Fractions of A Line

When we talk about a fraction, we are always referring to some whole. That whole can be a pie (a circular area) or a rectangle (a rectangular area).

But the whole does not have to be an area. It can be anything: a basket of apples, a group of people, the distance from one place to another, a bottle of water, or any other measurable quantity.

To illustrate this, let's play with fractions of a line.

1. A line has been divided into 12 parts or segments with equal length. Try clicking on the green line segments and see what happens. (Because the lines are thin, it can be a bit tricky to position the mouse for clicking.)

    

   Observe how the green and red fractions change when you make a click. Try different ways to make half of the line red and then type in the red fraction that you see:

   Denominator:   

   Numerator:   

2. Repeat the previous step but do it for one third of the line.

   Denominator:   

   Numerator:   

3. You may need to experiment with segments cut into different numbers of equal parts. The tool below creates line segments cut into the number of parts you select. Try a few different cuts:
   number of parts =    

    

4. From the lines displayed below, figure out whether 3/5 is greater than, equal to, or smaller than 1/2.

    
    

   Pick your answer: