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Professor Busken – 6.1 Ratios and Rates 1 Objectives: A Write Ratios as Fractions C Find Unit Rates B Write Rates as Fractions D Find Unit Prices Definition 1. A ratio is the quotient of two quantities. We write the ratio of 3 to 4 as 3 to 4 or 3 or 3:4. 4 However, we will use fraction notation to write ratios. Suppose a and b are both nonzero a b numbers. The ratio of a to b is not . b a Write each ratio as a fraction in simplest form. 1. 6 to 24 1. 2. 2 to 12 2. 3. 2 4. 1.68 miles to 4.8 miles 4. 5. 37 gallons to 0.001 gallons 5. 6. 1.6 meters to 0.16 meters 6. 13 2 to 1 3 15 3. Definition 2. A rate is a special type of kind of ratio. It is used to compare different kinds of quantities. Whenever we write rates as fractions we always include the units. For example, a recreational runner can run 4 miles in 44 minutes. We can write this rate as the fraction 4 miles 1 miles = . 44 minutes 11 minutes Write each rate as a fraction in simplest form. 7. 295 miles on 15 gallons 7. Professor Busken – 6.1 Ratios and Rates 2 Write the rate as a fraction in simplest form. 8. $1350 for 6 weeks 8. Definition 3. A unit rate is a rate that has a denominator of 1. For instance, 65 miles per hour is a unit rate. 65 miles 1hour Writing a Rate as a Unit Rate To write a rate as a unit rate, we simply divide the numerator of the rate by the denominator. Write each rate as a unit rate. 9. 10. 480 calories in 8 ounces 9. 520 miles in 8 hours 10. Definition 4. When a unit rate is ”money per item,” it is also called a unit price. unit price = price number of units For example, suppose a store charges $2.76 for a 12-ounce jar of pickles. What is the unit price? $0.23 $2.76 = unit price = 12 ounces 1 ounces So, the store charges $0.23 per ounce. Find each unit price and decide which is a better buy. 11. Treated lumber: $3.79 for an 8-foot board or $6.18 for a 12-foot11. board. 12. 50 aspirin tablets for $3.79 or 100 aspirin tablets for $5.85. 12.