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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.
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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.
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 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.
Is the product of two positive mixed numbers ever less than one?
No, the product of two positive mixed numbers can never be less than one.
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 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 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 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.
The product of two numbers that are less than zero is also less than zero.?
No. The product of two negative numbers is positive.
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.
Is the product of two positive fractio that are each less than 1 also less than 1?
Yes.
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
When you multiply two positive fractions is the product less than one?
It depends on the factions, but normally, yes. For example, you multiply one-fourth by one-half, you get one eighth, which is less than one.
When is the product of two nonzero integers less than or equal to both of the two factors?
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
Is the product of two positive mixed numbers less than one?
No, the product of two positive mixed numbers can never be less than one.
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.
