# How do you solve 40/56=k/7?

Jan 21, 2017

$k = 5$

#### Explanation:

To eliminate the fractions, multiply both sides of the equation by the $\textcolor{b l u e}{\text{lowest common multiple }} \left(L C M\right)$ of 56 and 7

multiply both sides by 56

${\cancel{56}}^{1} \times \frac{40}{\cancel{56}} ^ 1 = {\cancel{56}}^{8} \times \frac{k}{\cancel{7}} ^ 1$

$\Rightarrow 40 = 8 k$

To solve for k, divide both sides by 8

$\frac{40}{8} = \frac{\cancel{8} k}{\cancel{8}}$

$\Rightarrow k = 5 \text{ is the solution}$

$\textcolor{b l u e}{\text{Note}}$ the fraction on the left side can be simplified by dividing the numerator/denominator by 8

$\frac{40}{56} = \frac{k}{7}$

$\Rightarrow {\cancel{40}}^{5} / {\cancel{56}}^{7} = \frac{k}{7}$

Since the fractions are equal then k = 5