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Preview. Warm Up. California Standards. Lesson Presentation. Warm Up. Determine whether the ratios are proportional. Evaluate the expression. (16 – 8)  3 + (100  10). 5 8. 15 24. ,. 1. yes. 16 25. 12 15. ,. 2. no. A. 2 B. 18 C. 34 D. 104. 15 10. 20 16. ,.

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slide1

Preview

Warm Up

California Standards

Lesson Presentation

slide2

Warm Up

Determine whether the ratios are proportional.

Evaluate the expression.

(16 – 8)  3 + (100  10)

5

8

15

24

,

1.

yes

16

25

12

15

,

2.

no

A. 2

B. 18

C. 34

D. 104

15

10

20

16

,

3.

no

14

18

42

54

,

yes

4.

slide3

California

Standards

Number Sense (NS1.3) - Use proportions to solve problems (e.g., determine the value of N if = , find the length of a side of a polygon similar to a known polygon).Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

Also covered: AF2.2, AF2.3

N 21

4 7

slide5

Vocabulary

cross product

slide6

For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product.

If the two ratios form a proportion, then the cross products are equal.

5 · 6 = 30

2 · 15 = 30

6

15

2

5

=

slide8

Example 1: Solving Proportions Using Cross Products

Use cross products to solve the proportion.

9

15

m

5

The cross products are equal.

=

15 · m = 9 · 5

Multiply.

15m = 45

15m

15

=

Divide each side by 15.

45

15

m = 3

slide9

Check It Out! Example 2

Use cross products to solve the proportion.

6

7

m

14

The cross products are equal.

=

7 · m = 6 · 14

Multiply.

7m = 84

Divide each side by 7 to isolate the variable.

7m

7

84

7

=

m = 12

slide10

Check It Out! Example 3

Use cross products to solve the proportion.

7

84

12

h

The cross products are equal.

=

7 · h = 84 · 12

Multiply.

7h = 1008

Divide each side by 7 to isolate the variable.

7h

7

1008

7

=

m = 144

slide11

Check It Out! Example 4

Use cross products to solve the proportion.

5

140

12

v

The cross products are equal.

=

5 · v = 140 · 12

Multiply.

5v = 1680

Divide each side by 5 to isolate the variable.

5v

5

1680

5

=

v = 336

slide12

Check It Out! Example 5

Use cross products to solve the proportion.

1.2

n

8

12

The cross products are equal.

=

1.2 · 12= 8 · n

Multiply.

14.4= 8n

Divide each side by 8 to isolate the variable.

14.4

8

8n

8

=

1.8= n

slide13

Check It Out! Example 6

Use cross products to solve the proportion.

n

9.3

6

8

The cross products are equal.

=

8 · n = 9.3 · 6

Multiply.

8n = 55.8

Divide each side by 8 to isolate the variable.

8n

8

55.8

8

=

n = 6.975

slide14

It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order.

16 mi

4 hr

8 mi

x hr

16 mi

8 mi

4 hr

xhr

=

=

16 mi

4 hr

8 hr

x mi

=

slide15

Example 9: Problem-Solving Application

A piglet can gain 3 pounds in 36 hours. If this rate continues, when will the piglet reach 18 pounds?

slide16

Example 10: Problem-Solving Application

S. Petey drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

slide17

Example 11: Problem-Solving Application

The ratio of dogs to cats at a kennel is exactly 4 to 5. If there are 36 dogs at the kennel, how many cats are at the kennel?

slide18

Example 12: Problem-Solving Application

Pho Toeh reduced a print that was 9 inches wide and 15 inches long. If the width of the reduction is 3 inches, what is the length?

slide19

Home Learning

On-Line Tutoring

slide20

x

9

19

57

=

2.

Lesson Quiz

Use cross products to solve each proportion.

45

t

25

20

1.

=

t = 36

x = 3

2

3

r

36

n

10

28

8

=

n = 35

3.

r = 24

4.

=

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