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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.
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 know about the product if one of the factors is less than one?
The product will be less than the other factor.
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.
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.
If you multiply two decimals less than 1 can you predict whether the product will be less than or greater than either of the factors Explain?
When you multiply two decimals that are both less than 1, the product will always be less than either of the factors. This is because each factor represents a fraction of a whole, and multiplying these fractions results in an even smaller fraction. For example, multiplying 0.5 and 0.3 yields 0.15, which is less than both 0.5 and 0.3. Thus, the product is guaranteed to be less than either factor.
What is the product of factors that are both positive proper fractions?
The product of two positive proper fractions is always a positive proper fraction. A proper fraction is defined as a fraction where the numerator is less than the denominator. Therefore, when multiplying two fractions, the result will have a numerator smaller than the denominator, maintaining its status as a proper fraction.
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 '.
Why the product of two fractions that are each less than 1 will always be less than 1?
When you multiply two fractions that are each less than 1, you are essentially taking a portion of a portion. Since each fraction represents a part of a whole, their product results in an even smaller part. Mathematically, if ( a < 1 ) and ( b < 1 ), then ( a \times b < a ) and ( a \times b < b ), ensuring that the product ( ab < 1 ). Therefore, the product of two fractions less than 1 will always be 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.
If two positive fractions are less than 1 why is their product also less than 1?
If two positive fractions are less than 1, it means that both fractions can be expressed as ( a/b ) and ( c/d ), where ( a < b ) and ( c < d ). When you multiply these fractions, the product is ( (a/b) \times (c/d) = (a \times c) / (b \times d) ). Since both ( a ) and ( c ) are less than their respective denominators ( b ) and ( d ), the numerator ( a \times c ) will also be less than the denominator ( b \times d ). Thus, the product remains a positive fraction less than 1.
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 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
Is the product of two positive fractions that are less than 1 also less than 1?
Yes, the product of two positive fractions that are both less than 1 is also less than 1. When you multiply two numbers that are each less than 1, the result is a smaller number, as you are essentially taking a portion of a portion. For example, multiplying ( \frac{1}{2} ) by ( \frac{1}{3} ) gives ( \frac{1}{6} ), which is less than 1. Thus, the product remains 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.
How can you determine if the least common multiple of 2 numbers is the product of the 2 numbers or less than the product of the 2 numbers?
If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.
