Arithmetic/Adding Fractions

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Adding fractions[edit]

Before we go into fractions, let's have a think about what addition is. Answer these really simple questions.

  • What is 1 bird + 5 birds?
  • What is 3 elephants + 9 elephants?
  • What is 6 birds + 2 elephants?

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.