Question
Find $ 5 ~ \dfrac{ 2 }{ 9 } - 3 ~ \dfrac{ 3 }{ 5 } $
Answer
$$ 5 ~ \dfrac{ 2 }{ 9 } - 3 ~ \dfrac{ 3 }{ 5 } = \dfrac{ 73 }{ 45 } $$
Explanation
| $5 ~ \dfrac{ 2 }{ 9 } - 3 ~ \dfrac{ 3 }{ 5 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 5 } ~ \dfrac{ 2 }{ \color{red}{ 9 } } = \frac{ \color{red}{ 9 } \cdot \color{blue}{ 5 } + 2 }{ \color{red}{ 9 } } = \frac{ 47 }{ 9 }$$$$\color{blue}{ 3 } ~ \dfrac{ 3 }{ \color{red}{ 5 } } = \frac{ \color{red}{ 5 } \cdot \color{blue}{ 3 } + 3 }{ \color{red}{ 5 } } = \frac{ 18 }{ 5 }$$ | |||
| = | $\dfrac{ 47 }{ 9 } - \dfrac{ 18 }{ 5 }$ | = | Make denominators the same by multiplying the first fraction by 5 and, the second fraction by 9.$$\dfrac{ 47 }{ 9 } = \frac{ 47 \color{blue}{\cdot 5 } }{ 9 \color{blue}{ \cdot 5 }} = \frac{ 235 }{ 45 }$$$$\dfrac{ 18 }{ 5 } = \frac{ 18 \color{blue}{\cdot 9 } }{ 5 \color{blue}{ \cdot 9 }} = \frac{ 162 }{ 45 }$$ | ||
| = | $\dfrac{ 235 }{ 45 } - \dfrac{ 162 }{ 45 }$ | = | Subtract the numerators to get the result | ||
| = | $\dfrac{ 73 }{ 45 }$ |
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