Subtracting Absolute Value
Absolute value is a way to measure how far a number is from zero on the number line. Because absolute value measures distance, and not direction, all absolute values are positive. Absolute value is written with the symbols | | either side of the number.
+3 is 3 units away from 0 on the number line, so:
-3 is also 3 units away from 0 on the number line, so:
As a quick way to remember how to do absolute values, for positive numbers, the absolute value is the same. For negative numbers, simply remove the negative sign.
To subtract absolute values, you will need to first calculate the absolute values in the problem.
Take the following problem:
To solve this, we use order of operations to first calculate what the absolute value of each of the figures.
10 has a distance of 10 units from 0 and therefore has an absolute value of 10. For positive numbers, the absolute value is the same as the regular value.
-8 is 8 units away from 0, and therefore has an absolute value of 8. For negative numbers, you can quickly calculate the absolute value by removing the negative sign.
The problem is now a simple subtraction question. 10 – 8 is 2, so this is the answer.
Using absolute values in calculations requires you to solve the absolute values first, before proceeding on with the numbers as normal.