1. Aim: How do we solve proportion problems?
PROPORTIONS

2. Aim: How do we solve proportion problems?
RATIO REVIEW
Ratio - comparison between 2 numbers by division.
*Note: To find the ratio of 2 quantities, both quantities must be expressed in the same unit of measure before finding their quotient. For example, to compare the value of a nickel to a penny, we first convert the nickel to 5 pennies and then find the ratio, which is 5:1 (i.e. a nickel is worth 5 times as much as a penny).

3. Aim: How do we solve proportion problems?
Proportion - an equation that states that two ratios are equal
(AKA: equivalent ratios)
a and d are called extremes (1st and 4th terms, 'outers');
b and c are called means (2nd and 3rd, 'inners')
Note: In a proportion, the product of the means is equal
to the product of the extremes

4. Aim: How do we solve proportion problems?
Using your knowledge of ratios, what is another way you can write this proportion?
a : b = c : d

5. Aim: How do we solve proportion problems?
A 6-foot man casts a 10-foot shadow. How many
feet tall is a nearby tree that casts a 50-foot shadow
at the same time?
= x
= 10 x
x= 30 ft

6. Aim: How do we solve proportion problems?
Is 5 ­4 16 20 =
a "TRUE" proportion?
To check, you can:
a) Multiply the means and the extremes to see if they are equivalent
b) Reduce each ratio to simplest form to see if they become the same
c) Use a calculator to find the decimal form of each ratio
NO, not a proportion because
-4(20) = 5(16)
-80 = 80

7. Aim: How do we solve proportion problems?
GUIDED PRACTICE 3. 1. 4.
2. 25:x = 5:2

8. Aim: How do we solve proportion problems?
GUIDED PRACTICE 3.
2x(n) = 4r(m)
2xn = 4rm
2n n
x= 2rm n 1.
4(42) = 6(x)
168 = 6x
28 = x 2. 4.
25 = 5 x
50 = 5x
250 = 25x
10 = x
3(x-3) = x+7
3x-9 = x+7
2x = 16
x = 8

9. Aim: How do we solve proportion problems?
INDEPENDENT PRACTICE
CHALLENGE:
7x-1 5 =
3x+3 3

10. Aim: How do we solve proportion problems?
INDEPENDENT PRACTICE
yes
yes no
We will go over these in class
CHALLENGE:
7x-1 5 =
3x+3 3

11. HW textbook pg. 146: 18, 22, 44, 48