Page 26 - MarceAlgebra Demystified

CHAPTER 1 Fractions 13

1 7 1 8 7 3 8 21 29
2: þ ¼ þ ¼ þ ¼
3 8 3 8 8 3 24 24 24

5 1 5 9 1 7 45 7 38
3: ¼ ¼ ¼
7 9 7 9 9 7 63 63 63

3 1 3 2 1 14 6 14 20 5
4: þ ¼ þ ¼ þ ¼ ¼
14 2 14 2 2 14 28 28 28 7
3 11 3 18 11 4 54 44 98 49
5: þ ¼ þ ¼ þ ¼ ¼
4 18 4 18 18 4 72 72 72 36

Our goal is to add/subtract two fractions with the same denominator. In the
previous examples and practice problems, we found a common denominator.
Now we will find the least common denominator (LCD). For example in
1 þ , we could compute
1
3 6
1 1 1 6 1 3 6 3 9 1
þ ¼ þ ¼ þ ¼ ¼ :
3 6 3 6 6 3 18 18 18 2
1
But we really only need to rewrite :
3
1 1 1 2 1 2 1 3 1
þ ¼ þ ¼ þ ¼ ¼ :
3 6 3 2 6 6 6 6 2
While 18 is a common denominator in the above example, 6 is the smallest
common denominator. When denominators get more complicated, either by
being large or having variables in them, you will find it easier to use the LCD
to add or subtract fractions. The solution might require less reducing, too.
In the following practice problems one of the denominators will be the
LCD; you only need to rewrite the other.

Practice

1 1
1: þ ¼
8 2
2 5
2: ¼
3 12
4 1
3: þ ¼
5 20

7 2
4: ¼
30 15