Absolute Value

The absolute value of a number is how far it is from zero, written |−5| = 5.

Absolute value is the distance of a number from zero, ignoring direction.

Never negative

Distance cannot be negative, so an absolute value is never below zero.

Size is not order

−9 has a bigger absolute value than −4, but −9 is the smaller number.

Where it matters

A debt of 200 is bigger than a debt of 50, even though −200 is the smaller number.

Distance, with the direction thrown away

The absolute value of a number is its distance from zero on the number line. |−7| = 7 and |7| = 7. Distance has no direction, so absolute value is never negative — which is the whole point of the idea.

The notation

Two vertical bars mean absolute value: |−7|. It is not brackets and does not mean multiplication. Read it as "the absolute value of negative seven" or "the distance of negative seven from zero".

Absolute value and size are different questions

−7 is less than −3, but |−7| is greater than |−3|. Asking which number is smaller and asking which is further from zero give opposite answers here. Read the question carefully — this distinction is exactly what such questions test.

Where it is used

A bank cares whether you are £50 overdrawn — the size of the debt — separately from the fact that it is a debt. A thermometer reading 7 degrees from freezing could be either side. Absolute value is how you talk about magnitude alone.