Arithmetic/Adding Fractions

Adding fractions
Before we go into fractions, let's have a think about what addition is.  {Answer these really simple questions; and don't forget units!}

{What is 1 bird + 5 birds? { 6 birds (i) }
 * type="{}"}

{What is 3 elephants + 9 elephants? { 12 elephants (i) }
 * type="{}"}

{What is 6 birds + 2 elephants? { 8 animals (i) }
 * type="{}"}
 * Hopefully you could answer the first two, but you might have had trouble with the third. Why?  Because we can't add up two different things!  However, before we add them up, we can change them into something else.  We can say that 6 birds are also 6 animals, and 2 elephants are also 2 animals, so now    6 birds + 2 elephants = 8 animals.

You probably did all this in your head without even thinking about it - so what has it all got to do with fractions?

To add or subtract two fractions, you first need to change the two fractions so that they have the same type. The simplest way to do this is to multiply the numerator and denominator of each fraction by the denominator of the other.

For instance,

$$\frac{2}{3} + \frac{1}{4} = \frac{2 \times 4}{3 \times 4} + \frac{1 \times 3}{4 \times 3} = \frac{8}{12} + \frac{3}{12} = \frac{(8+3)}{12} = \frac{11}{12}$$

A more advanced way is to use the LCM of the denominators, which will be explained later in this section. Then you can add or subtract the numerators and put the common denominator as the denominator of the solution.

Adding Mixed Numbers
There are two things you should know before you learn about how to add mixed numbers.

This is a mixed number, 5 3/4

We will be using 5 3/4 and 3 2/3 in our problem

Set = one mixed number

To add two mixed numbers, first you can turn the mixed number into an improper fraction. To do that you multiply the whole number by the denominator of your fraction. For this problem you would get 20 for the first set and 12 for the second set. Before you move on don’t forget to add the numerator to your other number such as 20+3 for the first problem. After that you change those numbers into fractions like this 23/4 and 12/3. Next you add them. You would get 35/9 after you add in this problem. Finally, you can turn that back into a mixed number by dividing the denominator by the numerator. After you divide you should get 3 8/9 as your mixed number. Also, no you cannot simplify. Now you know how to add mixed numbers!