**Grade 6 Module 1** Lesson 3

**Equivalent Ratios** • Understanding of equivalent ratios. • Use tape diagrams • Formalize a definition of equivalent ratios

**Exercise 1** • Write a one-sentence story problem about a ratio.

**Sample** The ratio of the number of sunny days to the number of cloudy days in this city is 3:1.

**Exercise 1** Write the ratio in two different forms

**Answers** • 3:1 3 to 1

**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.

**Represent ratio in a table**

**Represent ratio in a table**

**Represent ratio in a table**

**Tape Diagram** Shanni Mel

**Tape Diagram** What does each unit on the tape diagram represent?

**Tape Diagram** What if each unit on the tape diagrams represent 1 inch? What are the lengths of the ribbons? What is the ratio of the lengths of the ribbons?

**Tape Diagram** What if each unit on the tape diagrams represents 2 meters? What are the lengths of the ribbons? How did you find that?

**Tape Diagram** What is the ratio of the lengths of Shanni’s ribbon to the length of Mel’s ribbon now? What if each unit represents 3 inches? What are the lengths of the ribbons? Record

**Tape Diagram** If each of the units represents 3 inches, what is the ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon?

**Tape Diagrams** We just explored three different possibilities for the length of the ribbon; did the number of units in our tape diagrams ever change? What did these 3 ratios, 7:3, 14:6, 21:9, all have in common?

**Tape Diagram** Mathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3?

**Tape Diagram** Draw a tape diagram to represent this ratio: 7:3 7 inches to 3 inches 14:6 14 meters to 6 meters 21:9 21 inches to 9 inches

**Tape Diagram** Shanni Mel 7 inches to 3 inches 7:3

**Tape Diagram** Shanni Mel 14 inches to 6 inches 14:6

**Tape Diagram** Shanni Mel 21 inches to 9 inches 21:9

**Exercise 3 (a)** Mason Laney

**Exercise 3 (a)** Mason = 4 miles Laney = 6 miles

**Exercise 3 (a)** Mason = 4 miles Laney = 6 miles

**Exercise 3 (b)** Mason = 620 m Laney = 930 m

**Exercise 3 (b)** Mason = 620 m Laney = 930 m

**Exercise 3(c)** What ratios can we say are equivalent to 2:3?

**Exercise 3(c)** 4:6 and 620:930

**Exercise 4(a)** Wrong = 8 Right = ?

**Exercise 4(a)** Wrong = 8 Right = 36

**Exercise 4(b)** Wrong = 20 Right = ?

**Exercise 4(b)** Wrong = 20 Right = 90

**Exercise 4(d)** Wrong = Right = ?

**Closing** Two ratios A:B and C:D 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.