Write down a few simple positive fractions.
Now create a new fraction, such that its numerator equals the sum of all the numerators you wrote down and the denominator equals the sum of all the denominators.

Example: you wrote down 1/3, 2/7, 4/15 so the new fraction is 7/25.

Prove: the new fraction is smaller than the largest on the initial list
and bigger than the smallest.