What is the easiest way to cancel & multiply fractions?
I’m studying for my GED and I’ve been doing SO well, until I came across canceling and multiplying fractions. I am so lost. I need help. I DON’T get it. One problem I am stuck on is 9/14 times 10/11. Can someone describe to me in FULL detail how to do this? Thanks!
Its one of the easiest things to do…you just multiply straight across… top number * top number and bottom number * bottom number.
so in your example of 9/14 times 10/11 (9*10 = 90) and (14*11 = 154) and you end up with 90/154. However the hard part is that 90/154 can be reduced.
Fractions that need to be reduced is like saying I have 2/4 of a cup of water instead of saying 1/2. This is the hardest part. Finding which number will fit into both the top and bottom number. 6/9 can be reduced to 2/3 by dividing both the top and bottom numbers by 3. But the trick is everything must divide equally without leftovers.
There are a few tricks to help you out. Take the 6/9. use the smallest number (6) and figure out what you can multiply together to get 6. There’s 1×6 and 2×3. 6 doesn’t divide equally into 9 and neither does 2. But 3 does. 6 divided by 3 = 2 and 9 divided by 3 = 3 and you end up with 2/3. This is called reduced by 3 because 3 was the only number that divided equally into both the top and bottom number.
Going back to your problem of 9/14 times 10/11 = 90/154. 90/154 can only be reduced by 2 leaving you with 45/77. I know it’s confusing, but I hope this helps. Good luck on the GED.
December 1st, 2009 at 9:27 pm
There are many ways to do this but the easiest way I feel is to use this method. Many people struggle with fractions.
Non traditional but probably the easiest way for you
Remember you always multiply fractions straight across: so 9/14 x 10/11 = 90/154
First get your answer
Then Do factor tree for 90 and 154 untill ALL number are prime numbers
90 154
9 x 10 2 x 77
3 x 3 x 2 x 5 2 x 7 x 11
Cross out the numbers that are in both numbers that is the GCF = 2
The numbers that are left is the fraction simplified to lowest term
3 x 3 x 5 = 45
7 x 11 = 77
answers is 45/77
Traditional method:
reduce fraction using cross multiplication
S0 9/14 x 10/11
= 9/7 x 5/11 = 45/77
References :
December 1st, 2009 at 10:07 pm
oddly, multiplying fractions is the easiest operation of them all. it is regular multiplication across the top and also across the bottom.
So,
multiple 9 x 10
and 14 x 11
and combine into one fraction, the numerators’ product stays on top, and multiplying bottoms stays on bottom.
canceling fractions need to have common factors. and you cancel opposite terms, one in the denominator with one in the numerator.
for example in the one above, the answer can be reduced by dividing out and cancelling the common factor of 2
90/154 = 2(45)/2(77) = 45/77
**Danette
cross multiplication has nothing to do with this topic, and you explained it wrong. it is an algebraic technique for find the missing term in fractions that are set equal. don’t teach if you don’t know what you’re talking about.
References :
December 1st, 2009 at 10:51 pm
Its one of the easiest things to do…you just multiply straight across… top number * top number and bottom number * bottom number.
so in your example of 9/14 times 10/11 (9*10 = 90) and (14*11 = 154) and you end up with 90/154. However the hard part is that 90/154 can be reduced.
Fractions that need to be reduced is like saying I have 2/4 of a cup of water instead of saying 1/2. This is the hardest part. Finding which number will fit into both the top and bottom number. 6/9 can be reduced to 2/3 by dividing both the top and bottom numbers by 3. But the trick is everything must divide equally without leftovers.
There are a few tricks to help you out. Take the 6/9. use the smallest number (6) and figure out what you can multiply together to get 6. There’s 1×6 and 2×3. 6 doesn’t divide equally into 9 and neither does 2. But 3 does. 6 divided by 3 = 2 and 9 divided by 3 = 3 and you end up with 2/3. This is called reduced by 3 because 3 was the only number that divided equally into both the top and bottom number.
Going back to your problem of 9/14 times 10/11 = 90/154. 90/154 can only be reduced by 2 leaving you with 45/77. I know it’s confusing, but I hope this helps. Good luck on the GED.
References :