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Which is a correct comparison of the fractions? 4/5 and 5/6

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3 Answers

Hannah
 
When comparing two fractions, the best thing to do is to get both fractions to have the same denominator (or a "common denominator") and then compare numerators.  For the two fractions 4/5 and 5/6, the least common denominator is 30. 
 
The fraction 4/5 is equivalent to 24/30 (To get this I multiplied both the numerator and denominator by 6).
 
The fraction 5/6 is equivalent to 25/30 (To get this I multiplied both the numerator and denominator by 5).
 
Now I can compare 24/30 against 25/30.  Since 25 is greater than 24, 25/30 (or originally 5/6) is the larger fraction.
 
Hope this helps!
 
George T.
 
First, it helps to know what the numbers in a fraction represent.  The top number tells how many parts you have.  The bottom number tells how many parts are needed to make one whole thing.  
 
So, 4/5 means you've got 4 parts, but need one more to make a whole. 5/6 means you have 5 parts and six are needed to make a whole.  Ugh!  Clearly we must be talking about different kinds of parts!  
 
This is where finding the least common multiple, also known as the least common denominator comes in.  We need to maintain the value of each fraction, but change its form so that we can look at the same kind of part.
 
Multiplying 4/5 by 6/6 gives us 24/30.  Multiplying 5/6 by 5/5 gives us 25/30.  Now both fractions describe the parts we have out of 30, and it is much easier to see that 25 parts is more than 24 parts.
 
Hope this helps! 
Cross multiplication method:
Assume a>0, b>0, c>0, d>0.
If you want to compare a/b with c/d, you only need to compare ad and bc.
If ad > bc, then a/b > c/d. (Proof: Divide both sides of ad > bc by bd)
 
If ad < bc, then a/b < c/d. (The same as above)
So, when you compare 4/5 with 5/6, you go:
since 24 < 25, 4/5 < 5/6

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