true or false- the product of two fractions that are each between 0 and 1 is also between 0 and 1
True. Check it by multiplying several pairs of fractions.
True
To determine whether the product of two fractions between 0 and 1 is also between 0 and 1, we can refer to the properties of multiplication and the given range of the fractions.
Let's say we have two fractions, a/b and c/d, where a, b, c, and d are positive integers and b and d are larger than 0.
To find the product of these fractions, we multiply the numerators and denominators:
(a/b) * (c/d) = (a * c) / (b * d)
Since a, b, c, and d are positive integers, their product will always yield a positive numerator and a positive denominator. Therefore, the sign of the resulting fraction does not change.
To analyze the range of the resulting fraction, we need to consider the values of a * c and b * d.
Given that each fraction is between 0 and 1, it means that a/b is less than 1, which implies a < b. Similarly, c/d is also less than 1, implying c < d.
If a * c is less than b * d, it suggests that the numerator of the resulting fraction is smaller than the denominator. In this case, the resulting fraction will be less than 1.
On the other hand, if a * c is greater than b * d, it suggests that the numerator of the resulting fraction is larger than the denominator. In this case, the resulting fraction will be greater than 1.
However, if a * c is equal to b * d, then the numerator and denominator will be equal, resulting in a fraction equal to 1.
In summary, the statement is FALSE. The product of two fractions between 0 and 1 can be less than, greater than, or equal to 1, depending on the specific values of the fractions.