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8.09 Equivalent fractions on a number line

Lesson

Are you ready?

Remembering how to compare fractions will help you solve problems in this lesson. Let's give this problem a try.

Think about the fractions $\frac{1}{4}$14 and $\frac{1}{5}$15.

  1. Plot the number $\frac{1}{4}$14 on the number line.

    01

  2. Plot the number $\frac{1}{5}$15 on the number line.

    01

  3. The two numbers can be shown on the same number line like this:

    Which number is smaller?

    $\frac{1}{4}$14

    A

    $\frac{1}{5}$15

    B

Learn

We can show that two fractions are equal if they are the same point on a number line. Let's look at an example.

Let's show the fraction $\frac{3}{6}$36 on a number line. It looks like this:

Now let's show the fraction $\frac{2}{4}$24 on a number line. It looks like this:

As you can see, the number lines are split into different sized parts, but the two fractions $\frac{3}{6}$36 and $\frac{2}{4}$24 are the same length. This means that the two fractions are equal.

Apply

The fractions $\frac{1}{2}$12 and $\frac{2}{3}$23 are shown on the number lines below.

012223242

0132333435363

  1. Are the two fractions equal?

    Yes

    A

    No

    B

Remember!

If two fractions are at the same point on a number line, then those two fractions are the same size.

Outcomes

3.NF.A.3

Explain equivalence of fractions and compare fractions by reasoning about their size.

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