Question
Find $ 2 ~ \dfrac{ 1 }{ 3 } + 1 ~ \dfrac{ 3 }{ 4 } $
Answer
$$ 2 ~ \dfrac{ 1 }{ 3 } + 1 ~ \dfrac{ 3 }{ 4 } = \dfrac{ 49 }{ 12 } $$
Explanation
| $2 ~ \dfrac{ 1 }{ 3 } + 1 ~ \dfrac{ 3 }{ 4 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 2 } ~ \dfrac{ 1 }{ \color{red}{ 3 } } = \frac{ \color{red}{ 3 } \cdot \color{blue}{ 2 } + 1 }{ \color{red}{ 3 } } = \frac{ 7 }{ 3 }$$$$\color{blue}{ 1 } ~ \dfrac{ 3 }{ \color{red}{ 4 } } = \frac{ \color{red}{ 4 } \cdot \color{blue}{ 1 } + 3 }{ \color{red}{ 4 } } = \frac{ 7 }{ 4 }$$ | |||
| = | $\dfrac{ 7 }{ 3 } + \dfrac{ 7 }{ 4 }$ | = | Make denominators the same by multiplying the first fraction by 4 and, the second fraction by 3.$$\dfrac{ 7 }{ 3 } = \frac{ 7 \color{blue}{\cdot 4 } }{ 3 \color{blue}{ \cdot 4 }} = \frac{ 28 }{ 12 }$$$$\dfrac{ 7 }{ 4 } = \frac{ 7 \color{blue}{\cdot 3 } }{ 4 \color{blue}{ \cdot 3 }} = \frac{ 21 }{ 12 }$$ | ||
| = | $\dfrac{ 28 }{ 12 } + \dfrac{ 21 }{ 12 }$ | = | Add the numerators to get the result | ||
| = | $\dfrac{ 49 }{ 12 }$ |
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