Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2?

The number 3 can be expressed as a fraction 3/1. If we multiply the fraction 1/6 by 3/1 we get:

1/6 x 3/1 = (1 x 3) / (6 x 1)

(1 x 3) / (6 x 1) = 3/6

Now just simplify the fraction:

3/6 = 1/2

Because 1/2 of 6 = 1/3 and 1/2*1/3=1/6