# Solve Proportions.

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Solve Proportions

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 <

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

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

= 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

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)

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

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

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

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

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

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)

Notes start here

Solve Proportions

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)

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. =

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:

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

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 = = =

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. =

= 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? =

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) = =

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)