Lesson 8 Equivalent Fractions on the Number Line

• Let’s use number lines to reason about equivalent fractions.

Warm-up Estimation Exploration: A Shaded Portion

If the entire diagram represents 1 whole, about what fraction is shaded?

Make an estimate that is:

too low

too high

Problem 1

Andre used number lines to find fractions that are equivalent to . He drew this number line:

Then, he drew three more lines and wrote a fraction for the point on each line:

How did Andre use the number lines to find fractions equivalent to ? Explain your thinking to a partner.

Problem 2

How can number lines be used to show whether the following fractions are equivalent?

1. and

2. and

Problem 3

Find three fractions that are equivalent to . Explain or show how Andre’s number lines can help.

Activity 2 Can It Be Done?

1. Priya wants to find fractions that are equivalent to , other than . She wonders if she can find equivalent fractions with denominator 9, 10, and 12.

Can it be done? Use number lines to show your reasoning.

2. Represent on a number line. Then, find two fractions that are equivalent to . How would you use the number line to show that they are equivalent to ?

3. Can you find an equivalent fraction for with 100 for the denominator? Explain or show your reasoning.

Problem 1

Which of these could be the fraction that the point represents? Explain your reasoning.