Ratios and Unit Rates

Lesson 6-1 & 6-2

Ratios

• A ratio is a comparison between two numbers by division.

• It can be written in three different ways:

5 to 25 : 2 5

2

Equal Ratios

• When two ratios name the same number, they are equal. It’s like writing an equivalent fraction.

20 : 30Equal Ratios:

10 : 15 2 : 3 80 : 120

Ratios in Simplest Form

• Ratios can be written in simplest form.• Divide both terms in the ratio by their

GCF.

Example: 12 to 8

3 to 2

Vocabulary

• A rate is a ratio that compares two quantities measured in different units.

• The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.

Vocabulary

• A rate is a ratio that compares two quantities measured in different units.

• The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.

ExamplesRate: 150 heartbeats

2 minutes

Unit Rate (Divide to get it):

150 ÷ 2 = 75 heartbeats per minute.

Find the Unit RateAmy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?)

88 pages4 hours

22 pages / hour

Using Unit Rates

• You can find the missing terms of equal ratios.

• Use the unit rate, and set it equal to another ratio.

• Solve for what is missing by dividing or multiplying.

ExampleJoe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline?

25 miles1 gallon

Unit Rate =8 gallons

x 8

x 8

25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.

Comparing Unit Prices

• Use division to find the unit prices of the two products in question.

• The unit rate that is smaller (costs less) is the better value.

Example

Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy?

$2.0748 fl.oz.

0.043125 $0.04 per fl.oz.

$1.6432 fl.oz.

0.05125 $0.05 per fl.oz.

The 48 fl.oz. bottle is the better value.

Classwork: Check out this interactive

for ratios and unit rates. You can click on lessons,

interactives, or applications. Try it at BRAINCAMP

Homework Time:6-1 and 6-2 Handout