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4-1 Ratios and Proportions

Objective: To determine if two ratios are equal and to solve proportions.

NEW STAMP LOG!

Vocabulary•Ratio: A comparison of 2 numbers using

division

▫Examples:

•Proportion: An equation stating that two ratios are equal

▫Examples:

22 :1 2 1

1to

5 1

10 23

4 2

x

Examples1. Write the ratio of “x to y”.

2. If there are 12 cats and 4 dogs, write the ratio of:1. Cats to Dogs

2. Dogs to Cats

Sidenote: You can (and should) reduce a ratio!!!

x

y

12

44

12

3

11

3

Comparing Ratios

•To tell if two ratios are equivalent (create a proportion), find the cross product.

6 22

8 28

6•28 8•22

168 176≠

Answer: Not a proportion

TOO: Is it a proportion?1) 2)

Answers:1)Yes2)No

4 16

5 20

8 16

9 17

Proportion: We already know that the fractions are equal•Solve the Proportion

CROSS MULTIPLY

No more fractions!

6x

24 4x4

3

4 8

x

4

(8)(3) = (4)(x)

TOO: Solve the proportion

1) 2)

Answers:1)a = 92)y = -63/16

3

45 15

a 7

9 16

y

Example

•Cross Multiply

•Distribute

•Solve

3 2

5 6

x

5 10 18x 10 105 8x 5 5

8

5x

5(x + 2) = (3)(6)

Try with me1) 2) 3)

Answers:1) w = 52) x = -103) x = 9

2 7

5 5

w 3 6

10 5

x

2 10

3 5 x

TOO: Watch your Negatives!!!

1) 2) 3)

Answers:1) r = 3/52) y = -13/43) x = -7/4

7 12

4 6

r r

2 5

6 2

y y

10 6

2 4x x

Homework

•Pg. 199 # 14 - 34