Question

Question #f972f

Answer 1

One half of one fourth (which is one eighth) is the same as one fourth of one half (also one eighth).

Explanation:

a) See the picture below:

We start with one fourth (the blue shaded area in the first picture) and, after dividing it into two, we see that one half of that is one eighth (the blue shaded area in the second picture).

b) See the picture below:

We start with one half (the blue shaded area in the first picture) and, after dividing it into four, we see that one fourth of that is one eighth (the blue shaded area in the second picture).

This geometrical result can be verified by multiplying the respective fractions as well.

a) One half of one fourth:
`1/4xx1/2=1/8`

b) One fourth of one half:
`1/2xx1/4=1/8`

Hence, we see that from both the geometrical and arithmetical calculations the values of one half of one fourth and one fourth of one half are the same: one eighth.