notes on ratios and proportions

1. RATIOS &
PROPORTIONS
Section 2.6 pages 111-118

2. Ratio
■ A comparison of two numbers by division
■ The ratio of x to y can be written as :
– 𝑥 𝑡𝑜 𝑦
– 𝑥: 𝑦
–
𝑥
𝑦

3. Proportion
■ Two ratios set equal to each other
■ Examples:
16
24
=
2
3
or
0.349
10,000
=
3.49
100,000

4. Means & Extremes
Given the proportion
𝑎
𝑏
=
𝑐
𝑑
rewrite in : form 𝑎: 𝑏 = 𝑐: 𝑑
𝑎: 𝑏 = 𝑐: 𝑑
Means
In the middle
Extremes
On the extreme outside
Multiply the Means = Multiply the Extremes

5. 𝑎
𝑏
=
𝑐
𝑑
𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑀𝑒𝑎𝑛𝑠𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝐸𝑥𝑡𝑟𝑒𝑚𝑒𝑠 =
𝑎𝑑 = 𝑏𝑐
Sometimes called “Cross Multiply”

6. Solve the proportion
𝑟
8
=
25
40
8 × 2540 × 𝑟 =
40𝑟 = 200
÷ 40 ÷ 40
𝑟 = 5

7. Solve the proportion
𝑥 − 2
14
=
2
7
14 × 27(𝑥 − 2)
7 𝑥 − 2 = 28
7𝑥 − 14 = 28
7𝑥 = 42
𝑥 = 6

8. In the past 2 years, a retailer has opened 232
stores. If the growth rate remains constant,
how many stores will the retailer open in the
next 3 years?
232 𝑠𝑡𝑜𝑟𝑒𝑠
2 𝑦𝑒𝑎𝑟𝑠
=
𝑋 𝑠𝑡𝑜𝑟𝑒𝑠
3 𝑦𝑒𝑎𝑟𝑠
𝑠𝑡𝑜𝑟𝑒𝑠
𝑦𝑒𝑎𝑟𝑠
696 = 2𝑋
348 = 𝑋
The retailer will open 348 stores in the next 3 years.

9. Homework
Page 114-117
#15-29 odds
#30-42