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?

Question

Esmeralda Molina

Mathematics

12 December, 07:46

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?

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Answers (1)

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Jackson Maldonado · 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