Fractions and mixed numbers

Q:  Solve for k:

k / 9 1/8(mixed number) = 20/73

A:  So we have 9 and 1/8 as a mixed number… Kind of hard to write clearly on this blog, but basically:

k / “9 and 1/8” = 20 / 73

I don’t like mixed numbers and neither should you.  We will get rid of them at all costs…

9 and 1 / 8 = 72/8 and 1/8 = 73/8

So, now we have

k / (73/8) = 20/73

Now, we also know that dividing by a fraction is the same as multiplying by its reciprocal:

(k/1) / (73/8) = 20/73

(k/1) * (8/73) = 20/73

Simplified:

(8/73)*k = 20/73

Now, I want to get k by itself… So, to cancel that 8/73, I will multiply everything by 73/8:

(73/8) * (8 / 73) * k = (73 / 8) * (20/ 73)

Now, cancel things out and reduce:

(73/8) * (8 / 73) * k = (73 / 8) * (20/ 73)

k = 8/20

k = 2/5