Distance and Absolute Value

≈ 35 min

Distance and Absolute Value

Distance tells how far apart two positions are, so it is never negative. Absolute value measures distance from zero: $|-7|=7$ . To find the distance between two integers, count spaces on a number line or subtract and take the absolute value: distance from $a$ to $b$ is $|a-b|$ .

Worked example

The distance from $-6$ to 4 is $|-6-4|=|-10|=10$ . On a line you cross six spaces to zero and four more to 4: ten spaces.

Exam method

Mark both positions. 2. Count the gaps or subtract the coordinates. 3. Make the final distance positive and label the unit if there is one.

Find the distance between $-3$ and 5 on a number line.

Which statement is true?

$|-9|=9$

$|-9|=-9$

Distance from 0 to -9 is -9

$|9|=-9$

A lift moves from floor $-5$ to floor 7. How many floors does it travel?

Complete: The distance from a number to zero is its ______ value.