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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 less than its factors?
If the fractions are both proper fractions ... equivalent to less than 1 ... thenthat's always true ... the product is always less than either factor.
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 do you do greater than or less than or equal to with fractions?
easy, just cross multiply
Why do numbers get smaller when multiplied by fractions less than 1?
If you multiply by 1 they stay the same. If you multiply by more than 1 they increase. Fractions less than 1 are less than unity so the products decrease because you are only taking a fraction of the number.
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.
When you multiply two positive fractions is the product less than one half?
No, not necessarily. 3/4 x 3/4 = 9/16 > 1/2
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.
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.
Why is the product of two positive proper fractions always less than either fraction?
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
When you multiply an integer less than 1 and an integer less than -1 the product is what?
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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.
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 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.
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.
When is the product of two fractions less than its factors?
If the fractions are both proper fractions ... equivalent to less than 1 ... thenthat's always true ... the product is always less than either factor.
When you multiply an integer less than 1 and an integer less than -1 what is the product?
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