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A proper fraction is less than 1. Whenever you multiply something by a number < 1, the result (product) is less than the original number. So when you multiply a proper fraction by a number less one (such as another proper fraction, the product is less than the original proper fraction.

The only time a product involving a given number is larger than the given number is when you multiply the given number by a number that is > 1. Since all proper fractions are < 1, products involving them are always less than the original given number.

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The product of two POSITIVE fractions less than one is less than either factor. Try thinking of multiplication as ‘of’ when performing multiplication of fractions less than one. E.g. 1/4 x 1/4 = is asking what is one quarter of one quarter, which is one sixteenth 1/4 x 1/4 = 1/16 (multiply 1 x 1 to get the numerator and 4 x 4 to get the denominator (1/16)

Q: Why is the product of two proper fractions less than either of the fractions?

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If the numbers have to be positive, at least one of the two factor must be 1. In that case the product will be greater than or equal to 1 and equal to the other factor.If the numbers can be negative, in addition to the first case, any product of a positive and a negative integer will be less than or equal to both of the two factors. The product is negative so it's automatically less than the positive factor. If the positive factor is 1, the product is equal to the negative factor; if the positive factor is > 1 the product is less than the negative factor. E.g.1 * -14 = -14 which is equal to -14 and less than 1-3 * 5 = -15, which is less than both 5 and -3

One less than the product of 8 and 9

Product of 6 and 5 is 30. 30 is 19 less than 49

Rule #1 When two fractions have the same denominator, the bigger fraction is the one with the bigger numerator. Rule # 2 When comparing fractions that have the same numerator, the bigger fraction is the one with the smaller denominator. Rule # 3 You can convert the fractions and then just put the greater than, less than or equal to sign to see what the comparison is between the fractions.

When the numerator is less than the denominator. For example 1/2, 3/4, 18/27, ...

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If the fractions are both proper fractions ... equivalent to less than 1 ... thenthat's always true ... the product is always less than either factor.

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.

You don't. Proper fractions are less than one, improper fractions are greater.

That's only true if the fractions are "proper" fractions ... with numerator smaller than denominator. The reason is: If you take (a piece less than the whole thing) out of (a piece less than the whole thing), you wind up with a piece smaller than either of the original pieces.

Proper fractions.

Proper fractions are fractions having a numerator that is smaller than the denominator.A proper fraction is when its numerator is less than its denominator as for example 3/4

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

No.

yes

because when you multiply the denominators it creates a much smaller proportion. for example multiply 0.5 by 0.5, the result is 0.25 in fractions it is 1/2 x 1/2, the result 1/4

A proper fraction is when the numerator is less than the denominator as for example 3/4

Yes. Natural numbers are counting numbers, equal to or greater than 0. The only ways a product can be less than its multiplicands is when multiplying fractions by fractions or multiplying a positive number by a negative number.

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