# How do you simplify (2/15)(25/49)(-63/72)?

Feb 5, 2018

$- \frac{5}{84}$

#### Explanation:

$\text{note that "-63/72" can be simplified}$

$\text{by "color(blue)"cancelling "" numerator/denominator by 9}$

$\Rightarrow - \frac{63}{72} = - {\cancel{63}}^{7} / {\cancel{72}}^{8} = - \frac{7}{8}$

$\text{thus the calculation becomes}$

$\frac{2}{15} \times \frac{25}{49} \times - \frac{7}{8}$

$\text{simplify further by cancelling 2/8, 15/25 and 7/49}$

${\cancel{2}}^{1} / {\cancel{15}}^{3} \times {\cancel{25}}^{5} / {\cancel{49}}^{7} \times - {\cancel{7}}^{1} / {\cancel{8}}^{4}$

$\text{multiply the remaining values on the }$
$\text{numerator/denominator}$

$= \frac{1 \times 5 \times - 1}{3 \times 7 \times 4} = - \frac{5}{84}$

Feb 5, 2018

$- \frac{5}{84}$

#### Explanation:

Start by cancelling with any common factors in the numerators and denominators.

$\frac{2}{15} \times \frac{25}{49} \times - \frac{63}{72}$

$\div 5 \left(15 \mathmr{and} 25\right) \mathmr{and} \div 7 \left(49 \mathmr{and} 63\right)$

$= - \frac{2}{\cancel{15}} ^ 3 \times {\cancel{25}}^{5} / {\cancel{49}}^{7} \times {\cancel{63}}^{9} / 72$

$= - \frac{\cancel{2}}{3} \times \frac{5}{7} \times \frac{\cancel{9}}{{\cancel{72}}^{{\cancel{8}}^{4}}}$

$\div 9 \left(9 \mathmr{and} 72\right) \mathmr{and} \div 2 \left(2 \mathmr{and} 8\right)$

$= \frac{5}{3 \times 7 \times 4}$

$= - \frac{5}{84}$

There are different ways of cancelling. The order is not important.

This is easier than multiplying all the tops together and all the bottoms together and then trying to simplify.