1. ## Fractions help

Questions: One fraction divides into another fraction 3 1/4 times. List two possible pair of fractions.

&&

If Kylie divides 4 2/3 by a fraction less than 1, the answer is a whole number. List three possible fractions.

Is there a rule/formula you can use for these questions, if so please tell me. Thank you

2. Originally Posted by puppy_wish
Questions: One fraction divides into another fraction 3 1/4 times. List two possible pair of fractions.
Choose an arbitrary fraction.

Let one of the fractions be 4/5 say, we want a fraction x such that:

(4/5)/x = 3 1/4 = 13/4

=> x = (4/5)/(13/4) = (4/5)*(4/13)=16/65

so, one pair of such fractions is 4/5 and 16/65

For the second pair, choose another arbitrary fraction.
Let one of the fractions be 7/4 say, we want a fraction x such that:
(7/4)/x = 13/4
=> x = (7/4)/(13/4) = (7/4)*(4/13) = 7/13

so another pair of fractions with the desired property is 7/4 and 7/13

3. Originally Posted by puppy_wish
Questions: One fraction divides into another fraction 3 1/4 times. List two possible pair of fractions.

OK, if one fraction divides into another 3 1/4 times that means fraction1 = 3 1/4 * fraction2. Since 3 1/4 = 13/4, f1=(13f2)/4.
At this point, pick any fraction for f2 and you can find a corresponding f1. For example, I'll choose 1/2.f1=(13f2)/4 =(13 * 1)/(4*2) =13/8
So 1/2 and 13/8 fit. You can easily find any number of pairs by substituting any f2 you'd like.
Originally Posted by puppy_wish
If Kylie divides 4 2/3 by a fraction less than 1, the answer is a whole number. List three possible fractions.

First, I'd convert 4 2/3 to an improper fraction. (4*3+2)/3=14/3.

I made an equation, w = (14/3)/F where w is a whole number. In other words, a whole number equals 14/3 divided by a fraction.
Solving for F,
w = (14/3)/F
Fw = 14/3
F = 14/(3w)
Substitute a small whole number in for w and see if the resulting F fits the criteria (less than 1).
F = 14/(3*2)
= 14/6
14/6 is not less than 1, and, as you can see, the greater w is, the smaller the fraction is (the larger the denominator, the smaller the fraction, assuming the numerator remains unchanged). Pick a larger w.
F = 14/(3w)
= 14/(3*9)
= 14/27
14/27 is less than one, and (14/3)/(14/27) = 9 (which is whole), so 14/27 is an answer. Repeat the process with different whole numbers as w to get as many more as you need.
Originally Posted by puppy_wish

Is there a rule/formula you can use for these questions, if so please tell me.
Not really... Logic and a bit of formula manipulation work best here.
-Pulsar

edit: formatting got all messed up. Kind of fixed it... :/

4. there you have it puppy_wish, and a nice layout of a method too, the closest you'd get to a formula

Originally Posted by Pulsar06

edit: formatting got all messed up. Kind of fixed it... :/
That's much better, thanks