why is the product smaller when i multiply a fraction by another fraction

Question

Like my teacher asked if the number will get larger and we said yes but we are wrong it gets smaller but how does it get smaller does it get smaller because your dividing or ..............

Answer 1

That will be true as long as the fraction is less than one. The reason is that you are taking a FRACTION of the number, not a whole of it, or more than a whole of it. So, if you take 1/2 or 1/3 or 1/10 of a number, you are taking a FRACTION (not a whole) of that number, so the result will be smaller (less). Now, if the fraction you multiply by is greater than one, for example, 5/3, then the answer will be greater than the original number. This is not a mathematical explanation, just a logical one. Probably a math major will answer this and give you a more mathematically derived answer.