Question

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

Answer 1

`f=8`

Explanation:

`color(blue)("Method 1")`

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

So by the laws that govern ratio we have:

`(42-:7)/(56-:7)=6/8`

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

`56/42=f/6`

Multiply both sides by 6

`56/42xx6=(fxx6)/6`

`56/42xx6=(fxx6)/6`

`(4xx14)/(3xx14)xx6=fxx6/6`

Note that both `6/6 and 14/14` are the same as 1

`4xx2=f`

`f=8`