Chapter 5: Fractions 65Suppose you want to subtract^13227. In order to do this operation, you need to make the denomina-
tors of the two fractions match. First, find the lowest common multiple of the two denominators.
The lowest common multiple of 3 and 7 is 21. Multiply
1
3
7
7(^3) and^2
7
3
3
(^3) to change them to fractions
with the same value but a different look.
Then you are able to subtract.
Sometimes you’ll look at two denominators and know quickly what number can serve as a
common denominator, but if the numbers are large, you may need more of a game plan. To find
the lowest common denominator, take a moment first to factor each denominator.
Suppose you need to add
7
30
5
42
(^1). You look at 30 and 42 and don’t see a common denominator
immediately. Think about the factors of each denominator. 30 = 2 v 3 v 5 and 42 = 2 v 3 v 7.
Both denominators have factors of 2 and 3, but 30 also has a factor of 5. 42 has a factor of 7. The
lowest common denominator will be the product of the 2 and 3 they have in common and the 5
and 7 they don’t.
LCD = 2 v 3 v 5 v 7 = 210
Multiply 307477 , because 30 doesn’t have the factor of 7, and 425355 , because 42 doesn’t have the
factor of 5. Give each fraction what it’s missing, then add and simplify.
WORLDLY WISDOM
It is not always necessary to have the lowest common denominator. Sometimes you
simply want to add or subtract the fractions as quickly as possible. You can fall back
on this strategy. Multiply the two denominators for a common denominator. Multiply
the lower right denominator times the upper left numerator and put the result in the
upper left numerator’s position. Multiply the lower left denominator by the upper
right numerator and put the result in the upper right numerator’s position. Add or
subtract the numerators and simplify if necessary.
You can handle mixed numbers in addition and subtraction by changing them to improper
fractions, as you did in multiplication, but you don’t always have to. In addition, you can just
combine the fractions and add the whole numbers on to that sum at the end.^4
3
5
25
8
(^1) is really
4 3
5
2 5
8
(^111) , so you can rearrange to^3
5
5
8
(^11142).
1
3
2
7
7
21
6
21
1
21
25 2 5
49
210
25
210
74
210
37
105
155