Ordering Fractions on a Number Line

Instructor: Sarah Kaiser

Sarah has taught 3rd and 5th grade and has a master's degree in education.

In this lesson, you will learn how to order fractions with a like, or common, denominator on a number line by comparing the size of each fraction. You will do this by creating and labeling a number line with equal parts.

Ordering Fractions on a Number Line

Imagine being at a sleepover with two of your friends. While watching a movie, the three of you scarf down an entire extra-large pizza! Your friend's mom comes down to check on you and sees the pizza has been eaten. She asks, 'Who ate all of this pizza?!' You each want to say another person ate the most, but how can you decide who the culprit was? You can think of the slices you ate as fractions of a whole and order the fractions to find out.

Let's say you ate 2/8 of the pizza. Your friend, Sam, ate 5/8 of the pizza, while Doug ate only 1/8 of the pizza. We can use a number line to show who ate the most pizza. First, draw a straight line horizontally for your number line. All of the fractions of pizza eaten were between 0 and 1, with 0 being none of the pizza and 1 being the whole pizza. So label the left end of your number line with 0, and the right end with 1:

number line

Now, it's time to start ordering our fractions. When we have a set of fractions that have the same denominator, we must compare the numerators to order the fractions. Looking at the set of fractions you and your friends ate, we can see that Doug ate only 1/8, which is less than you ate, 2/8. Last, we can see that Sam ate 5/8. Since 5 is bigger than both numerators 1 and 2, Sam ate the most. Now that we've ordered the fractions, let's place them on our number line!

Creating the Number Line

To determine what intervals to use for your number line, we can look at the denominator. When we have fractions that have like denominators, it's best to use the denominator as the guideline for making tick marks on your number line.

For example, in this problem our denominator is 8. That means we need to divide our number line into 8 equal parts. In order to do this, draw 7 tick marks equally spaced in order to create 8 spaces on the number line. (It's helpful to start with a tick mark right in the middle to represent one half of the number line, then divide each half into fourths, and then into eighths.)

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