Lesson 2-6 Ratios & Proportions

Goals Compare ratios. Solve proportions.

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

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

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

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

Use cross products to determine whether the pairs of ratios below forms a proportion 0.25 0.6 ≟ 1.25 2 2 0.25 ≟ 0.6 1.25 0.5≠0.75 Not a proportion 2 2.5 ≟ 32 40 32 2.5 ≟ 2 40 80=80 Is a proportion

Solve the Proportions (round to hundredth if necessary) 5 𝑎 = 30 54 30𝑎= 5 54 30 30 𝑎=9 𝑚 3 = 8 7 7𝑚=24 7 7 𝑚=3.248571426… 𝑚≈3.25

Solve the Proportions (round to hundredth if necessary) 14 49 = 𝑥 7 49𝑥= 7 14 49 49 𝑥=2 7 9 = 8 𝑢 7𝑢=72 7 7 𝑚=10.28571429… 𝑚≈10.29

Real-World Example: Rate & Time Monica paints a room that has 400 square feet of wall space in 2 1 2 hours. At this rate, how long will it take her to paint a room that has 720 square feet of wall space? 400 2.5 = 720 ℎ 400ℎ=1800 400 400 ℎ=4.5 hours

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=123 5 5 𝑚=24.6 𝑚𝑖𝑙𝑒𝑠

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