We can think of 6 divided by 3/4 as how many 3/4’s are in 6?

It means you divide with .

When you divide a fraction, you reciprocate it meaning divide it by or switch the numerator and the denominator. The reciprocated one will be:

Multiply 6 with 4/3 and you get:

goes times in :D

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4