Equivalent Ratios

New York State Common Core Math Grade 6, Module 1, Lesson 3

Download Worksheet for Common Core Grade 6, Module 1, Lesson 3

Video solutions to help Grade 6 students learn about equivalent ratios.

Lesson 3 Student Outcomes

• Students develop an intuitive understanding of equivalent ratios by using tape diagrams to explore possible quantities of each part when given the part-to-part ratio.
• Students use tape diagrams to solve problems when the part-to-part ratio is given and the value of one of the quantities is given.
• Students formalize a definition of equivalent ratios: Two ratios, A:B: and C:D , are equivalent ratios if there is a positive number, c, such that C = cA and D = cB.

The following diagram shows how to use tape diagrams to solve equivalent ratio problems. Scroll down the page for more examples and solutions.

 

Lesson 3 Summary

• Two ratios and are equivalent ratios if there is a positive number, c, such that C = cA and D = cB.
• Ratios are equivalent if there is a positive number that can be multiplied by both quantities in one ratio to equal the corresponding quantities in the second ratio.
• This description can be used to determine whether two ratios are equivalent.

Lesson 3
Exercise 1
Write a one-sentence story problem about a ratio.
Write the ratio in two different forms.

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Exercise 2
Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.
Draw a tape diagram to represent this ratio.

Exercise 3
Mason and Laney ran laps to train for the long-distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3.
a. If Mason ran 4 miles, how far did Laney run? Draw a tape diagram to demonstrate how you found the answer.
b. If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine how you found the answer.
c. What ratios can we say are equivalent to 2:3?

Exercise 4
Josie took a long multiple-choice, end-of-year vocabulary test. The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9.
a. If Josie missed 8 questions, how many did she get right? Draw a tape diagram to demonstrate how you found the answer.
b. If Josie missed 20 questions, how many did she get right? Draw a tape diagram to demonstrate how you found the answer. c. What ratios can we say are equivalent to 2:9?
d. Come up with another possible ratio of the number Josie got wrong to the number she got right.
e. How did you find the numbers?
f. Describe how to create equivalent ratios.

Problem Set

1. Write two ratios that are equivalent to 1:1.
2. Write two ratios that are equivalent to 3:11.
3. a. The ratio of the width of the rectangle to the height of the rectangle is ____ to ____.
   b. If each square in the grid has a side length of 8 mm, what is the length and width of the rectangle?
4. For a project in their health class, Jasmine and Brenda recorded the amount of milk they drank every day. Jasmine drank 2 pints of milk each day, and Brenda drank 3 pints of milk each day.
   a. Write a ratio of number of pints of milk Jasmine drank to number of pints of milk Brenda drank each day.
   b. Represent this scenario with tape diagrams.
   c. If one pint of milk is equivalent to 2 cups of milk, how many cups of milk did Jasmine and Brenda each drink? How do you know?
   d. Write a ratio of number of cups of milk Jasmine drank to number of cups of milk Brenda drank.
   e. Are the two ratios you determined equivalent? Explain why or why not.

Lesson 3 Ratio Word Problem
For every $5 that Mrs. Cramer spends, Mrs. Erno spends $7.
a. Determine a ratio to describe the money that Mrs. Cramer spent to the money that Mrs. Erno spent.
b. If Mrs. Erno spends $84, how much did Mrs. Cramer spend?

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