# How do you solve 42/56=6/f?

May 1, 2017

$f = 8$

#### Explanation:

$\textcolor{b l u e}{\text{Method 1}}$

You spot that 7 is a factor of both 42 and 56. You also spot that
$42 \div 7 = 6$

So by the laws that govern ratio we have:

$\frac{42 \div 7}{56 \div 7} = \frac{6}{8}$

Thus $f = 8$
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$\textcolor{b l u e}{\text{Method 2}}$
You can do this! Turn everything upside down so that the $f$ in a numerator (on top)

$\frac{56}{42} = \frac{f}{6}$

Multiply both sides by 6

$\frac{56}{42} \times 6 = \frac{f \times 6}{6}$

$\frac{56}{42} \times 6 = \frac{f \times 6}{6}$

$\frac{4 \times 14}{3 \times 14} \times 6 = f \times \frac{6}{6}$

Note that both $\frac{6}{6} \mathmr{and} \frac{14}{14}$ are the same as 1

$4 \times 2 = f$

$f = 8$