Fractions and One

You may already know that fractions are relative to a certain whole which can be anything: a pie, a basket of apples, a rectanglar area, a bucket of water, or a length of line.

We usually use the number 1 to represent the whole. A part of the whole is then represented by some proper fraction such as 1/3, or 2/5. If you add all the fractions for the parts in the whole, the sum would be 1.

1. A rectangle has been divided into 6 equal parts (their areas are equal) in a 2 × 3 grid. If you are unfamiliar with this type of grid, click on the grid and see what happens.

    

   Observe how the red, green, and blue fractions change when you make clicks.

2. First, make only one column blue, and the rest green. It says 2/6 are blue and 4/6 are green. Can these columns be represented as thirds? Explain your answer below.

   Now consider the sum of the blue and green fractions.

   2   6

   +

   4   6

   =

   6

3. Write down an equation for the sum of the fraction parts in green, blue, and red created by clicking some of the squares in the grid above. For example 1/6 (red) + 2/6 (green) + 3/6 (blue) = 6/6.

   Please pick an answer.