Page 287 - Basic College Mathematics with Early Integers

264 C HAPTE R 3 I FRACTIONS

Definitions and Concepts Examples
Section 3.6 Complex Fractions, Order of Operations, and Mixed Numbers

A fraction whose numerator or denominator or both Complex Fractions:
contain fractions is called a complex fraction.
11 1
- 11
4 6
,
7 4
10 3
One method for simplifying complex fractions is to 1 1 1
multiply the numerator and the denominator of the 6 - 11 6a 6 - 11b 6a b - 6(11)
6
complex fraction by the LCD of all fractions in its 4 = 4 = 4
numerator and its denominator. 6a b 6a b
3 3 3
1 - 66 -65 65
= = =-
8 8 8

TO WRITE A MIXED NUMBER AS AN IMPROPER FRACTION ƒ
#
2 7 5 + 2 35 + 2 37
1. Multiply the denominator of the fraction by the whole ƒ 5 = = =
number. 7 7 7 7
2. Add the numerator of the fraction to the product
from Step 1.
3. Write this sum from Step 2 as the numerator of the
improper fraction over the original denominator.
TO WRITE AN IMPROPER FRACTION AS A MIXED NUMBER
OR A WHOLE NUMBER 17 2
= 5
1. Divide the denominator into the numerator. 3 3
2. The whole number part of the mixed number is the
5
quotient.The fraction is the remainder over the
317
original denominator.
15
remainder
quotient 2
original denominator
Section 3.7 Operations on Mixed Numbers

#
To multiply with mixed numbers or whole numbers, first 1 1 7 1 7 1 7
2 # = # = =
write any mixed or whole numbers as improper fractions 3 9 3 9 3 9 27
#
and then multiply as usual.
#
5 7 21 55 21 16 21 16
To divide with mixed numbers or whole numbers, first 2 , 3 = , = # =
#
8 16 8 16 8 55 8 55
write any mixed or whole numbers as fractions and then
1
# #
divide as usual. 21 2 8 42
= =
#
8 55 55
1
1 7
To add or subtract with mixed numbers, add or subtract Add: 2 + 5
2 8
the fractions and then add or subtract the whole
numbers. 1 4
2 = 2
2 8
7 7 Copyright 2012 Pearson Education, Inc.
+ 5 = 5
8 8
11 3 3
7 = 7 + 1 = 8
8 8 8