1. Bellwork 4/5
Do the Integrated Review
Page 567 (31-45 odd)

2. Today’s Objective
To be able to solve a proportion and use a proportion to solve a problem.

3. 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.

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

5. Black is to White as Red is to _________.
Proportional
Black is to White as Red is to _________.
Round is to Basketball as Oblong is to ________.
Green
Football

6. Proportional

7. Proportional

8. 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 3•8 = 4•6 or = 24

9. 4/y = 24/30 24y = 120 (cross multiply) 24y/24 = 120/24 y = 5
Solving a Proportion
4/y = 24/30
24y = 120 (cross multiply)
24y/24 = 120/24
y = 5

10. 3/y = 5/8 5y = 24 (cross multiply) 5y/5 = 24/5 y = 24/5
Solving a Proportion
3/y = 5/8
5y = 24 (cross multiply)
5y/5 = 24/5
y = 24/5

11. x/(x + 4) = 2/x x2 = 2(x + 4) (x multiply) x2 = 2x + 8 x2 - 2x - 8 = 0
Solving a Proportion
x/(x + 4) = 2/x
x2 = 2(x + 4) (x multiply)
x2 = 2x + 8
x2 - 2x - 8 = 0

12. x2 - 2x - 8 = 0 (x - 4)(x + 2) = 0 x - 4 = 0 & x + 2 = 0
Solving a Proportion
x2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
x - 4 = 0 & x + 2 = 0
x = 4 & x = -2

13. 3/y = 12/28 12y = 84 (cross multiply) 12y/12 = 84/12 y = 7
Solving a Proportion
Your Turn
3/y = 12/28
12y = 84 (cross multiply)
12y/12 = 84/12
y = 7

14. x(x + 7) = 10(x + 1) x2 + 7x = 10x + 10 x2 - 3x - 10 = 0
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

15. x2 - 3x - 10 = 0 (x - 5)(x + 2) = 0 x - 5 = 0 & x + 2 = 0
Solving a Proportion
x2 - 3x - 10 = 0
(x - 5)(x + 2) = 0
x - 5 = 0 & x + 2 = 0
x = 5 & x = -2

16. Classwork
Do Worksheet 11.1(1-18)
Homework page 565 (7-21)