Question

If you are adding two fractions that are both less than 1/2, What must be true about the sum? Give three examples to support your thinking.

Answer 1

First assume that the fractions are all positive.
Next, add 1/2 and 1/2; the sum is 1. Thus, the two fractions must each be smaller than 1/2.

Let's try adding 5/16 and 7/16. Both are smaller than 1/2. Their sum is 12/16, or 3/4, which is less than 1.

Choose a couple other pairs of fractions which are between 0 and 1/2. Then find the sum of each pair. What do you observe about the size of these sums?

Answer 2

if both fractions are less than 1/2 then the sum has to be less than 1

1/8 + 3/8 = 4/8 = 1/2 , less than 1

7/16 + 1/4 = 11/16, less than 1

3/16 + 1/16 = 4/16 = 1/4, less than 1