# Integers and Absolute Value

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

## 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 $$12$$!

### 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: $$6 \ × \ \frac{ 24}{3}= 6 \ × \ 8=48$$

### 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: $$\frac{12}{3} \ × \ 5=4 \ × \ 5=20$$

### 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: $$\frac{18}{9}×3=2×3=6$$

### 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

### Evaluate.

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

• $$\color{blue}{41}$$
• $$\color{blue}{133}$$
• $$\color{blue}{46}$$
• $$\color{blue}{44}$$
• $$\color{blue}{33}$$
• $$\color{blue}{15}$$

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