1. Rates and Ratios

2. Ratios and Rates ratio – a comparison of two numbers by division written in several different forms.

3. Ratios and Rates rate – a ratio that compares different kinds of units by division to obtain a unit rate or rate per unit.

4. Ratios and Rates The order of the numbers in a ratio should match the order of the words in a ratio. apples to oranges 2 to 3

5. Ratios and Rates Ratios can be written in several different ways. 3 to 1 3 : 1 3/1 red to black

6. Ratios and Rates Ratios can show comparisons between: part to part red to green 1 to 2 green to red 2 to 1

7. Ratios and Rates Ratios can show comparisons between: part to whole red to whole 1 to 3 green to whole 2 to 3

8. Ratios and Rates Ratios can show comparisons between: whole to part whole to red 3 to 1 whole to green 3 to 2

9. Ratios and Rates Compare octagon to all shapes 1 to 8 1 out of 8 1 : 8 1/8

10. Ratios and Rates Compare all shapes to trapezoid 8 to 18 : 1 8/18/1

11. Ratios and Rates Compare pentagons to hexagons 2 to 32 : 32 : 3 2/32/3

12. Ratios and Rates Give each ratio in three forms. 8 roses out of 24 flowers 8 to 248 : 24 3 dogs out of 12 animals 3 to 123 : 12

13. Ratios and Rates A ratio in fraction form can be expressed in simplest form by dividing the numerator and denominator by a common factor. ÷ 8 = ÷ 3 =

14. Ratios and Rates To express a ratio as a rate per unit, write the ratio as a fraction and then divide the numerator by the denominator. 395 miles in 5 hours = 79 miles per hour miles hours miles hours

15. Ratios and Rates Express each ratio as a rate. 5 inches of rain in 30 days = inch of rain per day 120 words in 3 minutes = 40 words per minute words per minute ÷ 5

17. Proportion A proportion is an equation that shows two equivalent ratios. 2:3 = 8:12 =

18. Fill in the table The ratio of boys to girls is 7 to 6: 76 14? 21? 28? 35? 42?

19. Fill in the table The ratio of pens to pencils are 12 to 7 127 36 48 72 84 96

20. What about word problems?

21. Using Cross Multiplication to Complete Proportions In the case that we need to find a missing value in a proportion we will use cross multiplication. Steps Set-up Cross Multiply Divide

22. Examples: 1. For every 8 minutes you answer 7 questions. How many questions could you answer in 32 minutes? 8 = 32 7 n Solution: Use the cross product method 8n= 224 8n = 224 divide both side by 8 8 n = 28 therefore, 8 = 32 7 28

23. 1 You can run a distance of 2 blocks in 3 minutes. How many blocks can you run in 18 minutes?

24. 2 You can read 5 pages of a novel in 3 minutes. How many pages of the novel can you read in 60 minutes?

25. 3 It takes you 5 minutes to mow 7 square yards of a lawn. How long would it take to mow 630 square yards?

26. 4 A running faucet sends 14 gallons of water down the drain every 3 minutes. How many gallons will go down the drain in 90 minutes?

27. 5 A clothes washer uses 170 gallons of water for 4 loads. How many gallons would be used for 240 loads?

28. 6 A volunteer beach clean up crew collected 20 bags of trash in 3 hours. How many hours would it take them to collect 1,000 bags of trash?

29. 7 The average American uses about 145 pounds of paper every 3 months. How many pounds of paper are used in 24 months?