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Can the quotient of two fractions be ever equal to one?
Yes, but only if the two fractions are the same or equivalent fractions (other than 0).
What is Nine less than the quotient of two and a number xxx?
The expression "the quotient of two and a number xxx" can be represented as 2 / xxx. Nine less than this quotient would be 2 / xxx - 9.
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.
Why is the quotient of two fractions less than 1 always greater than either fraction?
There can be no answer because it is not necessarily true. Suppose f1 and f2 are two fractions.Suppose f1 = 1/2, which is less than 1;suppose f2 = -1/4, which is also less than 1.Then f1/f2 = -2 which is, in fact, smaller than either fraction. Go figure!
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.
