)

**Solution:**

First solve \(|8 \ – \ 2|, →|8 \ – \ 2|=|6|\), the absolute value of \(6\) is \(6\), \(|6|=6\)

\(6 \ × \ \frac{ |- \ 4 \ × \ 6|}{3}=\)

Now solve \(|- \ 4 \ × \ 6|, → |- \ 4 \ × \ 6|=|- \ 24|\), the absolute value of \(- \ 24\) is \(24\), \(|- \ 24|=24\)

Then: \(6 \ × \ \frac{ 24}{3}= 6 \ × \ 8=48 \)

### Integers and Absolute Value – Example 2:

Solve. \(\frac{ |- \ 12|}{3} \ × \ |9 \ – \ 4|=\)

**Solution:**

First find \(|- \ 12| , →\) the absolute value of \(- \ 12\) is \(12\), then: \(|- \ 12|=12\)

\(\frac{12}{3} \ × \ |9 \ – \ 4|= \)

Next, solve \(|9 \ – \ 4|, → |9 \ – \ 4|=| \ 5|\), the absolute value of \( \ 5\) is \(5\). \(| \ 5|=5\)

Then: \(\frac{12}{3} \ × \ 5=4 \ × \ 5=20\)

### Integers and Absolute Value – Example 3:

Solve. \(\frac{ |-18|}{9}×|5-8|=\)

**Solution:**

First find \(|-18| , →\) the absolute value of \(-18\) is \(18\), then: \(|-18|=18\)

\( \frac{18}{9}×|5-8|=\)

Next, solve \(|5-8|, → |5-8|=|-3|\), the absolute value of \(-3\) is \(3\). \(|-3|=3\)

Then: \(\frac{18}{9}×3=2×3=6\)

### Integers and Absolute Value – Example 4:

Solve. \(|10-5|×\frac{ |-2×6|}{3}=\)

**Solution:**

First solve \(|10-5|, →|10-5|=|5|\), the absolute value of \(5\) is \(5, |5|=5\)

\( 5×\frac{ |-2×6|}{3}= \)

Now solve \(|-2×6|, → |-2×6|=|-12|\), the absolute value of \(-12\) is \(12, |-12|=12\)

Then: \(5×\frac{ 12}{3}= 5×4=20\)

## Exercises for Solving Integers and Absolute Value Problems

### Evaluate.

- \(\color{blue}{|-43| – |12| + 10}\)
- \(\color{blue}{76 + |-15-45| – |3|}\)
- \(\color{blue}{30 + |-62| – 46}\)
- \(\color{blue}{|32| – |-78| + 90}\)
- \(\color{blue}{|-35+4| + 6 – 4}\)
- \(\color{blue}{|-4| + |-11|}\)

### Download Integers and Absolute Value Worksheet

## Answers

- \(\color{blue}{41}\)
- \(\color{blue}{133}\)
- \(\color{blue}{46}\)
- \(\color{blue}{44}\)
- \(\color{blue}{33}\)
- \(\color{blue}{15}\)