2. 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

3. 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.

4. 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.

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

6. Write and solve a proportion
EXAMPLE 3
Write and solve a proportion
Seals
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 ?
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

7. 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.

8. Solve the proportion. Check your solution.
EXAMPLE 1
GUIDED PRACTICE
for Examples 1,2, and 3
Solve the proportion. Check your solution. = 4 a 24 30 1. = 4 a 24 30
Write original proportion.
= a 24
Cross products property
120 = 24a
Simplify.
5 = a
Divide each side by 24.
The solution is 5. Check by substituting 5 for a in the original proportion.
ANSWER

9. Use the cross products property for Examples 1,2, and 3
GUIDED PRACTICE
Use the cross products property
for Examples 1,2, and 3
CHECK 4 5 24 30 = ?
Substitute 5 for a.
30 4 = 24 5 ?
Cross products property
120 = 120
Simplify. Solution checks.

10. The value of x is 18. Check by substituting 18 for x in the
EXAMPLE 2
GUIDED PRACTICE
for Examples 1,2, and 3 3 x = 2
– 6 2. 3 x = 2
– 6
Write original proportion.
3(x – 6) = 2 x
Cross products property
3x – 18 = 2x
Distrubutive property
18 = x
Subtract 3x from each side.
The value of x is 18. Check by substituting 18 for x in the
original proportion.
ANSWER

11. EXAMPLE 1 GUIDED PRACTICE for Examples 1,2, and 3 CHECK 3 18 2 18 – 6= ?
Substitute 18 for x.
3(18 – 6) = 18 2 ?
Cross products property
54 – 18 = 36 ?
Simplify
36 = 36
Simplify. Solution checks.

12. EXAMPLE 2 GUIDED PRACTICE for Examples 1,2, and 3 4 m 5 = m – 6 3. m 5
Write original proportion.
m 4 = 5(m – 6)
Cross products property
4m = 5m – 30
Simplify
m = 30
Subtract 5m from each side.

13. EXAMPLE 3 GUIDED PRACTICE for Examples 1,2, and 3
WHAT IF? In Example 3, suppose the seal weights 260 pounds. How much food should the seal be fed per day?
SOLUTION
STEP 1
Write a proportion involving two ratios that compare the amount of food with the weight of the seal. 8
100 x
260 =
amount of food
weight of seal

14. Write and solve a proportion for Examples 1,2, and 3
GUIDED PRACTICE
Write and solve a proportion
for Examples 1,2, and 3
STEP 2
Solve the proportion. 8
100 x
260 =
Write proportion.
= 100 x
Cross products property
2080 = 100x
Simplify.
20.8 = x
Divide each side by 100.
ANSWER
A 260 pound seal should be fed 20.8 pounds of food per
day.

15. 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.

16. Use the scale on a map EXAMPLE 4
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.

17. 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.
SOLUTION
It is about km

18. 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.

19. The actual length of the Queen Elizabeth II is about 960 feet.
EXAMPLE 4
Use the scale on a map
GUIDED PRACTICE
for Example 4
SOLUTION
Write and solve a proportion to find the length l of the Queen Elizabeth II. 1
600 =
1.6 l
1 . l =
Cross products property
l = 960
Simplify.
ANSWER
The actual length of the Queen Elizabeth II is about 960 feet.