Ratios and Unit Rates

Ratio – a comparison of two quantities by division

Ratios can be written in three ways:

1) as a fraction in simplest form

2) with the word “ to ”

3) with a colon “ : ”

Examples:

• Four out of five dentists surveyed recommend sugarless gum for their patients who chew gum

4 4 to 5 4:5

5

• 9 people out of 20 like chocolate ice cream

9 9 to 20 9:20

20

In a class of thirty students, thirteen are boys. Write a ratio for the number of boys to students in the class.

13/30 13 to 30 13:30

Write a ratio for the number of boys to the number of girls.

13/17 13 to 17 13:17

Out of 100 students, 40 said they had afterschool jobs. Write a ratio for the number of students who had jobs to the number who did not.

40/60 = 2/3

40 to 60 = 2 to 3 40:60 = 2:3

6 freethrows made out of 10 attempts

6/10 = 3/5 3 to 5 3 : 5

24 questions correct on a 100-question test

24/100 = 6/25 6 to 25 6 : 25

5 cookies eaten out of 20 cookies

5/20 = ¼ 1 to 4 1 : 4

Unit Rate – a rate for “one” of something; a ratio with a denominator of 1.

If three bananas cost $1.89, how much does one banana cost?

$1.89/3 = .63/1 banana

Examples:

You need to buy soda for a party. The store sells 3 12-packs for $7.80. Find the unit rate for one 12-pack?

$7.80/3 = $2.60/1

You travel 300 miles in five hours. Find the unit rate per hour.

300/5 = 60 miles/1 hour

A girl can jump rope 200 times in 4 minutes. What is the unit rate per minute?

200 / 4 = 50 times/1 minute

Determine which is the better buy:

You need to buy pizzas for a class party. You can buy 4 large pizzas for $10.00, or you can 7 large pizzas for $19.25. Which is the better buy?

$10.00 / 4 = $2.50/1

$19.25 / 7 = $2.75/1

It is cheaper to buy 4 pizzas.