Ratios & Unit Rates 6-1

VOCABULARY Ratio – a comparison of two quantities by division Rate – ratio that compares quantities in different units Unit Rate – a rate that has a denominator of 1

WRITING RATIOS Key Concepts: A ratio compares two quantities through division. You can write a ratio in many different ways. Statistics: In the United States, about 10 out of every 15 people eligible to vote are registered to vote. The numbers 10 and 15 form a ratio. 10 to 15 10:15 10 or 2 15 3 Note: When writing in fraction form, always simplify!

Example 1 A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form. Response Number Have a job 40 Don’t have a job 60 TOTAL 100 a. Students with jobs to students without jobs Students with jobs = 40 = 2 Students w/o jobs 60 3 b. Students without jobs to all students surveyed Students w/o jobs = 60 = 3 Students surveyed 100 5

FINDING RATES AND UNIT RATES We know that a ratio that compares quantities with different units of measurement is called a rate. A unit rate is a rate that has a denominator of 1. We will use unit rates when comparing prices, gas mileage, speed, etc.

Example 2 Unit Prices: The table shows prices for different sizes of the same dish detergent. Which size has the lowest unit price? Regular: price = $1.20 volume 12 fl. oz Size Volume (fl. oz.) Price Regular 12 $1.20 Family 28 $2.24 Economy 40 $3.60 $.10/fl. oz. Family: price = $2.24 volume 28 fl. oz $.08/fl. oz. Economy: price = $3.60 volume 40 fl. oz Therefore, the family size has the lowest unit price. $.09/fl. oz.

CONVERTING UNITS Sometimes, you will have to convert units of measurement in order to solve the problem at hand. Example: convert inches to feet days to months ounces to liters

Example 3 Convert 10 mi/h to ft/min 10 mi/h = 10 mi 5,280 ft 1h ` 1 h 1 mi 60 min 88 10 mi 5,280 ft 1 h ` 1h 1 mi 60 min 1 10 88 ft 1 = 880 ft 1 1 1 min min Therefore, 10 mi/h is the same as 880 ft/min