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?

diagram. Rectangle partitioned into two unequal parts. 1 part shaded. Shaded portion is about 1 tenth of total rectangle. 

Make an estimate that is:

too low

about right

too high

Activity 1 Handy Number Lines

Problem 1

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

number line. 6 evenly spaced tick marks. First tick mark, 0. Point at second tick mark, 1 fifth. Last tick mark, 1.

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

Number line from 0 to 1. Evenly spaced by tenths. Point at 2 tenths.
number line. 16 evenly spaced tick marks. First tick mark, 0. Fourth tick mark, 3 fifteenths. Last tick mark, 1.
Number line. 20 tick marks. First tick mark, 0. Fourth tick mark, 4 twentieths. Twentieth tick mark, 1. 

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.

    Number line. Scale from 0 to 1,  4 evenly spaced tick marks. First tick mark, 0. Second, blank. Third, 2 thirds. Fourth, 1. Point located on 2 thirds.
    Number line. Scale, 0 to 1. 4 evenly spaced tick marks. First tick mark, 0. Last tick mark, 1.
    Number line. Scale, 0 to 1. 4 evenly spaced tick marks. First tick mark, 0. Last tick mark, 1.
    Number line. Scale, 0 to 1. 4 evenly spaced tick marks. First tick mark, 0. Last tick mark, 1.

  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 ?

    Number line. Scale 0 to 1.
    Number line. Scale 0 to 1.

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

Practice Problem

Problem 1

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