trying to study for gre and feel dumb?

Question

I am looking at a study maual and have come upon multiplication of fractions and i just cant remember how to do it. The fractions to multiply are 10/9*3/4*8/15. How do i do this. I know there has to be some reducing either vertically or diangonally but i dont know how. Can someone please explain this in detail.

Answer 1

When multiplying fractions, simply multiply all the top numbers (numerators) together and write them on top, then multiply all the bottom numbers (denominators) together and write them on the bottom. Then divide both the top and the bottom by the greatest common denominator to reduce the fraction to its simplest form. Thus: 10*3*8=240; 9*4*15=540. You now have 240/540. However this can be reduced by dividing both by 20, which is the greatest common denominator, giving you a result of 12/27.

Answer 2

You want to find greatest common factors that numbers in the numerator and denominator have. 10 * 3 * 8 is the numerator
9* 4* 15 is the denominator. The idea is that multiplying or dividing by 1 keeps the fraction unchanged. One selects 1 in a tricky way that makes the problem easier. One pairs a number from the numerator with a number that has common factors from the denominator. (10, 15), (8, 4), (3, 9)
Looking at the first pair (10,15)
10 = 2 x 5
15 = 3 x 5
so if we multiply the numerator and the denominator by 1/5, the value of the fraction stays constant, but the numbers get easier to work with, [we multiply by one in the form of (1/5 over 1/5)] now it is (2,3) and the fraction is

2*3*8
--------
9*4*3

Looking at the second pair (8,4)
8 = 2 x 4
4 = 1 x 4
so if we multiply the numerator and the denominator by 1/4, the value of the fraction stays constant, but the numbers get easier to work with, now it is (2,1) and the fraction is

2*3*2
--------
9*1*3

We could either use the third pair (3,9) or make a new pair with the leftover from the first pair (3,3). If we use (3,9) the greatest common factor is three, so we divide numerator and denominator by three and get

2*1*2
--------
3*1*3

If we use (3,3) the greatest common factor is still three, so we divide numerator and denominator by three and get

2*1*2
--------
9*1*1

either way the answer is 4/9. I mentioned the second way since sometimes you can take multiple factors out of one of the numbers, so you can reduce several terms with just one number. For example
12
----
2*3
you can divide top and bottom by 2 as well as top and bottom by three.

Answer 3

You should look into getting A GRE study manaul. I liked the one that is put out by the Princeton reviewbecasue it emaplins how to solve the problems as well as provides test take strategies.

Reduce the fractions diagonally the multiple straight accross I got 4/9.

Answer 4

Better go through the preps in detail.