# 6.1 + – fractions

To add or subtract 2 fractions, they must have the same denominator (bottom).

For example, $1/4+3/8$. We can’t convert the 2nd term to $1.5/4$, because this includes a decimal! Therefore, we change the 1st term to $2/8$. Note $2/8=1/4$, same number. So we add $2/8+3/8=(2+3)/8=5/8$.

Another example, $1/2-1/4$. We convert the 1st term to $2/4$, since $2/4=1/2$, same number. So we have $2/4-1/4=(2-1)/4=1/4$.

A common denominator (bottom) is what is crucial with both adding and subtracting fractions. It is the key to solving these sorts of problems, and simply means both fractions being added/subtracted need to have the same bottom. But to do this, you need to do what you do to the bottom, to the top, to keep the fraction balanced (same as it was before).

# Adding and subtracting mixed numbers

To add or subtract mixed numbers, there are 2 methods:

1. Convert to improper fractions, obtain a common denominator, and then add. For example, $1\dfrac{1}{2}+2\dfrac{3}{4}=3/2+11/4=6/4+11/4=(6+11)/4=17/4$. This can then be converted back to a mixed number, i.e. $4\dfrac{1}{4}$
2. Alternatively, add the whole numbers first, and then add the fractions. For example, $1\dfrac{1}{2}+\dfrac{3}{4}=(1+2) + (1/2+3/4)=3+(2/4+3/4)=3+(5/4)=4+1/4=4\dfrac{1}{4}$

I prefer the 2nd method as I find it simpler.