1. 7-4 Solving Proportions Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

2. 7-4 Solving Proportions Warm Up
Pre-Algebra
7-4
Solving Proportions
Warm Up
Find two ratios that are equivalent to each given ratio.
Possible answers: 3 5 9 15 6 10 , 10 12 5 6 , 20 24 1. 2. 45 30 3 2 , 90 60 8 9 16 18 , 24 27 3. 4.

3. Problem of the Day
Replace each • with a digit from 1 to 7 to write a proportion. Use each digit once. The digits 2 and 3 are already shown. •• • 23 = 14 7 23 56 =
Possible answer:

4. Learn to solve proportions.

5. Vocabulary
cross product

6. Unequal masses will not balance on a fulcrum if they are an equal distance from it; one side will go up and the other side will go down.
Unequal masses will balance when the following proportions is true:
mass 2
length 1
mass 1
length 2 =
Mass 1
Mass 2
Fulcrum
Length 1
Length 2

7. One way to find whether ratios, such as those above, are equal is to find a common denominator. The ratios are equal if their numerators are equal after the fractions have been rewritten with a common denominator. 72 96 6 8 = 72 96 9 12 = 9 12 6 8 =

9. The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators.
Helpful Hint

10. Additional Example 1A: Using Cross Products to Identify Proportions
Tell whether the ratios are proportional. 4 10 6 15 = ? A. 4 10 6 15 60
Find cross products. 60
60 = 60
Since the cross products are equal, the ratios are proportional.

11. Additional Example 1B: Using Cross Products to Identify Proportions
A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?
4 parts gasoline
1 part oil = ?
15 quarts gasoline
5 quarts oil
Set up ratios.
Find the cross
products.
4 • 5 = 20
1 • 15 = 15
20 ≠ 15
The ratios are not equal. The mixture will not be correct.

12. = Try This: Example 1A Tell whether the ratios are proportional. 2 4 510 = ? A. 2 4 5 10 20
Find cross products. 20
20 = 20
Since the cross products are equal, the ratios are proportional.

13. Try This: Example 1B
A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct?
3 parts tea
1 part sugar = ?
12 tablespoons tea
4 tablespoons sugar
Set up ratios.
Find the cross
products.
3 • 4 = 12
1 • 12 = 12
12 = 12
The ratios are equal. The mixture will be correct.

14. When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

15. Additional Example 2: Solving Proportions
Solve the proportion. 5 6 p 12 =
6p = 12 • 5
Find the cross products.
6p = 60
Solve.
; the proportion checks. 5 6 10 12 =
p = 10

16. Find the cross products.
Try This: Example 2
Solve the proportion. 2 3 14 g =
14 • 3 = 2g
Find the cross products.
42 = 2g
Solve.
; the proportion checks. 2 3 14 21 =
21 = g

17. Additional Example 3: Physical Science Application
Allyson weighs 55 lbs and sits on a seesaw 4 ft away from its center. If Marco sits 5 ft away from the center and the seesaw is balanced, how much does Marco weigh?
mass 1
length 2 =
mass 2
length 1
Set up the proportion.
Let x represent Marco’s weight. x 4 55 5 =
55 • 4 = 5x
Find the cross products.
220 = 5x
Multiply. 5x 5
220 =
Solve. Divide both sides by 5.
44 = x
Marco weighs 44 lb.

18. Try This: Example 3
Robert weighs 90 lbs and sits on a seesaw 5 ft away from its center. If Sharon sits 6 ft away from the center and the seesaw is balanced, how much does Sharon weigh?
mass 1
length 2 =
mass 2
length 1
Set up the proportion.
Let x represent Sharon’s weight. x 5 90 6 =
90 • 5 = 6x
Find the cross products.
450 = 6x
Multiply. 6x 6
450 =
Solve. Divide both sides by 5.
75 = x
Sharon weighs 75 lb.

19. = = = = Lesson Quiz Tell whether each pair of ratios is proportional.48 42 = ? 16 14 20 15 = ? 3 4 1.
yes 2. no
Solve each proportion. 45 18 n 12 = n 24 6 9 = 3.
n = 30 4.
n = 16
5. Two weights are balanced on a fulcrum. If a 6lb weight is positioned 1.5 ft from the fulcrum, at what distance from the fulcrum must an 18 lb weight be placed to keep the weights balanced?
0.5 ft