Locating Fractions on a Number Line

Instructor: Kadoria Burgess

I have a Bachelor's degree in Elementary Education and Spanish. I have taught for 5 years in bilingual classrooms of various elementary grade levels.

Who doesn't love candy bars? Well, locating fractions on a number line is as simple as cutting a candy bar and dividing it among friends, and this lesson will show you how.

Fractions in Real Life

Have you ever eaten a one-pound Hershey's candy bar? Well, if you look at it closely, you'll see that it has been cut into 16 pieces: four rows with four pieces in each row. Break off a row, and you'll notice that the four pieces make a line. This line is a lot like a number line.

Now, break off one of the pieces from one of the rows and eat it. How many pieces from the row are gone now? One. How many pieces did you start with in the row? Four. So, you have eaten one fourth of the row.

The amount you have eaten represents a fraction, or a part of a whole. A fraction is written by putting the value of the part, or the numerator, above the line and the amount of the whole, or the denominator, below the line. In the Hershey's bar example, '1' is the numerator because it represents the part that you have eaten and '4' is the denominator because it represents the number of pieces in the whole row. So, the fraction eaten would be '1/4'.

Fractions and Number Lines

A standard number line starts at 0 and includes a series of numbers written in order: 1, 2, 3, 4, 5, etc. To find fractions on a number line, you will have to pull out your magnifying glass and zoom in on the spaces between the numbers. The picture below shows the space between 0 and 1. Now, see if you can use the candy bar strategy to find the fractions hidden in between those two numbers.

Close up of a number line
zero to one number line

You can cut a number line into pieces in much the same way you broke up the Hershey's bar to find a fraction. You will have to divide the space between the numbers into the amount needed to make a whole. This number will be the denominator for all of the fractions that fall in between those two numbers. So, in the case of the row from the Hershey's bar, the denominator would be '4'.

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