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Equivalent Ratios & Unit Rates Vocabulary ( you should already have this written in your notes – you do not have to copy again!) • • • • A ratio is the comparison of two numbers written as a fraction.(division) 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. In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. Example: Your school’s basketball team has won 7 games and lost 3 games. What is the ratio of wins to losses? Because we are comparing wins to losses the first number in our ratio should be the number of wins and the second number is the number of losses. The ratio is ___________ games won games lost = _______ 7 games 3 games = __ 7 3 Example: You can travel 120 miles on 6 gallons of gas. What is your fuel efficiency in miles per gallon? Rate = ________ 120 miles 6 gallons = ________ 20 miles 1 gallon Your fuel efficiency is 20 miles per gallon. Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute. Find the Unit Rate Amy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?) 88 pages 4 hours ? Pages 1 hour Writing the units when comparing each unit of a rate is called unit analysis. You can multiply and divide units just like you would multiply and divide numbers. When solving problems involving rates, you can use unit analysis to determine the correct units for the answer. Example: How many minutes are in 5 hours? 5 hours • 60________ minutes 1 hour = 300 minutes To solve this problem we need a unit rate that relates minutes to hours. Because there are 60 minutes in an hour, the unit rate we choose is 60 minutes per hour. Example Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? x8 Unit Rate 25 miles 1 gallon = 8 gallons x8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas. If the average person lives for 75 years, how long would that be in seconds? ** I will check your answer tomorrow. Please show your work and attempt to answer.