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Fractions in fractions (with variables!)

Q:  Solve for f:

(4/12) / f = 10/21

A:  OK… On the left-side we have 4/12 DIVIDED by f!  A fraction inside of a fraction.  This is the same thing as 4/12 divided by f/1 right?  Like so:

(4/12) / (f/1) = 10/21

So, dividing by a fraction is the same as multiply by the reciprocal… This means that 4/12 DIVIDED by f/1 is the same as 4/12 TIMES 1/f :

(4/12) * (1/f) = 10/21

Now, multiply across the top and across the bottom:

4/(12f) = 10/21

Now we can cross-multiply:

4 * 21 = 12f * 10

84 = 120*f

Divide both sides by 120:

84/120 = f

Now reduce your fraction:

7/10 = f

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