1. Solve Proportions

2. 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
<

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

4. 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

5. = 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

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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)

13. Notes start here

14. Solve Proportions

15. 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)

16. 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. =

17. 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:

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

19. 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 = = =

20. 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. =

21. = 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? =

22. 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) = =

23. 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)