If 1/4 x 1/4 is 1/16, why 1/4+1/4 is not equals 1/8?

Question

Why only numerators are added and denominators not added when you add two fractions, while denominators and numerators are multiplied when you multiply two fractions?

Answer 1

Always understand fractions as part of a whole and the denominator represents the total number of equal parts in one whole. The numerator represents the part we are talking about.

When you add two fractions with the same denominator, the resulting fraction also will have the same number of equal parts in one whole. Only the parts we talk about get added.

When you multiply two fractions, we are talking about a fraction of another fraction. 1/4 x 1/4 implies 1/4 of 1/4.

In this case, the resulting fraction will have a different number of equal parts in one whole, since the fraction is cut into smaller parts, the whole also has to be cut into parts of equal size.

Please watch the video for more understanding.

Answer 2

The answer is 1/16 because when one multiplies two fractions one is effectively saying "What is 1/4 of 1/4?" so one ends up with a smaller number in this case because one is finding a fraction of a fraction (1/16 is 1/4 of 1/4).

When one is adding fractions one is effectively saying "What is 1/4 and 1/4?" so one ends up with a larger number in this case because one is combining two fractions (1/2 is 1/4 and 1/4).

So when one is multiplying fractions one says "Fraction1 of Fraction2" and when one is adding fractions one is saying "Fraction1 and Fraction2".