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# Simplifying complex fractions

Learn how to take complex looking fractions and make them much, much simpler.

## Want to join the conversation?

• Why can't you swap the reciprocal fractions when multiplying?

When you turn the division problem into a multiplication by transforming the fraction on the right into the reciprocal of the fraction on the left, why can't you switch them around and make the fraction on top or on the left the reciprocal of the fraction on the right?
• It is kind of like saying 9 divided by 3, why cant we switch the numbers around and say 3 divided by 9. You can, but these two ways mean different things and you will get different answers. Hope this helps :)
• how do we simplify normal fractions tho
• It's defo a tricky thing to see until you get it like i just did lol but there's 2 ways you simplify fractions, first is the one where you Simplify by finding the Greatest Common Factor (GCF) for the top and bottom numbers of your answer then divide them both by it.

Then the other is where you Simplify an improper fraction into a mixed number by dividing the numerator (top number) by the denominator (bottom number), and you'll get a number with a remainder so you write the number as your whole number then write the remainder next to it, draw a line under it and write the original denominator of the fraction you just simplified under it.

Well you need to use the GCF one for just Proper Fractions and then the one changing it into a mixed fraction for any improper fractions.

Why? because from numbers 100 and above it becomes too hard and takes too long to keep writing all the common factors for it but just to give it a process to follow people just choose to use GFC for only proper fractions and change it into a mixed fraction only for improper fractions.

For bigger Proper Fractions say... 110/200 you just have to look at the numbers and ask yourself What number goes both into 110 and 200? well look at the last 2 numbers first so clearly... 10 will go into both 110 and 200 so divide both by 10 to simplify it to the smallest possible fraction :) eventually you'll then just become good at looking at the numbers than having to keep writing the common factors.
• from to , Sal explains how to simplify 2/2/3. However, I could reason differently. I could simplify the 2/2, resulting in 1, and end up with 1/3. Their are other ways to get 1/3 too. I could break all the fractions to get 2÷2÷3, which I think could be 3 or 1/3 depending on how I look at it. How do I know which way I should do?
• How do u put the time he said it in the video in your question/ comment?? I need help plz!
(1 vote)
• So how would you do something like 1 / 1/2? Would it just be 1/2?
• if you mean (1/1)/2 then yes because 1/1 is 1 and that leaves 1/2.
If you meant 1/(1/2) then the answer is different:
with the last expression you are dividing 1 by 1/2, or in other words you are asking how many times does 1/2 fit into 1? Because we are dealing with very small numbers you can just count halves until you reach 1, in this case 2 halves go into 1 so your answer is 2. If you take a different approach that will work with any number you can use the rule that something divided by something else is the same as multiplying by its reciprocal. So 1/(1/2) = 1 x 2/1 = 2

hope it helped :)
• At why did he flip 3/7?
• Because that's what you when a fraction is being divided. If you want to multiply it, then flip the denominator.
• I get how to simplify, but do you guys have anything that could help me solve the complex fractions. All I can find is simplifying complex fractions. I just want to solve them.
• Well you simplify like this...
for example 4/5 / 5/6 can be written as 4/5 divided by 5/6 so the answer is 24/25 and simplify fractions is the same as solving it.
Use this http://www.wikihow.com/Simplify-Complex-Fractions
• For 2x 3/2 why didn't he change 2 to 2/1?
(1 vote)
• Because it's not needed. It's an easy problem, doable with mental math.
• This math is my greatest foe. It's really Hard.
• Ill give you an idea about how to do it, I dont think its that effective though. It'll take time to understand

Lets say...

27/54

1. Find which times table both numbers occur in: 9
2. What does 9 need to be multiplied with to get to 27/54: 3 and 6
Wait...
4. WE NEED TO SIMPIFY IT FURTHER. I dont know how to use the first part of the strategy on this part(I think the fraction is not applicable due to the numbers being tool small) but let me know if you do. When you think about 3/6 its obviously going to remind you of A HALF. AND A HALF IS WRITTEN AS 1/2

5. The answer to simplifying 27/54 IS 1/2. Finally we're done!

PS: This took me 24 minutes to type: I had to adjust the numbers and put in variables
(1 vote)
• how do you do the simplify fraction work?