Page 27 - MarceAlgebra Demystified

14 CHAPTER 1 Fractions

5 5
5: þ ¼
24 6

Solutions

1 1 1 1 4 1 4 5
1: þ ¼ þ ¼ þ ¼
8 2 8 2 4 8 8 8

2 5 2 4 5 8 5 3 1
2: ¼ ¼ ¼ ¼
3 12 3 4 12 12 12 12 4

4 1 4 4 1 16 1 17
3: þ ¼ þ ¼ þ ¼
5 20 5 4 20 20 20 20
7 2 7 2 2 7 4 3 1
4: ¼ ¼ ¼ ¼
30 15 30 15 2 30 30 30 10

5 5 5 5 4 5 20 25
5: þ ¼ þ ¼ þ ¼
24 6 24 6 4 24 24 24
9
There are a couple of ways of finding the LCD. Take for example 1 þ .We
12 14
could list the multiples of 12 and 14—the first number that appears on each
list will be the LCD:
12, 24, 36, 48, 60, 72, 84 and 14, 28, 42, 56, 70, 84.
9
Because 84 is the first number on each list, 84 is the LCD for 1 and . This
12 14
method works fine as long as your lists are not too long. But what if your
denominators are 6 and 291? The LCD for these denominators (which is
582) occurs 97th on the list of multiples of 6.
We can use the prime factors of the denominators to find the LCD more
efficiently. The LCD will consist of every prime factor in each denominator
(at its most frequent occurrence). To find the LCD for 1 and 9 factor 12 and
12 14
14 into their prime factorizations: 12 ¼ 2 2 3 and 14 = 2 7. There are two
2s and one 3 in the prime factorization of 12, so the LCD will have two 2s
and one 3. There is one 2 in the prime factorization of 14, but this 2 is
covered by the 2s from 12. There is one 7 in the prime factorization of 14, so
the LCD will also have a 7 as a factor. Once you have computed the LCD,
divide the LCD by each denominator. Multiply each fraction by this number
over itself.
LCD ¼ 2 2 3 7 ¼ 84