Page 377 - Basic College Mathematics with Early Integers

Objectives 5.1 RATIOS

Write Ratios as Fractions.

Write Rates as Fractions. Objective Writing Ratios as Fractions
Find Unit Rates. A ratio is the quotient of two quantities. A ratio, in fact, is no different from a frac-
tion, except that a ratio is sometimes written using notation other than fractional
Find Unit Prices. notation. For example, the ratio of 1 to 2 can be written as

1
1 to 2 or or 1 : 2
2
;
;
fractional notation colon notation
These ratios are all read as,“the ratio of 1 to 2.”
Concept Check How should each ratio be read aloud?
8 5
a. b.
5 8
In this section, we write ratios using fractional notation. If the fraction happens
to be an improper fraction, do not write the fraction as a mixed number. Why? The
mixed number form is not a ratio or quotient of two quantities.

Writing a Ratio as a Fraction
The order of the quantities is important when writing ratios.To write a ratio as a
fraction, write the first number of the ratio as the numerator of the fraction and
the second number as the denominator.

6 11
For example, the ratio of 6 to 11 is , not .
11 6

PRACTICE 1 Example 1 Write the ratio of 12 to 17 using fractional notation.
Write the ratio of 20 to 23 using 12
fractional notation. Solution: The ratio is .
17
Don’t forget that order is
important when writing ratios.The ratio
17 12
is not the same as the ratio .
12 17
Work Practice 1

To simplify a ratio, we just write the fraction in simplest form. Common factors
as well as common units can be divided out.

PRACTICE 2 Example 2 Write the ratio of $15 to $10 as a fraction in simplest form.
Write the ratio of $8 to $6 as a
fraction in simplest form. Solution:
1
Answers #
$15 15 3 5 3
20 4 = = =
1. 2. $10 10 2 # 5 2 Copyright 2012 Pearson Education, Inc.
23 3 1
Concept Check Answers Work Practice 2
a. “eight to five” b. “five to eight”
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