Question

Which numbers would you multiply -3/4 by to equal 1 ?

Answer 1

A negative times a negative gives us a positive value right?
So we know the number will need to be negative, since we're starting with a negative fraction and want to end up with POSITIVE 1.

Look at an easy example really quick:
If we had the number 3 and we wanted to change it to the number 1,
we would divide by 3.\[\large \frac{3}{3}\]Another way to think of this is multiplying by the RECIPROCAL of 3.\[\large 3\left(\frac{1}{3}\right)\]See how 1/3 is the same as \(\dfrac{3}{1}\) but flipped?

We can apply the same idea to our problem here.

To change -3/4 to 1, we divide by the same number.\[\huge \frac{-\frac{3}{4}}{-\frac{3}{4}}\]But as we showed with the example, this is the same as multiplying by the RECIPROCAL of the number we started with.\[\large -\frac{3}{4}\left(-\frac{4}{3}\right)\]

Answer 2

If that's too confusing, let me simplify it down a little :)

\(-\dfrac{3}{4}\)
We can multiply it by 4 first,\[-\frac{3}{\cancel4}\cancel4\]Then multiplying it by -1/3,\[\large -3\left(-\frac{1}{3}\right)\]

Answer 3

Whichever way makes more sense to you c: