This struck me as a good explanation for it:
http://www.math.com/school/subject1/lessons/S1U4L2GL.htmlThe key thing to remember here is that any number (except primes which only equal themselves when it's that number x 1) can be gotten by multiplying other whole numbers together to get it.
e.g.:
3 = 3 x 1
4 = 2 x 2
24 = 4 x 6
Though the components 4 and 6 can be broken in to even SMALLER pieces:
24 = 4 x 6 = 2 x 2 x 3 x 2
So with a fraction (10/42) you can break it down in to it's little pieces like so... the 10 can be broken in to 5 x 2 while the 42 can be broken in to 2 x 3 x 7. What you have then can be written as...
(5 x 2)/(2 x 3 x 7)
in algebra, when you have the same little number on top here AND on bottom (in this case: 2) they cancel each other out because any number divided by itself is 1. (And as we showed with the prime one in multiplication can change the way something looks but not the actual something.)
So with that 2 cancelled out...
5/(3x7) = 5/21
so 5/21 = 10/42
NOW with that above example and the link I provided you in mind try out the problem you have. Seriously give it a good one or two tries then check the solution I'm posting in the quote.. and don't be intimidated by the BIG quote box. It's actually very few steps, I just break it down in to teeny tiny steps and include LOTS more explanation.
(I suggest you write these examples down as you read them. I can't easily show the fractions on top in this window, but you know how to draw it so it makes sense to you - so do that.)
SOLUTIONS GIVE ME SOLUTIONS!
Your problem is 5/8 x 3/10. You need to show, that the result of this is 3/16 and reduce before multiplying.
Let's look at the 5/8 first. 5 is prime and can't be reduced. 8 is an even number, so not prime, and can be reduced. If we break 8 down to it's smallest component's: 8 = 2 x 2 x 2.
So 5/8 = 5/(2 x 2 x 2)
Now the 3/10. 3 is prime and won't get smaller. 10 though can be broken down. The easy, and in this case spot on, answer to how to break 10 down is that 10 = 5 x 2.
So 3/10 = 3/(5 x 2)
Now that we reduced the two fractions we need to multiply them. So let's line them up.
5/(2 x 2 x 2) x 3/(5 x 2)
Which really is:
(5 x 3)/(2 x 2 x 2 x 5 x 2)
Three things:
1) It may be hard to visualize with how this is written so I want you to write this down like the examples were written in the link I gave you.
2) When multiplying fractions it's important to remember that you multiply the numerator x numerator and the denominator x denominator. The stuff to the right of the / goes on bottom while the stuff to the left of the / goes on top.
3) Cancellation. Remember what I said about something over something where both somethings are the same being one and you can cancel it out? Look at the bolded numbers above. There are numbers in common in both the left and right fraction that can work with this. Do you see them?
The 5s cancel out. So you rewrite it as:
3/(2 x 2 x 2 x 2)
multiply the 2s
3/16
Let me know if that helps.
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