# How do you divide (4 sqrt(x^12))/(24 sqrtx^12)?

Mar 12, 2016

1/6

#### Explanation:

Given:$\textcolor{g r e e n}{\text{ } \frac{4 \sqrt{{x}^{12}}}{24 \sqrt{{x}^{12}}}}$

Write this as:

$\textcolor{g r e e n}{\text{ } \frac{4}{24} \times \frac{\sqrt{{x}^{12}}}{\sqrt{{x}^{12}}}}$

$\textcolor{b r o w n}{\text{But "sqrt(x^12)/sqrt(x^12) = 1" giving}}$

$\textcolor{g r e e n}{\text{ } \frac{4}{24} \times 1 = \frac{4}{24}}$

By the properties of ratios, what you do to the top (numerator) you do to the bottom (denominator)

Divide top and bottom by 4

$\textcolor{g r e e n}{\text{ } \frac{4 \div 4}{24 \div 4} = \frac{1}{6}}$