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If the fractions are both proper fractions ... equivalent to less than 1 ... then

that's always true ... the product is always less than either factor.

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โˆ™ 2012-11-09 00:56:42
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Q: When is the product of two fractions less than its factors?
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When multiplying proper fractions why is the product less than the both factors?

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.


What do you know about the product if one of the factors is less than one?

The product will be less than the other factor.


When is the product of two fractions greater than its factors?

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


What do you notice about the relationship between the factors and the product when multiplying two decimals less than 1?

The factors are greater than the product.


How can you determine whether the LCM of two numbers is the product of the numbers or is less than the product of the numbers?

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.


When one factor is less then 1 is the product greater or less than the other 2 factors?

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.


When two fractions less than one are multiplied the product is sometimes greater than 1?

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


What are regular fractions?

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.


If you multiply two decimals less than 1 can you predict wether the product will be less than or greater than either of the factors?

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.


When you multiply a whole number by a fraction is the product always less than the original whole number?

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.


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

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.


When will the quotient of two fractions less than 1 be greater than either fraction?

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


How can you determine whether the LCM of two numbers is the product of the numbers or is less than the product of the numbers explain?

If the two numbers have no common factors other than 1, the LCM will be their product. If there are other common factors, the LCM will be less.


Why is the product of two fractions smaller than two fractions thet were multiplied?

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.


When is the product of 2 fractions less than its factors?

The concept of factors is appropriate only for integers. In the case of fractions, every non-zero number is a factor of any number. [For example, 1/5 is a factor of 3/4: 1/5 goes into 3/4 exactly 3 3/4 times.] The product of two number is less than either number if both of them are in the interval [0, 1) or if one of them is negative and the other is greater than 1.


Is it true that when you multiply two natural numbers the product is never less than either of the two numbers?

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.


What pairs have a LCM that is less than the product?

Pairs with common factors other than 1.


How can you determine from the prime factorizations whether the least common multiple of two numbers is the product of the numbers or is less that the product of the two numbers?

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


How is the product of 2proper fractions greater than the fractions being multiplied?

It is not: they are the same. A "product" and "multiple" are synonyms.


What fractions are greater than 0 and less than 1?

Proper fractions.


What are 2 fractions greater than one half with a product less than one half?

2/3 x 3/5


If you multiply two decimals less than 1 can you predict whether the product will be less or greater than either of the factors?

No, you cannot. The answer can be greater than (or less than) neither, one or both numbers.For example,-4.5 and -2.2 are both less than 1. Their product is 9.9 which is greater than both.-4.5 and 0.2 are both less than 1. Their product is 0.9 which is less greater than one and less than the other.0.5 and 0.2 are both less than 1. Their product is 0.01 which is less than both.


Why is the quotient of two fractions less than 1 greater than both?

It need not be. The numbers 1/2 and (-1/2) are both fractions less than 1 but their quotient is -1, which is less than both the fractions.


When is the product of a negative integer and a positive integer less than both of its factors?

Always


When you multiply 23 by a fraction less than one how does the product compare to the factors?

23 is a prime and so its only factors are 1 and 23. The product will be smaller than 23 but it is not possible to be certain how the product will compare with 1.

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