Equivalent Fractions on the Number Line

Videos, examples, and solutions to help Grade 3 students learn how to place whole number fractions and unit fractions between whole numbers on the number line.

Common Core Standards: 3.NF.2a, 3.NF.2b, 3.NF.3c, 3.NF.3d, 3.MD.4

New York State Common Core Math Grade 3, Module 5, Lesson 16
Worksheets for Grade 3

The following diagram shows how to find equivalent fractions on a number line. Scroll down the page for more examples and solutions.

 

Lesson 16 Application Problem
Hannah bought 1 yard of ribbon to wrap 4 small presents. She wants to cut the ribbon into equal parts.
Draw and label a number line from 0 yd. to 1 yd. to show where Hannah will cut the ribbon.
Label all the fractions including 0 fourths and 4 fourths. Label 0 yd. and 1 yd., also.

Lesson 16 Concept Development

Let’s draw a number line with the endpoints 1 and 2.
The last few days our left endpoint was 0.
Where has 0 gone? It didn’t disappear; it is to the left of the 1. The arrow on the number line tells us that there are more numbers, but we just didn’t show them. It’s as if we took a picture of a piece of the number line but those missing numbers still exist.

We are going to partition this whole into 4 equal lengths.

Our number line doesn’t start at 0 so we can’t start at 0 fourths.
How many fourths are in 1 whole? 4 fourths.
So we will label 4 fourths at whole number 1. Label the rest of the fractions up to 2.
Check to see if you have the same number line.
What are the whole number fractions, the fractions equal to 1 and 2? 4 fourths and 8 fourths.

4 fourths is the same point on the number line as 1. We call that equivalence.
How many fourths would be equivalent to, or at the same point as 2? 8 fourths.
What fraction is equivalent to 3? 12 fourths.
Draw a number line with the end points 2 and 4. What whole number is missing from this number line? The number 3.
Let’s place the number 3. It should be equally spaced between 2 and 4. Let’s draw that in.
We will partition this line into 3 equal lengths.
To label the number line that starts at 2, we have to know how many thirds are equivalent to 2 wholes.
3 thirds made 1 whole. So, 6 units of thirds makes 2 wholes. 6 thirds are equivalent to 2 wholes.

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Lesson 16 Problem Set

1. Estimate to equally partition and label the unit fractions on the number line. Label the wholes as fractions and box them. The first one is done for you.
2. Partition each whole into 5 unit fractions. Label each fraction. Count up as you go. Box the whole numbers. Box the fractions that are located at the same points as whole numbers.
3. Partition each whole into 3 unit fractions. Label each fraction. Count up as you go. Box the fractions that are located at the same points as whole numbers.
4. Draw a number line with endpoints 0 and 3. Label the wholes. Partition each whole into 4 unit fractions. Label all the fractions from 0 to 3. Use a separate paper if you need more space.

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Lesson 16 Homework

1. Estimate to equally partition and label the fractional units on the number line. Label the wholes as fractions and box them. The first one is done for you.
   c. fourths
   e. fifths
2. Partition each whole into 6 unit fractions. Label each fraction. Count up as you go. Box the whole numbers. Box the fractions that are located at the same points as whole numbers.
3. Partition each whole into 2 unit fractions. Label each fraction. Count up as you go. Box the fractions that are located at the same points as whole numbers.
4. Draw a number line with endpoints 0 and 3. Label the wholes. Partition each whole into 5 unit fractions. Label all the fractions from 0 to 3. Use a separate paper if you need more space.

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