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7-1. Ratios and Rates. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 3. 25. 6. 4. 5. __. ___. __. __. __. 14. 52. 16. 26. 70. 1. 2. 1. __. __. __. 3. 6. 4. Warm Up Write each fraction in simplest form. 1. 2. 3. 4. Problem of the Day

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7-1

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  1. 7-1 Ratios and Rates Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 3 25 6 4 5 __ ___ __ __ __ 14 52 16 26 70 1 2 1 __ __ __ 3 6 4 Warm Up Write each fraction in simplest form. 1.2. 3.4.

  3. Problem of the Day What three consecutive odd numbers are factors of 105? 3, 5, 7

  4. Learn to write ratios and rates and to find unit rates.

  5. Vocabulary ratios equivalent ratios rate unit rate

  6. For a time, the Boston Symphony Orchestra was made up of 95 musicians. You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

  7. 29 29 12 ___ ___ ___ 12 12 29 For example, you can use a ratio to compare the number of violins (29) with the number of violas (12). This ratio can be written in three ways. 29 to 12 29:12 Terms Notice that the ratio of violins to violas, is different from the ratio of violas to violins, . The order of the terms is important. Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

  8. 29 ___ 12 Reading Math Read the ratio as “twenty-nine to twelve.”

  9. or 5 to 2 or 5:2 5 __ 2 Additional Example 1A: Writing Ratios Use the table to write the ratio. cats to rabbits Part to part

  10. 7 __ 14 or 7 to 14 or 7:14 Additional Example 1B: Writing Ratios Use the table to write the ratio. dogs to total number of pets Part to whole

  11. __ 5 14 or 14 to 5 or 14:5 Additional Example 1C: Writing Ratios Use the table to write the ratio. total number of pets to cats Whole to part

  12. 6 __ 18 or 6 to 18 or 6:18 Check It Out: Example 1A Use the table to write the ratio. birds to total number of pets Part to whole

  13. 3 __ 6 or 3 to 6 or 3:6 Check It Out: Example 1B Use the table to write the ratio. snakes to birds Part to part

  14. __ 9 18 or 18 to 9 or 18:9 Check It Out: Example 1C Use the table to write the ratio. total number of pets to hamsters Whole to part

  15. Equivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

  16. 3 9 1 1 3 3 9 3 __ __ __ __ __ __ __ __ 2 2 6 18 6 6 18 6 3 ÷ 3 ____ 6 ÷ 3 3 • 3 6 • 3 So , , and are equivalent ratios. Additional Example 2: Writing Equivalent Ratios Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern. number of diamonds There are 3 diamonds and 6 spades. = number of spades There is 1 diamond for every 2 spades. = = If you triple the pattern, there will be 9 diamonds for 18 spades. = =

  17. 3 9 1 1 3 3 9 3 __ __ __ __ __ __ __ __ 3 3 9 27 9 9 27 9 3 ÷ 3 ____ 9 ÷ 3 3 • 3 9 • 3 So , , and are equivalent ratios. Check It Out: Example 2 Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern. number of triangles There are 3 triangles and 9 hearts. = number of hearts There is 1 triangle for every 3 hearts. = = If you triple the pattern, there will be 9 triangles for 27 hearts. = =

  18. $0.99 price $1.98 $1.98 ÷ 2 $1.98 _____ ________ _____________ ________ _____ 2 1 2 liters number of liters 2 ÷ 2 Aratecompares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98. $1.98 for 2 liters rate = = When the comparison is to one unit, the rate is called a unit rate. Divide both terms by the second term to find the unit rate. $0.99 for 1 liter unit rate = = = When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

  19. $0.91 $2.79 $5.46 ÷ 6 $2.79 ÷ 3 $5.46 $0.93 _____ _________ _____ _____ _________ _____ 3 rolls 6 rolls ÷ 6 3 rolls ÷ 3 1 roll 1 roll 6 rolls Additional Example 3: Consumer Application A 3-pack of paper towels costs $2.79. A 6-pack of the same paper towels costs $5.46. Which is the better deal? Write the rate. Write the rate. Divide both terms by 3. Divide both terms by 6. $0.91 for 1 roll. $0.93 for 1 roll. The 6-pack of paper towels is the better deal.

  20. $0.62 $2.10 $5.58 ÷ 9 $2.10 ÷ 3 $5.58 $0.70 _____ _________ _____ _____ _________ _____ 3 pack 9 pack ÷ 9 3 pack ÷ 3 1 box 1 box 9 pack Check It Out: Example 3 A 3-pack of juice boxes costs $2.10. A 9-pack of the same juice boxes costs $5.58. Which is the better deal? Write the rate. Write the rate. Divide both terms by 3. Divide both terms by 9. $0.62 for 1 juice box. $0.70 for 1 juice box. The 9-pack of juice boxes is the better deal.

  21. 1 __ 2 Lesson Quiz Use the table to write each ratio. 1. tulips to daffodils 2. crocuses to total number of bulbs 3. total bulbs to lilies 4. A dozen eggs cost $1.25 at one market. At a competing market, 1 dozen eggs cost $2.00. Which is the better buy? 9:17 20:51 51:5 eggs from the first market

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