Lesson 6 Reteach - Weebly

Lesson 6 Reteach Solve Proportional Relationships ... You can also use cross products to solve proportions. ... Solve each proportion...

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Lesson 6 Reteach Solve Proportional Relationships A proportion is an equation that states that two ratios are equivalent. To determine whether a pair of ratios forms a proportion, use cross products. You can also use cross products to solve proportions.

Example 1 20 12 Determine whether the pair of ratios −− and −− form a proportion. 24 18 Find the cross products. 12  24 · 12 = 288 20 −−  −− 24 18  20 · 18 = 360

Since the cross products are not equal, the ratios do not form a proportion.

Example 2 k 12 Solve −− = −− . 30 70 k 12 −− = −− 30 70

Write the equation.

12 · 70 = 30 · k

Find the cross products.

840 = 30k

Multiply.

840 30k −−− = −−−

Divide each side by 30.

30

30

28 = k

Simplify.

Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

The solution is 28.

Exercises Determine whether each pair of ratios forms a proportion. 17 12 1. −− , −−

no

6 12 2. − , −−

yes

8 10 3. −− , −−

7 13 4. −− , −−

no

7 49 5. − , −−

yes

8 12 6. −− , −− no

10

5

15 32

4 12 7. − , −−

no

7 71

9 18

9 63

20 30 8. −− , −− 35 45

no

yes

12 15

24 28

18 3 9. −− ,− 24 4

yes

Solve each proportion. x 15 = −− 10. − 5

25

3

3 12 16 11. − = −− c 4

6 10 12. − = −− r 15 9 10 14 15.4 15. −− = −−

16 z = −− 13. −−

10

5 s 14. − = −−

w 2.8 = −− 16. −−

2.4

5 7 17. − y = −−−

24

6

15

7

8

12

16.8

7.5 12

Course 2 • Chapter 1 Ratios and Proportional Reasoning

t

11

x 7 3.5 18. −− = −− 18

36

13