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

1 Answer
Tony B
May 1, 2017

#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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#

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