Page 236 - Basic College Mathematics with Early Integers

S E C T I O N 3.4 I ADDING AND SUBTRACTING LIKE FRACTIONS, LEAST COMMON DENOMINATOR 213

If you prefer
If the number of factors of a prime number is equal, circle either one, but not working with exponents,
both. For example, circle the factor with the
# #
12=2 2 3 greatest exponent.
#
15=3 5 Circle either 3 Example 14:
but not both. 3 #
72=2 3 2
2 # #
# # #
The LCD is 2 2 3 5 = 60. 60=2 3 5
2
LCD = 2 3 # # 5 = 360
3
1 5 53
Example 15 Find the LCD of , , and .
15 18 54 PRACTICE 15
#
Solution: 15=3 5 7 1 13
# #
18=2 3 3 Find the LCD of 20 , 24 , and 45 .
# # #
54=2 3 3 3
# # # #
The LCD is 2 3 3 3 5 or 270.
Work Practice 15

1 1
Concept Check True or false? The LCD of the fractions and is 48.
6 8

Objective Writing Equivalent Fractions
To add or subtract unlike fractions in the next section, we first write equivalent frac-
tions with the LCD as the denominator.
1
To write as an equivalent fraction with a denominator of 6, we multiply by 1
3
2
#
in the form of . Why? Because 3 2 = 6 , so the new denominator will become 6, as
2
shown below.
#
1 1 # 1 # 2 1 2 2
= 1= = # =
3 3 3 2 3 2 6

2 =1
2
1 2
So = .
3 6

To write an equivalent fraction,
#
a = a # c = a c
#
b b c b c

where a, b, and c are nonzero numbers.

Answer
3 15. 360
Concept Check Which of the following is not equivalent to ?
4
Concept Check Answers
6 18 9 30 false; it is 24
a. b. c. d.
8 24 14 40 c