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Name:__________________________________________ Date:__________ Period:______
Four Methods to Solve Proportions
Problem:
Apples are on sale for 2 lbs for $3. How many pounds can you buy for $30?
Question 1: Is this a proportional situation? Why or why not?
Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Unit Rate: How many pounds for $30: Method III: Graph a point to represent the original ratio. How many pounds can you buy for $0? Record this additional point on the graph and connect the two points. Extend the line to predict how many pounds you can buy for $30. What is the slope of this line? How many pounds for $30? Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent number of dollars and p to represent number of pounds). Use this equation to calculate how many pounds for $30. Equation: How many pounds for $30: Pounds Dollars
Name:__________________________________________ Date:__________ Period:______ Problem:
Mary runs 5 km in 75 minutes. How long will it take her to run 2 km?
Question 2: Is this situation proportional? Why or why not?
Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how long it will take her to run 2 km. Unit Rate: How long to run 2 km: Method III: Graph a point to represent the original ratio. How far did she run in 0 minutes? Record this additional point on the graph and connect the two points. Extend the line to predict how long it will take to run 2 km. What is the slope of this line? How long will it take to run 2 km? Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent distance and t to represent time). Use this equation to calculate how long it will take her to run 2km. Equation: How long will it take to run 2 km? Kilometers Time (mins)
Name:__________________________________________ Date:__________ Period:______ 24
Situation/Question
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Unit Rate Table
Other/Equation Proportion
Situation/Question
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Unit Rate Table
Other/Equation
24 s for $14. or 6 for $3.
Proportion
Name:__________________________________________ Date:__________ Period:______ Comparing Methods
- Which of the four methods is easiest for you? Why?
- What are the benefits to using each method?
ANSWER KEY
Problem: Apples are on sale for 2 lbs for $3. How many pounds can you buy for $30? Question 1: Are these data proportional or not proportional? Why or why not? Yes, the data are proportional because the ratio between pounds and the cost is constant. Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Unit Rate (how much for 1 pound): How many pounds for $30: $ 1. 50 1 ๐๐
Method III: Graph a point to represent the original ratio. How many pounds can you buy for $0? Record this additional point on the graph and connect the two points. Extend the line to predict how many pounds you can buy for $30. What is the slope of this line? . / How many pounds for $30? 20 lbs Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent dollars and p to represent pounds). Use this equation to calculate how many pounds for $30. Equation: ๐ = 1. 50 ๐ How many pounds for $30: 30 = 1. 50 ๐ 20 = ๐
Pounds Dollars 2 lbs $ x lbs $ 2 3
60 = 3 ๐ฅ by cross products 20 = ๐ฅ $. / 345
$ 6. 78 6 34 $1.50/lb
Problem: Mary runs 5 km in 75 minutes. How long will it take her to run 2 km? Question 2: Are these data proportional or not proportional? Why or why not? Yes, they are proportional. Method I: Draw a double-sided number line , label the parts, set up a proportion and solve. Method II: Using any method, calculate unit rate and then calculate how long it will take her to run 2 km. Unit Rate (how long for 1 km): 97 :;< 7 =:
67 :;< 6 =: 15 min/km How long to run 2 km: 15 ๐๐๐๐ 1 ๐๐
Method III: Graph a point to represent the original ratio. How far did she run in 0 minutes? Record this additional point on the graph and connect the two points. Extend the line to predict how long it will take to run 2 km. What is the slope of this line? 15 How long will it take to run 2 km? 30 mins Method IV: Using the constant of proportionality (unit rate), write an equation to represent the original ratio (use d to represent distance and t to represent time). Use this equation to calculate how long it will take her to run 2 km. Equation: ๐ก = 15 ๐ How long will it take to run 2 km? ๐ก = 15 2 ๐ก = 30
x minutes 2 km 75 minutes 5 km Time Distance ๐ฅ ๐๐๐๐ 2 ๐๐
