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 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 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

24 questions correct on a 100-question test 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.