Basic Mathematics for College Students

418 Chapter 5 Ratio, Proportion, and Measurement

Self Check 6

Write the ratio6 feet to 3 yardsas

a fraction in simplest form. (Hint:

3 feet1 yard.)

Now TryProblem 41

EXAMPLE 5

Write the ratio to as a fraction in simplest form.

StrategyAfter writing the ratio as a fraction, we will use the method for

simplifying a complex fraction from Section 3.7 to obtain an equivalent ratio of

whole numbers.

WHYA ratio of whole numbers is easier to understand than a ratio of mixed

numbers.

Solution

The ratio of to can be written as.

The resulting ratio is a complex fraction. To write the ratio in simplest form, we

perform the division indicated by the main fraction bar (shown in red).

Write and as improper fractions.

Use the rule for dividing fractions: Multiply the first

fraction by the reciprocal of , which is.

We would normally simplify the result and write it as 4. But since a ratio compares

two numbers, we leave the result in fractional form.

4

1

Multiply the remaining factors in the numerator.

 (^) Multiply the remaining factors in the denominator.

4

1

To simplify the fraction, factor 14 as 27 and 6 as 23.

 (^) Then remove the common factors 3 and 7.

2  7

1

 2  3

1

3

1

 7

1

Multiply the numerators.

 (^) Multiply the denominators.

14  6

3  7

67 67



14

3



6

7

Write the division indicated by the main

 (^) fraction bar using a symbol.

14

3



7

6

4 23 1 61

4

2

3

1

1

6



14

3

7

6



4

2

3

1

1

6

1

1

6

4

2

3



1

1

6

4

2

3

Self Check 5

Write the ratio to as a

fraction in simplest form.

Now TryProblem 37

(^3 131 19)
Convert units to write ratios.
When a ratio compares 2 quantities, both quantities must be measured in the same
units. For example, inches must be compared to inches, pounds to pounds, and seconds
to seconds.
3
EXAMPLE (^6) Write the ratio 12 ounces to 2 poundsas a fraction in simplest
form.
StrategyWe will convert 2 pounds to ounces and write a ratio that compares
ounces to ounces. Then we will simplify the ratio.
WHYA ratio compares two quantities that have the sameunits. When the units
are different, it’s usually easier to write the ratio using the smaller unit of
measurement. Since ounces are smaller than pounds, we will compare in ounces.