Page 260 - Basic College Mathematics with Early Integers

S E C T I O N 3.6 I COMPLEX FRACTIONS, ORDER OF OPERATIONS, AND MIXED NUMBERS 237

Objective Writing Mixed Numbers as Improper Fractions

In Section 3.1, mixed numbers and improper fractions were both used to represent
the shaded part of figure groups. For example,

s
1

1s or f Thus, 1s f .

f

The following steps may be used to write a mixed number as an improper
fraction:

Writing a Mixed Number as an Improper Fraction

To write a mixed number as an improper fraction:
Step 1: Multiply the denominator of the fraction by the whole number.

Step 2: Add the numerator of the fraction to the product from Step 1.
Step 3: Write the sum from Step 2 as the numerator of the improper fraction
over the original denominator.

For example,
Step 1 Step 2
p p
v v
#
2 3 1 + 2 3 + 2 5 2 5
1 = = = or 1 = , as stated above.
3 3 3 3 3
Step 3
3 p
Example 8 Write each as an improper fraction. PRACTICE 8

#
#
2 9 4 + 2 36 + 2 38 8 11 1 + 8 11 + 8 19 Write each as an improper
a. 4 = = = b. 1 = = = fraction.
9 9 9 9 11 11 11 11
2 2 9 1
a. 5 b. 6 c. 10 d. 4
Work Practice 8 7 3 10 5

Objective Writing Improper Fractions as Mixed Numbers or
Whole Numbers

Just as there are times when an improper fraction is preferred, sometimes a mixed
or a whole number better suits a situation. To write improper fractions as mixed or
whole numbers, we use division. Recall once again from Section 1.7 that the fraction
bar means division.This means that the fraction

5 numerator means 35
3 denominator c
æ numerator
denominator

Answers
37 20 109 21
8. a. b. c. d.
7 3 10 5