Why do you use the reciprocal when dividing whole numbers by fractions?

Answer 1

Well, for one thing, it is easier to multiply than to divide. If you divide by a fraction, the answer is the same as multiplying by its reciprocal. For example, how much is 100 divided by 1/2? If you say 50, that's wrong. That's 100 times 1/2. Suppose you have $100 and you want to buy as many candy bars as you can at 50 cents each. That's 1/2 a dollar. If you bought 100 candy bars, that would cost $50. You have twice that much money, so you could buy twice as many. You could buy 200. So 100 divided by 1/2 is 200, not 50. The reciprocal of 1/2 is 2, and 100 times 2 is 200.