Basic Mathematics for College Students

Chapter 5 Summary and Review 479

CHAPTER 5 SUMMARY AND REVIEW

SECTION 5.1 Ratios and Rates

Ratiosare often used to describe important

relationships between two quantities.

A ratiois the quotient of two numbers or the

quotient of two quantities that have the same

units.

Ratios are written in three ways: as fractions, in

words separated by the word to, and using a

colon.

DEFINITIONS AND CONCEPTS EXAMPLES

The ratio 4 to5 can be written as.

The ratio 5 :12 can be written as.



5

12





4

5



STUDY SKILLS CHECKLIST

Propor tions and Unit Conversion Factors

Before taking the test on Chapter 5, make sure that you have a solid understanding of how to

write proportions and how to choose unit conversion factors. Put a checkmark in the box if you

can answer “yes” to the statement.

When converting from one unit to another, I know

that I must choose a unit conversion factor with

the following form:

For example, in the following conversion of 15

pints to cups, the units of pints are eliminated and

the units of cups are introduced by choosing the

unit conversion factor.

15 pt

15 pt

1



2 c

1 pt

30 c

2 c

1 pt

Unit I want to introduce

Unit I want to eliminate

To write a ratio as a fraction,write the first

number (or quantity) mentioned as the

numerator and the second number (or

quantity) mentioned as the denominator. Then

simplify the fraction, if possible.

Write the ratio 30 to 36 as a fraction in simplest form.

The word toseparates the numbers to be compared.



5

6

To simplify, factor 30 and 36. Then remove the common

factor of 6 from the numerator and denominator.

30

36



5  6

1

6

1

 6

When writing a proportion, I know that the units of

the numerators must be the same and the units of

the denominators must be the same.

This proportion is correctly written:



This proportion is incorrectly written:



Cost

 Ounces

2.75

3

50

x

Ounces 

Cost

Ounces

 Cost

3 

2.75

150

x

Ounces 

Cost