Absolute Value

Liam lives two miles east of the school, and Oliver lives two miles west. Despite opposite directions, both are exactly two miles away. This idea of distance without direction is absolute value.

On a number line, absolute value is a number's distance from zero. We write it using vertical bars.

Since distance can’t be negative, the absolute value is always 0 or positive.

For any real numbers a and b, the absolute value of the product equals the product of their individual absolute values. The same applies to the quotient.

For example, four times negative five is negative twenty, whose absolute value is twenty. This is the same as multiplying the individual absolute values of four and negative five.

The absolute value of a sum or difference is less than or equal to the sum of the individual absolute values of a and b.

For example, four plus negative five is negative one, whose absolute value is one, less than nine, the sum of their individual absolute values. Similarly, four minus negative five is nine, whose absolute value equals the sum of their individual absolute values.