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Solve Proportions

Solve Proportions. 3 5. 3 5. 1 2. 5 7. 5 7. 2 4. =. =. CROSS PRODUCT RULE. a b. c d. In the proportion = , the cross products, a · d and b · c are equal. 4. 4. uses. EX 1). 1. Prove proportionality. 2. Disprove proportionality. 21. 25.

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Solve Proportions

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  1. Solve Proportions

  2. 3 5 3 5 1 2 5 7 5 7 2 4 = = CROSS PRODUCT RULE a b c d In the proportion = , the cross products, a · d and b · c are equal. 4 4 uses EX 1) 1. Prove proportionality 2. Disprove proportionality 21 25 3. Compare fractions EX 2) < 21 25 < EX 3)

  3. 9 15 m 5 = You can use the cross product rule to solve proportions with variables. Which help you find missing values. EX 4) Set up proportion. Cross Multiply. = 45 15m Divide each side by 15 to isolate the variable. 15m 15 = 45 15 This is called the extreme and means ratio. m = 3

  4. Unit rate : a rate whose denominator is 1. It may not always look like a number; watch for words like per or each. EX 5) 200 miles / 4 hours Step 1: highlight rates How many miles traveled per hour? X 200 Miles Miles = Step 2: set up proportion 1 Step 3: Cross multiply and divide 4 Hours Hour 200 X 1 = 200 ÷ 4 = 50 X = 50 mph

  5. miles EX 6) 160 / 5 gallons How many miles per gallon? Step 1: highlight rates X 160 Miles Miles = Step 2: set up proportion 1 Step 3: Cross multiply and divide 5 Gal Gal 160 X 1 = 160 ÷ 5 = 32 X = 32 mpg

  6. EX 7) Convert 5,000 pounds to tons. 5,000 mx pounds tons 2,0001 1: Set up Proportion = • 2: Solve Proportion • Cross multiply • Divide 2000x = 5,000 x = 2.5 EX 8) Convert 24 pints to cups. c 24 cups pints 21 = 1 •c = 2 • 24 c = 48

  7. Sue needs 9 cups of flour to make 16 batches of cookies. How much flour does she need if she only wants to make a fourth of her recipe. EX 5) Determine Ratios. X cups 9 Cups = Set up proportion. X batches 4 batches 16 Cross Multiply. Divide 9 X 4 = 36 = 4 1 2 2 36 ÷ 16 = Cups 16 4

  8. Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density? EX 6) Determine Ratios. X Mass 9 g mass = 1 Volume cm3 3 cm 3 Set up proportion. Cross Multiply. Divide 9 X 1 = 9 Density = 3g/cm3 9 ÷ 3 = 3

  9. A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $1.28. Which drink is the better buy? EX. 7) 1 oz 12 oz = Step 1: highlight rates X 1.08 Since you are comparing you will set up two proportions $ $ Solve Step 2: set up proportion Step 3: Cross multiply and divide 1 16 oz oz = 1.28 X $ $ Solve

  10. 0 . 0 9 $1.08 X 1 = 1.08 1.08 ÷ 12 12 12 oz drink that cost $1.08 is $0.09 / oz Back 0 . 0 8 $1.28 X 1 = 1.28 1.28 ÷ 16 16 16 oz drink that cost $1.28 is $0.08 / oz The better buy is the cheaper drink The 16 oz is the better buy

  11. Try this on your own A car travels 480 miles in 8 hours and uses 16 gallons of gas. What is the average speed? ( miles per hour) What is the average gas mileage? ( miles per gallon)

  12. Notes start here

  13. Solve Proportions

  14. 3 5 1 2 2 4 5 7 = = CROSS PRODUCT RULE a b c d In the proportion = , the cross products, a · d and b · c are equal. uses EX 1) 1. 2. 3. EX 2) EX 3)

  15. 9 15 m 5 = You can use the cross product rule to solve proportions with variables. Which help you find missing values. EX 4) 1. 2. = 3. = This is called the extreme and means ratio. =

  16. Unit rate : a rate whose denominator is 1. It may not always look like a number; watch for words like per or each. miles / 4 hours EX 5) 200 Step 1: How many miles traveled per hour? Step 2: = Step 3:

  17. miles EX 6) 160 / 5 gallons How many miles per gallon? =

  18. EX 7) Convert 5,000 pounds to tons. pounds tons 1: Set up = • 2: _____ Proportion • C • D = = EX 8) Convert 24 pints to cups. cups pints = = =

  19. Sue needs 9 cups of flour to make 16 batches of cookies. How much flour does she need if she only wants to make a fourth of her recipe. EX 9) =

  20. Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume EX 10) Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density? =

  21. A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $1.28. Which drink is the better buy? EX11) = =

  22. Try this on your own A car travels 480 miles in 8 hours and uses 16 gallons of gas. What is the average speed? ( miles per hour) What is the average gas mileage? ( miles per gallon)

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