1. Lesson 2-6
Ratios & Proportions

2. Goals
Compare ratios.
Solve proportions.

3. Vocabulary ratio is a comparison of two numbers by division
proportion is an equation of two equal ratios
means are the middle terms of the proportion
extremes are the lowest and greatest terms of the proportion
In the proportion 𝑎 𝑏 = 𝑐 𝑑 , 𝑎 and 𝑑 are the extremes while 𝑏 and 𝑐 are the means

4. Vocabulary Continued
rate is a ratio of two measurements with different units
unit rate is a ratio of two quantities, the second of which is on 1 unit
scale model is a model to represent an object that is too large or too small to be built at actual size
scale is the relationship between the measurements on a drawing or model and the measurements of the real object

5. Means-Extremes Property of Proportion
In a proportion, the product of the extremes is equal to the product of the means. If 𝑎 𝑏 = 𝑐 𝑑 , then 𝑎𝑑=𝑏𝑐. 𝑏≠0 or 𝑑≠0 Since 3 6 = 5 10 , then 3 10 = 6 5 or 30=30 What is another name for this property that you have used in the past? Cross Multiply

6. Determine whether 10 12 & 15 18 are equivalent ratios
Simplify Each Ratio
Cross Multiply
10 12 ÷2 ÷2 = ÷3 ÷3 = 5 6
10 12 = = =180 Is a proportion

7. Use cross products to determine whether the pairs of ratios below forms a proportion
≟ ≟ ≠0.75 Not a proportion
2 2.5 ≟ ≟ =80 Is a proportion

8. Solve the Proportions (round to hundredth if necessary)
5 𝑎 = 𝑎= 𝑎=9
𝑚 3 = 8 7 7𝑚= 𝑚= … 𝑚≈3.25

9. Solve the Proportions (round to hundredth if necessary)
14 49 = 𝑥 7 49𝑥= 𝑥=2
7 9 = 8 𝑢 7𝑢= 𝑚= … 𝑚≈10.29

10. Real-World Example: Rate & Time
Monica paints a room that has 400 square feet of wall space in hours. At this rate, how long will it take her to paint a room that has 720 square feet of wall space?
= 720 ℎ 400ℎ= ℎ=4.5 hours

11. Real-World Example: Scale & Maps
On a road atlas, the scale for the map of Indiana is 5 𝑖𝑛𝑐ℎ𝑒𝑠 = 41 𝑚𝑖𝑙𝑒𝑠. What is the distance in miles represented by 3 𝑖𝑛𝑐ℎ𝑒𝑠 on the map?
5 41 = 3 𝑚 5𝑚= 𝑚=24.6 𝑚𝑖𝑙𝑒𝑠

12. Assignment
2-6 Skills Practice #1-25 Odds Do on a separate sheet of paper. Not on the worksheet.