Question
Find $ 2 ~ \dfrac{ 1 }{ 4 } + 3 ~ \dfrac{ 5 }{ 3 } $
Answer
$$ 2 ~ \dfrac{ 1 }{ 4 } + 3 ~ \dfrac{ 5 }{ 3 } = \dfrac{ 83 }{ 12 } $$
Explanation
| $2 ~ \dfrac{ 1 }{ 4 } + 3 ~ \dfrac{ 5 }{ 3 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 2 } ~ \dfrac{ 1 }{ \color{red}{ 4 } } = \frac{ \color{red}{ 4 } \cdot \color{blue}{ 2 } + 1 }{ \color{red}{ 4 } } = \frac{ 9 }{ 4 }$$$$\color{blue}{ 3 } ~ \dfrac{ 5 }{ \color{red}{ 3 } } = \frac{ \color{red}{ 3 } \cdot \color{blue}{ 3 } + 5 }{ \color{red}{ 3 } } = \frac{ 14 }{ 3 }$$ | |||
| = | $\dfrac{ 9 }{ 4 } + \dfrac{ 14 }{ 3 }$ | = | Make denominators the same by multiplying the first fraction by 3 and, the second fraction by 4.$$\dfrac{ 9 }{ 4 } = \frac{ 9 \color{blue}{\cdot 3 } }{ 4 \color{blue}{ \cdot 3 }} = \frac{ 27 }{ 12 }$$$$\dfrac{ 14 }{ 3 } = \frac{ 14 \color{blue}{\cdot 4 } }{ 3 \color{blue}{ \cdot 4 }} = \frac{ 56 }{ 12 }$$ | ||
| = | $\dfrac{ 27 }{ 12 } + \dfrac{ 56 }{ 12 }$ | = | Add the numerators to get the result | ||
| = | $\dfrac{ 83 }{ 12 }$ |
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