# How do you add 3/4+2/3?

Nov 23, 2016

See explanation.

#### Explanation:

To add (or subtract) fractions with different denominators you have to find the common denominator first. The easiest way is to find the denominator is to multiply both denominators, so here the common denominator will be $3 \cdot 4 = 12$

Now we have to expand both fractions to get the denominator found above:

$\frac{3 \cdot \textcolor{red}{3}}{4 \cdot \textcolor{red}{3}} + \frac{2 \cdot \textcolor{red}{4}}{3 \cdot \textcolor{red}{4}} = \frac{9}{12} + \frac{8}{12}$

Now to add (subtract) fractions with equal denominators you just add (subtract) the numerators. The denominator stays unchanged:

$\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$

Final step is to reduce the fraction and change it to a mixed number (if possible)

$\frac{17}{12}$ cannot be reduced but it is an improper fraction, so it can be written as a mixed number:

$\frac{17}{12} = 1 \frac{5}{12}$

The final answer is: The value of this expression is $1 \frac{5}{12}$