How do you solve $\frac{42}{56} = \frac{6}{f}$ $42/56=6/f$ ?

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How do you solve $\frac{42}{56} = \frac{6}{f}$ $42/56=6/f$ ?

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Answer 1 · 2017-05-01T21:50:04

$f = 8$ $f=8$

Explanation:

$Method 1$ $color(blue)("Method 1")$

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

So by the laws that govern ratio we have:

$\frac{42 \div 7}{56 \div 7} = \frac{6}{8}$ $(42-:7)/(56-:7)=6/8$

Thus $f = 8$ $f=8$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Method 2$ $color(blue)("Method 2")$
You can do this! Turn everything upside down so that the $f$ $f$ in a numerator (on top)

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

Multiply both sides by 6

$\frac{56}{42} \times 6 = \frac{f \times 6}{6}$ $56/42xx6=(fxx6)/6$

$\frac{4 \times 14}{3 \times 14} \times 6 = f \times \frac{6}{6}$ $(4xx14)/(3xx14)xx6=fxx6/6$

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

$4 \times 2 = f$ $4xx2=f$

$f = 8$ $f=8$

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How do you solve $\frac{42}{56} = \frac{6}{f}$ $42/56=6/f$ ?

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How do you solve $\frac{42}{56} = \frac{6}{f}$ $42/56=6/f$ ?