1. 7-1 Ratios and Rates Learn to write ratios and rates and to find unit rates.

2. 7-1 Ratios and Rates Vocabulary ratios equivalent ratios rate unit rate

3. 7-1 Ratios and Rates You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division. For a time, a local symphony orchestra was made up of 95 musicians. Trombones Harp Percussion Trumpets Basses Violas 36Horns 14Clarinets 58Double reeds 35Flutes 910Cellos 1229Violins

4. 7-1 Ratios and Rates 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. Notice that the ratio of violins to violas, is different from the ratio of violas to violins,. The order of the terms is important. 29 12 ___ 29 12 ___ 12 29 ___ 29 to 1229:12 Terms Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

5. 7-1 Ratios and Rates Read the ratio as “twenty-nine to twelve.” Reading Math 29 12 ___

6. 7-1 Ratios and Rates Additional Example 1A: Writing Ratios Use the table to write the ratio. cats to rabbits 2Rabbits 7Dogs 5Cats Animals at the Vet or 5 to 2 or 5:2 5 2 __ Part to part

7. 7-1 Ratios and Rates Additional Example 1B: Writing Ratios Use the table to write the ratio. dogs to total number of pets or 7 to 14 or 7:14 7 14 __ Part to whole 2Rabbits 7Dogs 5Cats Animals at the Vet

8. 7-1 Ratios and Rates Additional Example 1C: Writing Ratios Use the table to write the ratio. total number of pets to cats or 14 to 5 or 14:5 14 5 __ Whole to part 2Rabbits 7Dogs 5Cats Animals at the Vet

9. 7-1 Ratios and Rates Check It Out: Example 1A Use the table to write the ratio. birds to total number of pets 3Snakes 9Hamsters 6Birds Animals at the Vet or 6 to 18 or 6:18 6 18 __ Part to whole

10. 7-1 Ratios and Rates Check It Out: Example 1B Use the table to write the ratio. snakes to birds or 3 to 6 or 3:6 3 6 __ Part to part 3Snakes 9Hamsters 6Birds Animals at the Vet

11. 7-1 Ratios and Rates Check It Out: Example 1C Use the table to write the ratio. total number of pets to hamsters or 18 to 9 or 18:9 18 9 __ Whole to part 3Snakes 9Hamsters 6Birds Animals at the Vet

12. 7-1 Ratios and Rates 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.

13. 7-1 Ratios and Rates Additional Example 2: Writing Equivalent Ratios Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern. There are 3 diamonds and 6 spades. number of diamonds number of spades = 3 6 __ There is 1 diamond for every 2 spades. 3 6 __ = 3 ÷ 3 6 ÷ 3 ____ = 1 2 __ 3 6 = 9 18 __ = If you triple the pattern, there will be 9 diamonds for 18 spades. So,, and are equivalent ratios. 3 6 __ 1 2 9 18 __ 3 6 3

14. 7-1 Ratios and Rates Check It Out: Example 2 Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern. There are 3 triangles and 9 hearts. number of triangles number of hearts = 3 9 __ There is 1 triangle for every 3 hearts. 3 9 __ = 3 ÷ 3 9 ÷ 3 ____ = 1 3 __ 3 9 = 9 27 __ = If you triple the pattern, there will be 9 triangles for 27 hearts. So,, and are equivalent ratios. 3 9 __ 1 3 9 27 __ 3 9 3

15. 7-1 Ratios and Rates A rate compares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98. 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. When the prices of two or more items are compared, the item with the lowest unit rate is the best deal. rate = price number of liters _____________ $1.98 2 liters ________ = $1.98 for 2 liters unit rate = $1.98 2 _____ $1.98 ÷ 2 2 ÷ 2 ________ = $0.99 for 1 liter = $0.99 1 _____

16. 7-1 Ratios and Rates 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. $2.79 3 rolls _____ $2.79 ÷ 3 3 rolls ÷ 3 _________ Divide both terms by 3. $0.93 1 roll _____ $0.93 for 1 roll. Write the rate. $5.46 6 rolls _____ $5.46 ÷ 6 6 rolls ÷ 6 _________ Divide both terms by 6. $0.91 1 roll _____ $0.91 for 1 roll. The 6-pack of paper towels is the better deal.

17. 7-1 Ratios and Rates 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. $2.10 3 pack _____ $2.10 ÷ 3 3 pack ÷ 3 _________ Divide both terms by 3. $0.70 1 box _____ $0.70 for 1 juice box. Write the rate. $5.58 9 pack _____ $5.58 ÷ 9 9 pack ÷ 9 _________ Divide both terms by 9. $0.62 1 box _____ $0.62 for 1 juice box. The 9-pack of juice boxes is the better deal.