Adding Fractions

Date: 01/13/2003 at 22:00:55
From: Zaira
Subject: Adding fractions

2/25 + 2/15 equals what? 

Date: 01/14/2003 at 09:05:54
From: Doctor Rick
Subject: Re: Adding fractions

Hi, Zaira.

Remember that you can't add fractions unless they have the same 
denominator. Once they do, you just add the numerators, and keep the 
same denominator.

You need to find equivalent fractions for each that have the same 
denominator. The first task is to find a suitable denominator. Do you 
know how to find the least common multiple (LCM) of 15 and 25? For 
help, see:

   http://mathforum.org/library/drmath/sets/shortcuts/dm_lcm.html 

Once you've chosen a common denominator (and it doesn't have to be 
the LEAST), then you find the equivalent fractions with this 
denominator. Then finally you can add the fractions.

I'll do a similar problem for you:

  1/6 + 2/9 = ?

We need a common multiple of 6 and 9. One way is to multiply the 
numbers together: 6 * 9 = 54. But if we look at the factors of the 
numbers:

  6 = 2 * 3
  9 = 3 * 3

we see that they have a common factor, 3. This common factor appears 
twice in the factorization of 54:

  54 = 2 * 3 * 3 * 3

We can divide 54 by 3 to get 18, which is still a multiple of both 6 
and 9. So our LCM is 18.

Now we write 1/6 and 2/9 as fractions with this denominator. First 
1/6: since 18 is 3 times 6, we need to multiply the numerator by 3 as 
well.

  1/6 = 3/18

Then 2/9: since 18 is twice 9, we need to multiply the numerator by 2 
as well.

  2/9 = 4/18

Now we can add the numerators:

  3/18 + 4/18 = 7/18

That's the answer. We can't reduce it, because 7 and 18 have no 
common factors.

Does this help?

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/