# How to Solve Integers and Absolute Value Problems? (+FREE Worksheet!)

Two vertical lines around a number or expression are used to indicate the absolute value of that number or expression. Here, you can learn how to find the absolute value of a number and how to solve math problems containing absolute values and integers.

The absolute value of the real number $$a$$ Is written in the form of $$| a |$$ and is a positive number. Two vertical lines around a number or expression are used to indicate the absolute value of that number or expression. The output value of the absolute value is always greater than or equal to zero. Absolute value is used to indicate the distance of a number from zero on the line of real numbers.

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

1. The absolute value of a positive number is equal to the same positive number.
2. The absolute value of zero is equal to zero.
3. The absolute value of a negative number is the positive value of that number.
• Note: 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.

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

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

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