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Ratio tables and proportions


What is the ratio of greens to reds?

There are an infinite number of ratios that would correctly answer this question.

The table to the right shows some of them.

  • How are the two columns related to each other?
  • If there are 10 green tiles, how many reds would there be?

 You should see at least three relationships in this table:

Horizontal: Each value in the "green" column is multiplied by a constant to get the corresponding value in the "red" column.
Vertical: If the "green" value is multiplied by a number, then the "red" number is multiplied by the same number.
Addition: If two numbers in the "green" column are added together, then the corresponding "red" numbers also are added together.
All three tables show that there will be 30 reds if there are 10 greens.

 

Example 1

Use these three relationships to build a table that will answer this question:

A person who weighs 160 pounds on earth will weigh 416 pounds on Jupiter. If a person weighs 120 pounds on earth, how much would he weigh on Jupiter?
Earth Jupiter What was done
160 416  
40 104 divided by 4
120 312 multiplied by 3

A person who weighs 120 pounds on Earth would weigh 312 pounds on Jupiter.

 

 Example 2

There are 12 boys and 16 girls in a class. At that rate, how many boys would there be if there were 28 girls?
Boys Girls What was done
12 16  
6 8 divided by 2
3 4 divided by 2
21 28 multiplied by 7

If there were 28 girls in the class, then there would be 21 boys.

 

 

Self-Check

Question 1

 Three cups of water weigh 12 ounces. How heavy is 10 cups of water?

 

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Question 2

If five boys can eat 16 slices of pizza, then how many slices can 20 boys eat?

  

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Question 3

Martin can read 45 pages in 30 minutes. At this rate, how long will it take him to read a 300-page book?

 

 

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