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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 \(|-7|\)?
Your answer
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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

Interpret absolute value

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

Absolute value measures distance, not the signed direction of the original number.

02

Measure the distance

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

Negative seven lies seven units to the left of zero.

03

Report the value

\[7\]

Distance is nonnegative, so the absolute value is positive seven.

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Another way

  1. Opposites -7 and 7 have the same distance from zero, so both have absolute value 7.

!

Common mistake

Do not keep the negative sign. The number is negative, but its distance from zero is not.

Solution walkthrough video