1. 3.6 Cross Products

2. In the proportion the products a  d and b  c are called cross products. You can solve a proportion for a missing value by using the Cross Products Property

3. Additional Example 3A: Solving Proportions
Solve the proportion.
Use cross products.
3(m) = 9(5)
3m = 45
Divide both sides by 3.
m = 15

4. Additional Example 3B: Solving Proportions
Solve the proportion.
Use cross products.
6(7) = 2(y – 3)
42 = 2y – 6
48 = 2y
Add 6 to both sides.
Divide both sides by 2.
24 = y

5. Check It Out! Example 3a
Solve the proportion. Check your answer.
Use cross products.
–5(8) = 2(y)
–40 = 2y
Divide both sides by 2.
–20 = y

6. Check It Out! Example 3a Continued
Solve the proportion. Check your answer.
Check
Substitute –20 for y. 
–2.5 –2.5

7. Check It Out! Example 3b
Solve the proportion. Check your answer.
Use cross product.
4(g + 3) = 5(7)
4g + 12 = 35
–12 –12
4g = 23
Subtract 12 from both sides.
Divide both sides by 4.
g = 5.75

8. Check It Out! Example 3b Continued
Solve the proportion. Check your answer.
Check
Substitute 5.75 for b. 

9. Another common application of proportions is percents
Another common application of proportions is percents. A percent is a ratio that compares a number to 100. For example, 25% =
You can use the proportion to
find unknown values.

10. Additional Example 4A: Percent Problems
Find 30% of 80.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x = 2400
Find the cross product. Since x is multiplied by 100, divide both sides to undo the multiplication.
x = 24
30% of 80 is 24.

11. Additional Example 4B: Percent Problems
230 is what percent of 200?
Method 2 Use an equation.
230 = x  200
Write an equation. Let x represent the percent.
230 = 200x
Since x is multiplied by 200, divide both sides by 200 to undo the multiplication.
1.15 = x
The answer is a decimal.
Write the decimal as a percent. This answer is reasonable; 230 is more than 100% of 200.
115% = x
230 is 115% of 200.

12. Additional Example 4C: Percent Problems
20 is 0.4% of what number?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
2000 = 0.4x
Cross multiply.
Since x is multiplied by 0.4, divide both sides by 0.4.
5000 = x
20 is 0.4% of 5000.

13. Check It Out! Example 4a
Find 20% of 60.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x = 1200
Find the cross product. Since x is multiplied by 100, divide both sides to undo the multiplication.
x = 12
20% of 60 is 12.

14. Check It Out! Example 4b
48 is 15% of what number?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
4800 = 15x
Find the cross product. Since x is multiplied by 15, divide both sides by 15 to undo the multiplication.
x = 320
48 is 15% of 320.

15. Proportions are used to create scale drawings and scale models
Proportions are used to create scale drawings and scale models. A scale is a ratio between two sets of measurements, such as 1 in.:5 mi. A scale drawing, or scale model, uses a scale to represent an object as smaller or larger than the actual object. A map is an example of a scale drawing.

16. Additional Example 5A: Scale Drawings and Scale Models
A contractor has a blueprint for a house drawn to the scale 1 in.:3 ft.
A wall on the blueprint is 6.5 inches long. How long is the actual wall?
Write the scale as a fraction.
Let x be the actual length.
Use cross products to solve.
x  1= 3(6.5)
x = 19.5
The actual length is 19.5 feet.

17. Additional Example 5B: Scale Drawings and Scale Models
A contractor has a blueprint for a house drawn to the scale 1 in.:3 ft.
A wall in the house is 12 feet long. How long is the wall on the blueprint?
Write the scale as a fraction.
Let x be the blueprint length.
Use cross products to solve.
x  3 = 1(12)
x = 4
The blueprint length is 4 inches.

18. A scale written without units, such as 32:1, means that 32 units of any measure corresponds to 1 unit of that same measure.
Reading Math

19. Check It Out! Example 5a
The actual distance between North Chicago and Waukegan is 4 mi. What is the distance between these two locations on the map?
Write the scale as a fraction.
Let x be the map distance.
18x = 4
Use cross products to solve.
x ≈ 0.2
The distance on the map is about 0.2 in.

20. Check It Out! Example 5b
A scale model of a human heart is 16 ft long. The scale is 32:1 How many inches long is the actual heart that the model represents?
Write the scale as a fraction.
Let x be the actual distance.
Use cross products to solve.
32x = 16
x = 0.5
The actual heart is 0.5 feet or 6 inches.

21. Lesson Quiz: Part l
1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there?
162
Find each unit rate. Round to the nearest hundredth if necessary.
2. Nuts cost $10.75 for 3 pounds.
$3.58/lb
3. Sue washes 25 cars in 5 hours.
5 cars/h
Solve each proportion. 4. 6 5. 16

22. Lesson Quiz: Part ll
6. Find 20% of 80. 16
7. What percent of 160 is 20?
12.5%
8. 35% of what number is 40?
114.3
9. A scale model of a car is 9 in. long. The scale is 1:18. How many inches long is the actual car the model represents?
162 in.