Adding Mixed Numbers

Date: 04/13/99 at 22:11:14
From: gabriella Barrera
Subject: 5th grade math

How do you add mixed numbers with no renaming? Can you give me a few
examples, please?

Date: 04/14/99 at 09:01:25
From: Doctor Rick
Subject: Re: 5th grade math

Hi, Gabriella, welcome to Ask Dr. Math!

If the denominators of the fractional parts are different, you MUST 
rename. Fractions cannot be added until they have the same 
denominator.

I am guessing that you mean problems like this:

     5       7
  3 --- + 4 --- = ?
     8       8

Remember that this is the same as

       5         7
  3 + --- + 4 + --- = ?
       8         8

You can rearrange and group the numbers like this:

               5     7
  (3 + 4) + ( --- + --- ) = ?
               8     8

Add each group separately:

                 12
     7    +      ---
                  8

We aren't done yet because the fraction isn't a proper fraction. Since 
12 divided by 8 is 1 with remainder 4, the fraction equals

                    4
     7    +    1 + ---
                    8

Now we can add the whole numbers to get the answer:

       4
    8 ---
       8

Wait, we're not done yet. The fraction is a proper fraction, but it 
isn't in lowest terms. Since both 4 and 8 are multiples of 4, we can 
divide them both by 4, to get

       1
    8 ---
       2

At last, we're done. Fortunately, you don't have to write all this 
out; a lot of it can be done in your head once you get the idea. 

These are the steps I followed - you don't have to do all of them in 
just this order:

1. Group whole numbers and fractions separately. Add the whole 
   numbers.

2. If the denominators aren't the same, rename the fractions so they 
   are.

3. Add the numerators.

4. If the fraction is improper, rewrite it as a mixed fraction. Add 
   the whole numbers.

5. If the fraction isn't in lowest terms, divide the numerator and
   denominator by their common factor.

I'm not sure I understood your question correctly, so if I haven't 
answered it, please write again and explain.

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