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All courses Math Foundations · MF.SN.4 26 of 60
Interpret absolute value as distance and use it to compare quantities and errors.

Evaluate an absolute value

Problem
What is the value of |-7|?
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Hint

Look at the number inside the bars and ask: how far is -7 from 0 on the number line?

Absolute value means distance from 0, and distance is never negative.

Solution walkthrough

01

Notice the number inside the absolute value

\[|-7|\]

The expression asks for the absolute value of -7. Absolute value tells how far a number is from 0 on the number line.

02

Locate -7 relative to 0

\[-7~\text{is}~7~\text{units}~\text{to}~\text{the}~\text{left}~\text{of}~0\]

Negative 7 is not the answer yet. Its location matters because absolute value measures distance, not direction.

03

Use distance from zero

\[\text{distance}~\text{from}~0~\text{to}~-7~=~7\]

A distance is always nonnegative, so the distance from 0 to -7 is 7.

04

State the value

\[|-7|~=~7\]

So the value of the expression is 7.

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Another way

  1. Think of absolute value as dropping the sign when you report distance: the distance of -7 from 0 is 7.

  2. Check with opposites: 7 and -7 are the same distance from 0, so |-7| must equal |7| = 7.

!

Common mistake

Writing |-7| = -7 because the number inside is negative. Absolute value is distance from 0, and distance cannot be negative.