Given that #2/3 xx "some fraction"=4/5# determine the 'some fraction': ?

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Answer 1 · 2016-01-16T22:34:08

The other fraction#=6/5#

Let the unknown fraction be #x# then we have:

#color(brown)(2/3 x = 4/5)#

Multiply both sides by #color(blue)(3/2)# giving:

#color(brown)(2/3color(blue)(xx3/2)xx x = 4/5color(blue)(xx3/2))#

#color(white)(..)#

But #color(brown)(2/3)color(blue)(xx3/2)=6/6=1# giving:

#x=4/5xx3/2 #

#= 12/10#

#=6/5#

The other fraction#=x=6/5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check: #2/3xx6/5->4/5# Confirmed as correct.

Answer 2 · 2016-01-16T22:57:23

The same thing but it looks different.

The other fraction is #6/5#

Given: #2/3 xx "some fraction"=4/5#

#"some fraction" = 4/5 -: 2/3#

Standard shortcut instruction is to turn #2/3# up the other way and multiply.

#"some fraction" = 4/5 xx 3/2 #

#= (4xx3)/(5xx2) = 12/10#

Divide top and bottom by 2 giving:

#(12 -:2)/(10-:2)= 6/5#

So the other fraction is #6/5#