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Solve Proportions

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**uses < < a c In the proportion = , the cross products, b d**

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

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**You can use the cross product rule to solve proportions with variables**

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

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**Unit rate : a rate whose denominator is 1**

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 4 Step 3: Cross multiply and divide Hours Hour 200 X 1 = 200 ÷ 4 = 50 X = 50 mph

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**= EX 6) 160 gallons miles / 5 X 1 160 X 1 = 160 ÷ 5 = 32 X = 32 mpg**

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

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**Length Weight Capacity**

12 inches (in)= 1 foot (ft) 3 feet = 1 yard (yd) 5,280 feet = 1 mile (mi) Weight 16 ounces (oz) = 1 pound (lb) 2000 pounds = 1 ton Capacity 8 fluid ounces (fl oz) = 1 cup (c) 2 cups = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal)

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

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**Sue needs 9 cups of flour to make 16 batches of cookies**

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 9 cups Cups = Set up proportion. X 16 batches 4 batches Cross Multiply. Divide 9 X 4 = 36 4 16 2 = 1 4 2 36 ÷ 16 = Cups

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**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 = Volume 3 cm 3 1 cm3 Set up proportion. Cross Multiply. Divide 9 X 1 = 9 Density = 3g/cm3 9 ÷ 3 = 3

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

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**12 oz drink that cost $1.08 is $0.09 / oz**

. 9 $1.08 X 1 = 1.08 1.08 ÷ 12 12 12 oz drink that cost $1.08 is $0.09 / oz Back . 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

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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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Notes start here

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Solve Proportions

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**uses a c In the proportion = , the cross products, b d**

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

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**You can use the cross product rule to solve proportions with variables**

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

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**Unit rate : a rate whose denominator is 1**

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: How many miles traveled per hour? Step 2: = Step 3:

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

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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 = = =

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EX 9) 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. =

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**= 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? =

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**A 12 oz sport drink cost $1. 08 and a 16 oz. sport drink cost $1. 28**

A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $ Which drink is the better buy? EX 11) = =

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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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