Solve Proportions

CROSS PRODUCT RULEIn the proportion = , the cross products, a · d and b · c are equal.

ab

cd

EX 1) = 24

12

44uses

1. Prove proportionality

EX 2) = 57

35

2521 2. Disprove proportionality3. Compare fractions

EX 3) 57

35

2521 <<

You can use the cross product rule to solve proportions with variables. Which help you find missing values.

15m15m15

= 4515

m = 3

Set up proportion.

Cross Multiply.Divide each side by 15 to isolate the variable.

= m5

915

This is called the extreme and means ratio.

= 45

EX 4)

• Unit rate : a rate whose denominator is 1. It may not always look like a number; watch for words like per or each.

milesEX 5) 200 / 4 hours

How many miles traveled per hour?

Step 2: set up proportion=

Step 1: highlight rates

Miles Miles

Hours Hour

200

4

X1 Step 3: Cross multiply

and divide

200 X 1 = 200 ÷ 4 = 50 X = 50 mph

gallonsmilesEX 6) 160

/ 5

How many miles per gallon?

Step 2: set up proportion=Step 1: highlight rates

Miles Miles

Gal Gal

160

5

X1 Step 3: Cross multiply

and divide

160 X 1 = 160 ÷ 5 = 32 X = 32 mpg

Length12 inches (in)= 1 foot (ft)

3 feet = 1 yard (yd)5,280 feet = 1 mile (mi)

Weight16 ounces (oz) = 1 pound (lb)

2000 pounds = 1 tonCapacity

8 fluid ounces (fl oz) = 1 cup (c)2 cups = 1 pint (pt)

2 pints = 1 quart (qt)4 quarts = 1 gallon (gal)

Convert 5,000 pounds to tons.

1: Set up Proportion= pounds tons

2,000 1

2000x = 5,000

5,000 m x

x = 2.5

EX 7)

2: Solve ProportionCross multiplyDivide

Convert 24 pints to cups.

= cups pints

2 1

1 • c = 2 • 24c = 48

c 24

EX 8)

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.

Set up proportion.

Cross Multiply.Divide

=cups Cups9

16 XX

batches batches4

9 X 4 = 36

36 ÷ 16 = 416 2 1

4 2 = Cups

Determine Ratios.

EX 5)

Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density?

Set up proportion.

Cross Multiply.Divide

=Mass mass9 g

3 cm 3

X1Volume cm3

9 X 1 = 9

9 ÷ 3 =

Determine Ratios.

EX 6)

Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume

3

Density = 3g/cm3

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

Step 2: set up proportion

=

Step 1: highlight rates

oz

$$

oz16

1.28 X1 Step 3: Cross multiply

and divide

EX. 7)

Since you are comparing you will set up two proportions

=oz

$

oz12

1.08 X1

$

Solve

Solve

161.28

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

$1.08 X 1 = 1.08 ÷ 121.08 12.0 0 9

Back

16 oz drink that cost $1.28 is $0.08 / oz

$1.28 X 1 = 1.28 ÷ 16.0 0 8

The better buy is the cheaper drinkThe 16 oz is the better buy

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)

Try this on your own

Notes start here

Solve Proportions

CROSS PRODUCT RULEIn the proportion = , the cross products, a · d and b · c are equal.

ab

cd

EX 1) = 24

12

uses1.

EX 2) = 57

35

2. 3.

EX 3)

You can use the cross product rule to solve proportions with variables. Which help you find missing values.

=

=

1.

2.3.

= m5

915

This is called the extreme and means ratio.

=

EX 4)

How many miles traveled per hour?

miles

• 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

/ 4 hours

Step 2:

=

Step 1:

Step 3:

gallonsmilesEX 6) 160

/ 5How many miles per gallon?

=

Convert 5,000 pounds to tons.

1: Set up = pounds tons

=

=

EX 7)

2: _____ ProportionCD

Convert 24 pints to cups.

= cups pints

= =

EX 8)

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)

Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density?

=

EX 10)

Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume

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

=

EX 11)

=

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)

Try this on your own