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

2. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Warm Up
Find the unit rate.
1. 18 miles in 3 hours
2. 6 apples for $3.30
3. 3 cans for $0.87
4. 5 CD’s for $43
6 mi/h
$0.55 per apple
$0.29 per can
$8.60 per CD

3. Vocabulary 5-4 Identifying and Writing Proportions equivalent ratios
Course 2
5-4
Identifying and Writing Proportions
Vocabulary
equivalent ratios
proportion

4. Quick activity
In your group measure the length and width of each others heads. Length= Width=

5. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Students in Mr. Howell’s math class are measuring the width w and the length l of their heads. The ratio of l to w is 10 inches to 6 inches for Jean and 25 centimeters to 15 centimeters for Pat.

6. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions 10 6 25 15
These ratios can be written as the
fractions and . Since both simplify
to , they are equivalent. Equivalent
ratios are ratios that name the same comparison. 5 3

7. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 10 6 25 15 10 6 25 15 =
Read the proportion by saying “ten is to six
as twenty-five is to fifteen.”
Reading Math 10 6 = 25 15

8. Additional Example 1A: Comparing Ratios in Simplest Forms
Course 2
5-4
Identifying and Writing Proportions
Additional Example 1A: Comparing Ratios in Simplest Forms
Determine whether the ratios are proportional. 24 51 , 72
128
Simplify . 24 51
24 ÷ 3
51 ÷ 3 = 8 17
72 ÷ 8
128 ÷ 8 = 9 16
Simplify 72
128 8 17
Since = , the ratios are not proportional. 9 16

9. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Check It Out: Example 1A
Determine whether the ratios are proportional. 54 63 , 72
144
Simplify . 54 63
54 ÷ 9
63 ÷ 9 = 6 7
72 ÷ 72
144 ÷ 72 = 1 2
Simplify 72
144 6 7
Since = , the ratios are not proportional. 1 2

10. Identifying and Writing Proportions
Course 2
5-4
Identifying and Writing Proportions
Check It Out: Example 1B
Determine whether the ratios are proportional.
135 75 , 9 4
135 ÷ 15
75 ÷ 15 = 9 5
Simplify
135 75 9 4
is already in simplest form. 9 4 9 5
Since = , the ratios are not proportional. 4

11. Identifying and Writing Proportions Insert Lesson Title Here
Course 2
5-4
Identifying and Writing Proportions
Insert Lesson Title Here
Lesson Quiz:
In pre-school, there are 5 children for every
one teacher. In another preschool there are 20 children for every 4 teachers. Determine whether the ratios of children to teachers are proportional in both preschools. 20 4 5 1 =

12. 5-5 Solving Proportions Quick check
Course 2
5-5
Solving Proportions
Quick check
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

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

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

15. 5 · 6 = 30 6 2 = 15 5 2 · 15 = 30 5-5 Solving Proportions
Course 2
5-5
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

16. 5-5 Solving Proportions a c In the proportion = , the cross products,
Course 2
5-5
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.

17. Additional Example 1: Solving Proportions Using Cross Products
Course 2
5-5
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

18. Insert Lesson Title Here
Course 2
5-5
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

19. Understand the Problem
Course 2
5-5
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.

20. Additional Example 2 Continued
Course 2
5-5
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 =

21. Additional Example 2 Continued
Course 2
5-5
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.

22. Additional Example 2 Continued
Course 2
5-5
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

23. Understand the Problem
Course 2
5-5
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.

24. Check It Out: Example 2 Continued
Course 2
5-5
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 =

25. Check It Out: Example 2 Continued
Course 2
5-5
Solving Proportions
Check It Out: Example 2 Continued
Solve 3 6 10 p 25
Write the proportion. =
10 · x = 6 · 25
The cross products are equal.
10x = 150
Multiply.
10x 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.

26. Check It Out: Example 2 Continued
Course 2
5-5
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.

27. Insert Lesson Title Here
Course 2
5-5
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

28. Insert Lesson Title Here
Course 2
5-5
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