Question

Sarah said if you multiply two fractions that are both less than 1, you may sometimes get a product that is equal to or greater than 1. Is Sarah's statement true? Why or why not?

Answer 1

Sarah's statement is true, opposing popular belief.

A common misconception if that they are positive fractions, which they need not be. As a matter of fact, if one of them is positive, it is not possible for the product, no matter how large, to have a positive product.

Remember, a negative multiplied by a negative produces a positive. You simply need a negative fraction and a negative fraction that is at most the reciprocal of the first to produce a product that is greater or equal to 1.

Examples:

• -2, -1/2 (reciprocal)
• -5, -5
• -177777, -1
• -1231231312321, -1/8