Multiplying Absolute Value
Absolute value in Math is a way that we can measure how far a number is from 0, without taking into account the direction (whether the number is positive or negative). We denote absolute value by using the symbols | | either side of the number. The absolute value of x is written as | x |.
To find the absolute value of a positive number is simple because the values are the same. The number 7 is 7 units away from 0 on the number line, so:
To find the absolute value of a negative number you count how far it is from 0 in units. Another way to do this is just to remove the negative sign. –7 is 7 units away from 0 on the number line, so:
In order to multiply an absolute value, you need to first work out the absolute terms. Take the following example:
In order to solve this, we first need to work out the absolute values of the figures.
The absolute value of 6 is the distance of 6 from 0. 6 is 6 units away from 0. For positive numbers, their absolute value is the same as their non-absolute value, so we can keep that the same:
Next, we need to find the absolute value of | -3 |. -3 is 3 units distant from 0, and therefore has an absolute value of 3. For negative numbers, a quick way to calculate the absolute value is to just remove the negative sign.
That leaves a regular multiplication problem. 6 x 3 is 18, and so the answer is:
The trick with absolute value is to solve the absolute value first in the order of operations, before completing the rest of the problem.