1. 5-3 Solving Proportions Warm Up Problem of the Day Lesson Presentation
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 5-3 Solving Proportions Warm Up
Course 2
5-3
Solving Proportions
Warm Up
Determine whether the ratios are proportional. 5 8 15 24 1. ,
yes 12 15 16 25 2. , no 15 10 , 20 16 3. no 14 18 , 42 54 4.
yes

3. 5-3 Solving Proportions Problem of the Day
Course 2
5-3
Solving Proportions
Problem of the Day
If A = 1, B = 2, C = 3, D = 4, and so on, all the way to Z = 26, then what is A + B + C + D Z = ? (Hint: A + Z = B + Y.)
351

4. Course 2
5-3
Solving Proportions
Learn to solve proportions by using cross products.

5. Insert Lesson Title Here
Course 2
5-3
Solving Proportions
Insert Lesson Title Here
Vocabulary
cross product

6. 5 · 6 = 30 6 2 = 15 5 2 · 15 = 30 5-3 Solving Proportions
Course 2
5-3
Solving Proportions
For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a proportion.
5 · 6 = 30 = 2 5 6 15
2 · 15 = 30

7. 5-3 Solving Proportions a c In the proportion = , the cross products,
Course 2
5-3
Solving Proportions
CROSS PRODUCT RULE
In the proportion = , the cross products,
a · d and b · c are equal. a b c d
You can use the cross product rule to solve proportions with variables.

8. Additional Example 1: Solving Proportions Using Cross Products
Course 2
5-3
Solving Proportions
Additional Example 1: Solving Proportions Using Cross Products
Use cross products to solve the proportion. = m 5 9 15
15 · m = 9 · 5
The cross products are equal.
15m = 45
Multiply.
15m 15 = 45 15
Divide each side by 15 to isolate the variable.
m = 3

9. Insert Lesson Title Here
Course 2
5-3
Solving Proportions
Insert Lesson Title Here
Check It Out: Example 1
Use cross products to solve the proportion. 6 7 = m 14
7 · m = 6 · 14
The cross products are equal.
7m = 84
Multiply. 7m 7 84 7 =
Divide each side by 7 to isolate the variable.
m = 12

10. Course 2
5-3
Solving Proportions
When setting up a proportion to solve a problem, use a variable to represent the number you want to find. In proportions that include different units of measurement, either the units in the numerators must be the same and the units in the denominators must be the same or the units within each ratio must be the same.
16 mi
4 hr
8 mi
x hr
16 mi
8 mi
4 hr
x hr = =

11. Understand the Problem
Course 2
5-3
Solving Proportions
Additional Example 2: Problem Solving Application
If 3 volumes of Jennifer’s encyclopedia takes up 4 inches of space on her shelf, how much space will she need for all 26 volumes? 1
Understand the Problem
Rewrite the question as a statement.
Find the space needed for 26 volumes of the encyclopedia.
List the important information:
3 volumes of the encyclopedia take up 4 inches of space.

12. Additional Example 2 Continued
Course 2
5-3
Solving Proportions
Additional Example 2 Continued 2
Make a Plan
Set up a proportion using the given information. Let x represent the inches of space needed.
3 volumes
4 inches
26 volumes x
volumes
inches =

13. Additional Example 2 Continued
Course 2
5-3
Solving Proportions
Additional Example 2 Continued
Solve 3 3 4 26 x
Write the proportion. =
3 · x = 4 · 26
The cross products are equal.
3x = 104
Multiply. 3x 3
104 3
Divide each side by 3 to isolate the variable. = 2 3
x = 34 2 3
She needs 34
inches for all 26 volumes.

14. Additional Example 2 Continued
Course 2
5-3
Solving Proportions
Additional Example 2 Continued 4
Look Back
4 · 26 = 104 26 3 4 = 2 3 34
3 · 34 2 3 =
104
The cross products are equal, so 34 2 3
is the
answer

15. Understand the Problem
Course 2
5-3
Solving Proportions
Check It Out: Example 2
John filled his new radiator with 6 pints of coolant, which is the 10 inch mark. How many pints of coolant would be needed to fill the radiator to the 25 inch level? 1
Understand the Problem
Rewrite the question as a statement.
Find the number of pints of coolant required to raise the level to the 25 inch level.
List the important information:
6 pints is the 10 inch mark.

16. Check It Out: Example 2 Continued
Course 2
5-3
Solving Proportions
Check It Out: Example 2 Continued 2
Make a Plan
Set up a proportion using the given information. Let p represent the pints of coolant.
6 pints
10 inches p
25 inches
pints inches =

17. Check It Out: Example 2 Continued
Course 2
5-3
Solving Proportions
Check It Out: Example 2 Continued
Solve 3 6 10 p 25
Write the proportion. =
10 · p = 6 · 25
The cross products are equal.
10p = 150
Multiply.
10p 10
150 10
Divide each side by 10 to isolate the variable. =
p = 15
15 pints of coolant will fill the radiator to the 25 inch level.

18. Check It Out: Example 2 Continued
Course 2
5-3
Solving Proportions
Check It Out: Example 2 Continued 4
Look Back
10 · 15 = 150 6 10 15 = 25
6 · 25 = 150
The cross products are equal, so 15 is the answer.

19. Insert Lesson Title Here
Course 2
5-3
Solving Proportions
Insert Lesson Title Here
Lesson Quiz: Part I
Use cross products to solve the proportion. 25 20 45 t 1. =
t = 36 2. x 9 = 19 57
x = 3 2 3 r 36 3. =
r = 24 n 10 28 8 4. =
n = 35

20. Insert Lesson Title Here
Course 2
5-3
Solving Proportions
Insert Lesson Title Here
Lesson Quiz: Part II 5.
Carmen bought 3 pounds of bananas for $1.08. June paid $ 1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy?
5 pounds