Fraction Number Line Bars

This is a very versatile tool that can be used to illustrate a variety of number operations. The background of the workspace is marked by light gray grid lines. The default step-size of the grid lines is 1/10 unit.

Change the step-size of grid lines

Click on the blue spinner arrows below the workspace. You may choose any step size from 1/2  to 1/15.

Slide and Zoom to see different portions of the number line

The slider immediately below the workspace moves your view along the number line in either direction. The ZOOM buttons change the size of the part of the number line in view.

Enter a fraction bar to the workspace

Choose a fraction by using the fraction boxes at the lower left of the workspace. Click on the New Bar to add the fraction bar to the workspace. Positive bars are blue when they come into the workspace; negative bars are pink, but you can choose any color for any number bar.

Choose colors

To change the color of any bar, click to select it and then choose the desired color with a colored button.

Move a bar

You may drag a selected bar anywhere within the workspace. When you release the bar it will snap to fit the nearest fraction bar or nearest grid line.


Place fraction bars end-to-end to represent addition, starting at 0, or at a point of your choice. The step size should be set at the least common denominator of the two fractions.

Negative fractions can be placed in the workspace. For example, if -2/3 is typed in the fraction boxes at the lower left of the workspace, then clicking on the New Bar button will place a left-pointing bar of length -2/3. The default color for negative fractions is pink.


Subtraction, such as 3/4 - 1/3, can be shown by first placing a bar of length 3/4 along the number line with its left edge at zero.

Now place a left-pointing bar of length 1/3 on top of the 3/4-bar with their right edges lined up. Since the least common denominator is 12, set the step size to 1/12. You can now read from the number line grid that 3/4 - 1/3 is 5/12.

Another way to represent the subtraction 3/4 - 1/3 is to place a 3/4 bar along the number line with a 1/3 bar on top with the left edges aligned. Now set the step size to 1/12 and determine what size bar would be required to add to the 1/3-bar to fit the 3/4-bar.


When you first launch Fraction Bars, it will display the division of 7/5 by 1/2. The visualization of 7/5 by 1/2 is achieved by completing each of the following steps.

  1. First, place a 7/5-bar along the number line with its left edge at zero.

  2. How many 1/2-bars can be fitted next to a 7/5-bar? Place three yellow 1/2-bars along the top of the 7/5 bar.

  3. Set the step size to be the common denominator, 1/10.

  4. Now you can see that there are 2 and 4/5 yellow bars that can be fitted next to the 7/5 bar. So, 7/5 divided by 1/2 is 2 and 4/5 or 14/5.