# Adding Fractions and Mixed Numbers with Unlike Denominators

In this video we look at adding fractions and adding mixed numbers with unlike denominators.

## Adding Fractions with unlike denominators

In order to add (or subtract) fractions with different denominators, we just have to make the denominators the same.

## Example 1

Eli was making dinner, and the recipe called for $2\frac{3}{4}$ cups rice. He knew from past experience that he often wanted extra rice, so he added an extra $\tfrac{2}{3}$ of a cup. How much rice did Eli make?

 Original problem: $2\frac{3}{4} + \frac{2}{3}$ Find a common denominator: $2\frac{3 \color{green}{*3}}{4 \color{green}{*3}} + \frac{2 \color{green}{*4}}{3 \color{green}{*4}}$ $2\frac{9}{12} + \frac{8}{12}$ Add: $\color{green}{2\frac{17}{12}}$ Change the fraction to a mixed number: $2 + 1\frac{5}{12}$ Answer: $\color{red}{3\dfrac{5}{12}}$

## Example 2:

 $\color{blue} {\dfrac{7}{9} + \dfrac{5}{12} }$ Find a common denominator by finding a number that is a multiple of both: $\frac{7 \color{green}{*4}}{9 \color{green}{*4}} + \frac{5 \color{green}{*3}}{12 \color{green}{*3}}$ $\frac{28}{36} + \frac{15}{36}$ Add: $\color{green}{\frac{43}{36}}$ Change the fraction to a mixed number: $1\frac{7}{36}$ Answer: $\color{red}{\dfrac{43}{36} = 1\dfrac{7}{36} }$

## Three ways to find a Common Denominator

1. See if one number is a factor of the other.
2. Multiply the two denominators together, and use that for the common denominator.
3. Find the Least Common Multiple, or LCM, and use that for the common denominator. This is sometimes referred to as the Least Common Denominator, or LCD. ### A little confused?

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