Page 286 - Basic College Mathematics with Early Integers

CHAPTER HIGHLIGHTS 263

Definitions and Concepts Examples

Section 3.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions

Fractions that have the same denominator are called 1 2 5 6
- and ; and
like fractions. 3 3 7 7
To add or subtract like fractions, combine the numerators
2 3 5 ; Add the numerators.
and place the sum or difference over the common + = Keep the common denominator
7 7 7 ;
denominator.
7 4 3 ; Subtract the numerators.
- = Keep the common denominator
8 8 8 ;
1 5
The least common denominator (LCD) of a list of The LCD of and is 6 because 6 is the smallest
fractions is the smallest positive number divisible by all 2 6
positive number that is divisible by both 2 and 6.
the denominators in the list.
1 5
METHOD 1 FOR FINDING THE LCD OF A LIST OF FRACTIONS Find the LCD of and using Method 1.
USING MULTIPLES 4 6
Step 1: Write the multiples of the largest denominator 6 1 = 6 Not a multiple of 4
#
(starting with the number itself) until a multiple #
6 2 = 12 A multiple of 4
common to all denominators in the list is found.
Step 2: The multiple found in Step 1 is the LCD. The LCD is 12.
5 11
METHOD 2 FOR FINDING THE LCD OF A LIST OF FRACTIONS Find the LCD of and using Method 2.
USING PRIME FACTORIZATION 6 20
#
Step 1: Write the prime factorization of each denominator. 6=2 3
# #
Step 2: For each different prime factor in Step 1, circle 20=2 2 5
the greatest number of times that factor occurs in
any one factorization. The LCD is
Step 3: The LCD is the product of the circled factors. 2 2 3 5 = 60
# # #
Equivalent fractions represent the same portion of a Write an equivalent fraction with the indicated
whole. denominator.
2
=
8 16
#
2 2 4
#
8 2 = 16
Section 3.5 Adding and Subtracting Unlike Fractions

TO ADD OR SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS 3 2
Add: +
20 5
Step 1: Find the LCD. Step 1: The LCD of the denominators 20 and 5 is 20.
3 3 2 2 # 4 8
Step 2: Write each fraction as an equivalent fraction Step 2: 20 = 20 ; 5 = 5 4 = 20
whose denominator is the LCD.
3 2 3 8 11
Step 3: Add or subtract the like fractions. Step 3: + = + =
20 5 20 20 20
11
Step 4: Write the sum or difference in simplest form. Step 4: is in simplest form.
20