I have some difficulties with these math problems. Help?

Question

1. Jeff says, "The denominator of 2 fractions are prime numbers p and q. So the denominator of the product is p x q and the product is in lowest terms." Is Jeff right? Explain

2.Explain why all of these have the same quotient: / = divided
1/2 / 3/16 1 / 3/8 16 divided by 6 4 / 1 1/2(1 whole and a half)

3.Does the following method always work? Explain. WHen the demonitor is 2 more than the numerator in each fraction, the greater fraction has the greater denomintor. Which number is greater?
a. 1 whole and 5/7 or 1 whole and 4/6.
b. 3 wholes and 3/5 or 3 wholes and 5/7.

Answer 1

1) Not true. If the numerator of one fraction has the denominator of the other fraction as a factor, The product will not be in lowest terms.
Ex: (1/2)(2/3) = 2/6 = 1/3
2) All the pairs of numbers have the same quotient because all pairs of numbers are in a ratio of 8:3
(16)(!/2 : 3/16) = 8:3
(8)(1 : 3/8) = 8:3
(1/2)(16 : 6) = 8/3
(4 : 1 1/2) = (4 : 3/2)
2(4 : 3/2) = 8/3

3) The method works, but not for negative numbers.
a) Ignore the wholes:
5/7 is greater than 4/6 so the first is greater.
b) 5/7 is greater than 3/5, so the second is greater.