Algebra 1 Common Core Student Edition, Grade 8-9

Ratios, Rates, and

Conversions

Common Core State Standards

N-Q.A.1 Use units as a w ay to understand problems

and to guide the solution o f m ulti-step problems; choose

and interpret units consistently in fo rm u la s... Also

N-Q.A.2

MP 2, MP 3, MP 4, MP 5, MP 6

Objectives To find ratios an d rates

To convert units an d rates

Whoa—we're

comparing times

and distances. W hy

is i t im p o rta n t to

be precise with th e

units?

Lesson

Vocabulary

ratio

rate

unit rate

conversion fact o r

unit analysis

MATHEMATICAL

PRACTICES A ratio com pares two n u m b ers by division. The ratio of two n u m b ers a and b, w here

b i= 0, can be w ritten in th ree ways: |, a: b, and a to b. For every a u nits of one

quantity, you have b u n its of a n o th e r q uantity.

You can also th in k of a ratio as a m ultiplicative relationship. For example, if the ratio of

the n u m b e r of boys to the n u m b e r of girls in a class is 2 : 1 , th e n th e n u m b e r of boys is

two times the n u m b e r of girls.

A ratio that com pares quantities m easured in different units is called a rate. A rate with a

denom inator of 1 unit is a unit rate. In the Solve It, you can express each athlete's speed as

the num ber of m eters traveled per 1 second of time. This is an example of a unit rate.

Essent ial Und er st and ing You can write ratios an d find u n it rates to com pare

quantities. You can also convert units an d rates to solve problem s.

How can estimation

help you?

Use e stim atio n to solve a

simpler problem. You can

use th e given in fo rm a tio n

to estim ate th e u n it rates.

The estim ates can help

you find the solution.

Problem 1 Comparing Unit Rates

Shopping You are shopping for T-shirts. Which store offers the best deal?

Store A: $25 for 2 shirts Store B: $45 for 4 shirts Store C: $30 for 3 shirts

W rite each price as a ratio. Then write the ratio as a u nit rate to com pare.

Store A Store B Store C

$25 _ $12.50 $45 _ $11.25 $30 _ $10

2 sh irts 1 sh irt 4 shirts 1 shirt 3 sh irts 1 sh irt

Store C has

th e best deal

because its

unit rate is

the lowest.

116 Chapter 2 So l v i n g Eq u a t i o n s