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Ratios and Rates

Ratios and Rates. 100 km/h. __. 3. 4 : 7. 4. 11 : 14. By definition:. A ratio is a fraction that compares two numbers with the same units. A rate compares two numbers with different units. In this classroom, write the ratio for:. Boys to girls Dark hair to light hair

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Ratios and Rates

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  1. Ratios and Rates 100 km/h __ 3 4 : 7 4 11 : 14

  2. By definition: • A ratio is a fraction that compares two numbers with the same units. • A rate compares two numbers with different units

  3. In this classroom, write the ratio for: • Boys to girls • Dark hair to light hair • Short hair to long hair

  4. From a pocket full of change, write the ratios for - • Dimes to quarters – • Nickels to dimes – • Loonies to pennies –

  5. Rates compare numbers of different units: • 100 km / h (401) • $50.00 / week (allowance) • $8.00 / person (movies)

  6. Consider 2 baseball players: Ratios can be used to analyze information • Player 1 • 77 hits in 149 bats • Player 2 • 189 hits in 417 bats • Who is the better hitter?

  7. Player 2 • 189 hits in bats 417 bats • Player 1 • 77 hits in 149 bats • Who is the better hitter? 77 149 189 417 = 0.517 = 0.453

  8. When rates are expressed as unit rates, comparisons can be made. For Example: $67.50 for 6 hours work or $85.00 for 7 hours work Which is the better job?

  9. Which is the better deal? 200g of popcorn for $1.00 or 750g of popcorn for $2.70

  10. RRs are in lowest terms when the GCF is 1 • 4 : 8 = 1 : 2 • 10 : 25 = 2 : 5 • 6 : 48 = 1 : 8 • 7 : 21 = 1 : 3 Equivalent ratios form a proportion Proportions can be solved for unknown amounts

  11. Page 67 [1-27] odd 28,29 31,37,39 42,46 Hand in…

  12. Proportions

  13. Find the unknown quantity: • Orange juice powder and water must be mixed in the ratio 1:4 • If you have 3 cups of mix, how much water do you need? Mix = Water 1 = 4 3 X 1X = 12 X = 12

  14. How much mix will you need to go with 10 cups of water Mix = Water 1 = 4 X 10 4X = 10 1 4X = 10 4 4 1 X = 10 4 X = 2.5

  15. Proportions can be reduced to a unit rate. Proportions can then be compared

  16. Sheets

  17. Rates For this assignment: Copy down all the text in black Answer the homework questions assigned on the last slide Show Mr. Stokes both when you are finished

  18. A ratio compares 2 numbers in the same unit (3:4 or 2:13) • A rate compares two numbers in different units

  19. Speed limit on the 401 • 100 km / hour • km are one unit and hours are the other • Pay at McDonald’s • $7.00 / hour • Dollars are one unit and hours are the other

  20. Rates are most useful when they are written as a unit rate.To determine the unit rate, use division

  21. Pay 45 = = hour 5 • Suppose you make $45.00 in 5 hours. • How much do you make per hour? • To find pay per hour: $9 / hour

  22. cost CD 14.99 = 12 • Suppose 12 CDs cost $14.99 • How much does 1 CD cost? = $1.25 / CD

  23. Rates can be expressed in unit rates (used for comparisons) • 180 km in 2 hours • 180 / 2 = 90 km / h • $3.60 for 6 muffins • 3.60 / 6 = $.60 / muffin

  24. Homework Page 180 - 181

  25. Rates Spending money…

  26. By definition: • A ratio is a fraction that compares 2 numbers with the same units. • A rate compares 2 numbers with different units

  27. For comparisons, it is usually better to express the numbers in a unit rate To determine the unit rate, divide the 2 quantities being examined

  28. For example: A: 10 pack of CDs costs $11.99. B: 12 pack of CDs costs $12.99. Which is the better deal? (price/CD)

  29. A: 11.99 $1.20/CD = = Price 10 CD B: 12.99 Price $1.08/CD = = 12 CD B is a better deal!

  30. Ex 2: Laundry soap comes in 3 sizes and prices. Determine the best buy: Size (loads) Cost ($) A: 10 5.49 B: 20 8.49 C: 37 9.99

  31. The best buy will have the lowest cost per load.

  32. A: 5.49 $0.55/load = = 10 load Price B: 8.49 Price $0.42/load = = 20 load C: 9.99 Price $0.27/load = = 37 load

  33. C is the best deal

  34. Page 11 1-10 13,15,16 17,20,21

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