• Home

Simplifying Absolute Value Expressions

The absolute value of a product is the same as the product of the absolute values . For instance:

$\left|\left(9\right)\left(-3\right)\right|=\left|9\right|\left|-3\right|=\left(9\right)\left(3\right)=27$

$\left|\left(-11\right)\left(-10\right)\right|=\left|-11\right|\left|-10\right|=\left(11\right)\left(10\right)=110$

$\left|x^{3}y\right|=\left|x^3\right|\left|y\right|$

The same goes for quotients .

$\left|\frac{(10)}{(-5)}\right|=\frac{\left|10\right|}{\left|-5\right|}=\frac{10}{5}=2$

However, the same thing doesn't always work for addition and subtraction!

$\left|-3+7\right|=\left|4\right|=4,$ but

$\left|-3\right|+\left|7\right|=3+7=10$

So be careful!