1. Warm-up: Solve the proportion.
2.7 Solving Proportions Using Cross Products Essential Question: How do you solve proportions using cross products?
Warm-up: Solve the proportion.
Common
Core
CC.9-12.A.CED.1
CC.9-12.A.REI.3 1. 2. 3. 4.
3(2x – 1) – 11 = -2(1- x )
7x – 29 – 21x = 3 – (12 + 2x)

2. 2.6 Exercises 2-54 even 2) ½ , 1:2, 1 to 2 35 26) 36 28) 1
4) yes ) no, 7 to 8
8) ) ) 5
14) ) ) 56
20) B ) Multiply each side by 10, not one side by 10 and the other side by 20
) ) 1
) ) 2
) ) 19
42) ) yes
46) 7/ ) 3/ ) 21 pages
a) 70.3 ft b)
54)
Width (ft)
Length (ft) 20 37 25
46.25 30
55.5 35
64.75 40 74 a) b)
c. Your friend

3. Cross Products Property
Words The cross products of a proportion are equal.
Example 3 4 = 6 8
Algebra

4. Use the cross products property
EXAMPLE 1
Use the cross products property
Solve the proportion = 8 x 6 15 = 8 x 6 15
Write original proportion.
8 15 = x 6
Cross products property
120 = 6x
Simplify.
20 = x
Divide each side by 6.
The solution is 20. Check by substituting 20 for x in the original proportion.
ANSWER

5. Use the cross products property
EXAMPLE 1
Use the cross products property
CHECK 8 20 6 15 = ?
Substitute 20 for x.
8 15 = 20 6 ?
Cross products property
120 = 120
Simplify. Solution checks.

6. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice
What is the value of x in the proportion = ? 4 x 8 3
x – C 3 A
– 6 B
– 3 D 6
SOLUTION 4 x = 8
– 3
Write original proportion.
4(x – 3) = x 8
Cross products property
4x – 12 = 8x
Simplify.
–12 = 4x
Subtract 4x from each side.
–3 = x
Divide each side by 4.

7. EXAMPLE 2
Standardized Test Practice
The value of x is –3. The correct answer is B.
ANSWER A B C D

8. Write and solve a proportion
EXAMPLE 3
Write and solve a proportion
Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds.
How much food should the seal be fed per day?
Seals
SOLUTION
STEP 1
Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x
280 = 8
amount of food
100
weight of seal

9. Write and solve a proportion
EXAMPLE 3
Write and solve a proportion
STEP 2
Solve the proportion. 8
100 x
280 =
Write proportion.
= 100 x
Cross products property
2240 = 100x
Simplify.
22.4 = x
Divide each side by 100.
ANSWER
A 280 pound seal should be fed 22.4 pounds of food per
day.

10. EXAMPLE 1
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the proportion. Check your solution. = 4 a 24 30 1. 5
ANSWER

11. EXAMPLE 2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the proportion. Check your solution. 3 x = 2
– 6 2. 18
ANSWER

12. EXAMPLE 2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the proportion. Check your solution. 4 m 5 =
m – 6 3. 18
ANSWER

13. EXAMPLE 3
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the proportion. Check your solution.
WHAT IF? In Example 3, suppose the seal weighs 260 pounds. How much food should the seal be fed per day? 4.
20.8
ANSWER

14. EXAMPLE 4
Use the scale on a map
Maps
Use a metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati.
SOLUTION
From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters.

15. Cross products property
EXAMPLE 4
Use the scale on a map
Write and solve a proportion to find the distance d between the cities. =
4.2 d 1
centimeters 85
kilometers
1 d =
Cross products property
d = 357
Simplify.
ANSWER
The actual distance between Cleveland and Cincinnati is about 357 kilometers.

16. EXAMPLE 4
Use the scale on a map
GUIDED PRACTICE
for Example 4 5.
Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland.
about km
ANSWER

17. EXAMPLE 4
Use the scale on a map
GUIDED PRACTICE
for Example 4
Model ships 6.
The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.
ANSWER
about 960 ft

18. Classwork/homework
3.6 Practice B