Basic Mathematics for College Students

480 Chapter 5 Summary and Review

To write a ratio in simplest form,remove any

common factors of the numerator and

denominator as well as any common units.

Write the ratio 14 feet: 2 feetas a fraction in simplest form.

A colon separates the quantities to be compared.

Since a ratio compares two numbers, we leave the

 result in fractional form. Do not simplify further.

7

1

To simplify, factor 14. Then remove the common

factor of 2 and the common units of feet from

the numerator and denominator.

14 feet

2 feet



2

1

7 feet

2

1

feet

To simplify ratios involving decimals,multiply

the ratio by a form of 1 so that the numerator

and denominator become whole numbers.

Then simplify, if possible.

Write the ratio 0.23 to 0.71 as a fraction in simplest form.

To write this as a ratio ofwhole numbers,we need to move the decimal

points in the numerator and denominator two places to the right. This

will occur if they are both multiplied by 100.

1

Multiply the ratio by a form of 1.

To find the product of each decimal and 100, simply

move the decimal point two places to the right.

The resulting fraction is in simplest form.



23

71

Multiply the numerators.

 Multiply the denominators.

0.23 100

0.71 100



100

100

0.23

0.71



0.23

0.71

To simplify ratios involving mixed numbers,use

the method for simplifying complex fractions

from Section 3.7. Perform the division

indicated by the main fraction bar.

Write the ratio to as a fraction in simplest form.

Write and and as improper fractions.

Use the rule for dividing fractions: Multiply the

first fraction by the reciprocal of , which is.

Multiply the remaining factors in the numerator.

 Multiply the remaining factors in the denominator.

4

5

To simplify the fraction, factor 10, 6, and 25.

Then remove the common factors 3 and 5.



2  5

1

 2  3

1

3

1

 5

1

 5

Multiply the numerators.

Multiply the denominators.



10  6

3  25

6

25

25

6



10

3



6

25

Write the division indicated by the main

 fraction bar using a symbol.

10

3



25

6

3 31 4 61

3

1

3

4

1

6



10

3

25

6

4

1

6

3

1

3

When a ratio compares two quantities, both

quantities must be measured in the same units.

When the units are different, it’s usually easier

to write the ratio using the smaller unit of

measurement.

Write the ratio 5 inches to 2 feetas a fraction in simplest form.

Since inches are smaller than feet, compare in inches:

5 inchesto 24 inches Because 2 feet 24 inches.

Next, write the ratio in fraction form and simplify.

Remove the common units of inches.

5 inches

24 inches



5

24