Download 4-1 Ratios and Rates

Course 3 Chapter 4 4 -­‐1: Ratios A comparison of 2 numbers by division. Ratios can be written in 3 ways # of boys
9
1. As a fraction: = # of girls 12
2. Using a colon: # of boys : # of girls 9 : 12 3. Using “to”: # of boys to # of girls 9 to 12 When simplifying a ratio that compares measurements, be sure that the measurements are in the same unit of measure. Equivalent Ratios: Same as equivalent fractions-­‐-­‐-­‐-­‐-­‐Multiply or divide the numerator and denominator by the same number. Their cross products will be equal. 4/12 = 8/24 (4 x 24 = 96, 8 x 12 = 96) Simplifying Ratios: (just like simplifying a fraction) 1. Find the GCF of the numerator and denominator 2. Divide both by the GCF 3. Write resulting fraction 4. NO Mixed numbers-­‐-­‐-­‐keep as an improper fraction in simplest form when occurs Examples: 1. 6/4 = 3/2 GCF is 2 2. 9/12 = ¾ GCF is 3 Unit Rates and Proportional Reasoning Rate: A ratio of two measurements with different units Examples: $5 for 3 pounds, 15 grams per 5 servings, 15 minutes per 1.5 miles, 4 servings per ¼ pound, etc. Unit Rate A unit rate is a rate where the denominator is one-­‐-­‐-­‐-­‐the ratio is per 1 unit Examples: Miles per 1 hour, heartbeats per 1 minute, price per 1 gallon, population per 1 square mile (population density), pay per 1 hour If I buy 6 tickets for $240, what is the unit price? Course 3 Chapter 4 240 ?
= divide the numerator and denominator by 6 to get an 6
1
equivalent ratio 240 divided by 6 is 40 The price per ticket is $40 Unit rate is used to compare costs: What is better 48 fl. oz for $3.05 or 64 fl. oz. for $3.59? Find the cost per fl. oz and compare. 3.05/ 48 = .64/1 fl oz 3.59/64 = .56/ 1 fl.oz. The bigger bottle is the better buy.