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6-1: Ratios and Rates

6-1: Ratios and Rates. Ratios. A ratio is a comparison between two numbers by division. It can be written in three different ways:. 5 to 2. 5 : 2. 5. 2. Equal Ratios. When two ratios name the same number, they are equal. It ’ s like writing an equivalent fraction. 20 : 30.

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6-1: Ratios and Rates

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  1. 6-1: Ratios and Rates

  2. Ratios • A ratio is a comparison between two numbers by division. • It can be written in three different ways: 5 to 2 5 : 2 5 2

  3. Equal Ratios • When two ratios name the same number, they are equal. It’s like writing an equivalent fraction. 20 : 30 Equal Ratios: 80 : 120 2 : 3 10 : 15

  4. Ratios in Simplest Form • Ratios can be written in simplest form. • Divide both terms in the ratio by their GCF. Example: 12 to 8 3 to 2

  5. Unit Rates • 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.

  6. Examples Rate: 150 heartbeats 2 minutes Unit Rate (Divide to get it): 150 ÷ 2 = 75 heartbeats per minute.

  7. 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 22 pages per hour 4 hours

  8. Using Unit Rates • You can find the missing terms of equal ratios. • Use the unit rate, and set it equal to another ratio. • Solve for what is missing by dividing or multiplying.

  9. Example Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? x 8 25 miles = 1 gallon 8 gallons x 8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.

  10. Comparing Unit Prices • Use division to find the unit prices of the two products in question. • The unit rate that is smaller (costs less) is the better value.

  11. Example • Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 $0.04 per fl.oz. 0.043125 48 fl.oz. $1.64 $0.05 per fl.oz. 0.05125 32 fl.oz. The 48 fl.oz. bottle is the better value.

  12. Practice Time  • P 316 # 1-7

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