Todays Objective

1
Todays Objective

• To be able to solve a proportion and use a
  proportion to solve a problem.

2
Ratio

• A ratio is a comparison of one value to another.
• Like a is to b or a/b or 1/2.
• In other words a ratio is a FRACTION like 3/4.

3
Proportion

• A proportion is a comparison of one ratio to
  another ratio, like a/b c/d.
• 3/4 6/8

4
Proportional

• Black is to White as Red is to _________.
• Round is to Basketball asOblong is to ________.

Green
Football
5
Proportional
6
Properties of Proportions

• 1.) If a/b c/d, then b/a d/c
• 3/4 6/8, then 4/3 8/6
• 2.) If a/b c/d, then ad bc
• 3/4 6/8, then 38 46 or
  24 24

7
Solving a Proportion

• 4/y 24/30
• 24y 120 (cross multiply)
• 24y/24 120/24
• y 5

8
Solving a Proportion

• 3/y 5/8
• 5y 24 (cross multiply)
• 5y/5 24/5
• y 24/5

9
Solving a Proportion

• x/(x 4) 2/x
• x2 2(x 4) (x multiply)
• x2 2x 8
• x2 - 2x - 8 0

10
Solving a Proportion

• x2 - 2x - 8 0
• (x - 4)(x 2) 0
• x - 4 0 x 2 0
• x 4 x -2

11
Solving a Proportion
Your Turn

• 3/y 12/28
• 12y 84 (cross multiply)
• 12y/12 84/12
• y 7

12
Solving a Proportion
Your Turn

• x/(x 1) 10/(x 7)
• x(x 7) 10(x 1)
• x2 7x 10x 10
• x2 - 3x - 10 0

13
Solving a Proportion

• x2 - 3x - 10 0
• (x - 5)(x 2) 0
• x - 5 0 x 2 0
• x 5 x -2