Basic Math and Pre-Algebra For Dummies (52 page)

Subtracting mixed numbers when the denominators are different is just about the hairiest thing you're ever going to have to do in pre-algebra. Fortunately, though, if you work through this chapter, you acquire all the skills you need.

Suppose you want to subtract
. Because the denominators are different, subtracting the fractions becomes more difficult. But you have another question to think about: In this problem, do you need to borrow? If
is greater than
, you don't have to borrow. But if
is less than
, you do. (For more on borrowing in mixed-number subtraction, see the preceding section.)

In Chapter
9
, I show you how to test two fractions to see which is greater by cross-multiplying:

Because 28 is less than 33,
is less than
, so you do have to borrow. I get the borrowing out of the way first:

Now the problem looks like this:

The first step, subtracting the fractions, is the most time-consuming, so as I show you earlier in “Subtracting fractions with different denominators,” you can take care of that on the side:

The good news is that this fraction can't be reduced (72 and 77 have no common factors:
and
). So the hard part of the problem is done, and the rest follows easily: