Integers and Absolute Value

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.

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

Download Integers and Absolute Value Worksheet

Answers

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

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