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Q: When is the product of two fractions less than its factors?

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A proper fraction is less than 1. Any positive number multiplied by a positive number less 1 will be less than itself. In multiplying two proper fractions, each one is being multiplied by a number less than 1.

That only happens if they're both improper fractions, i.e. greater than ' 1 '.

The product will be less than the other factor.

Fractional multiplication results are always less than any of the factors. You can't hit ugly with an ugly stick and expect to get pretty. The above answer is only true is both your fractions are non-negative (in addition to being less than 1.

A number multiplied by 1 is equal to the original number. So: For fractions where the numerator (top) is LESS than the deonominator (bottom), the product will be LESS than the original number, because the fraction has a value of LESS than 1. For fractions where the numerator is MORE than the denominator, the product will be MORE than the original number because the fraction has a value of MORE than 1. For fractions where the numerator and denominator are the same, the product will be the same as the original number because the fraction has a value equal to 1.

Related questions

A proper fraction is less than 1. Any positive number multiplied by a positive number less 1 will be less than itself. In multiplying two proper fractions, each one is being multiplied by a number less than 1.

That only happens if they're both improper fractions, i.e. greater than ' 1 '.

The product will be less than the other factor.

The factors are greater than the product.

If the two numbers have no prime factors in common, their LCM will be their product. If there are prime factors in common, their LCM will be less than their product.

The product is less than either factor.

If there are three factors, then one of them being less than 1 does not imply anything about the product of all three and either of the other two factors. For example, 2 = 0.5*1*4 where the first factor is less than 1. The product 2 is less than one of the other factors but bigger than the last.

Fractional multiplication results are always less than any of the factors. You can't hit ugly with an ugly stick and expect to get pretty. The above answer is only true is both your fractions are non-negative (in addition to being less than 1.

Certainly. -31/2 and -41/2 are both less than 1 and their product is 15.75

Regular fractions are the fractions with a numerator that is less than the denominator and irregular fractions are fractions with a denominator less than the numerator.

Yes. Consider two negative fractions. Since they are negative, both are less than 1. But their product is positive and so greater than either.

A number multiplied by 1 is equal to the original number. So: For fractions where the numerator (top) is LESS than the deonominator (bottom), the product will be LESS than the original number, because the fraction has a value of LESS than 1. For fractions where the numerator is MORE than the denominator, the product will be MORE than the original number because the fraction has a value of MORE than 1. For fractions where the numerator and denominator are the same, the product will be the same as the original number because the fraction has a value equal to 1.

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