Question
Find $ 4 ~ \dfrac{ 1 }{ 2 } : 2 ~ \dfrac{ 2 }{ 3 } $
Answer
$$ 4 ~ \dfrac{ 1 }{ 2 } : 2 ~ \dfrac{ 2 }{ 3 } = \dfrac{ 27 }{ 16 } $$
Explanation
| $4 ~ \dfrac{ 1 }{ 2 } : 2 ~ \dfrac{ 2 }{ 3 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 4 } ~ \dfrac{ 1 }{ \color{red}{ 2 } } = \frac{ \color{red}{ 2 } \cdot \color{blue}{ 4 } + 1 }{ \color{red}{ 2 } } = \frac{ 9 }{ 2 }$$$$\color{blue}{ 2 } ~ \dfrac{ 2 }{ \color{red}{ 3 } } = \frac{ \color{red}{ 3 } \cdot \color{blue}{ 2 } + 2 }{ \color{red}{ 3 } } = \frac{ 8 }{ 3 }$$ | |||
| = | $\dfrac{ 9 }{ 2 } : \dfrac{ 8 }{ 3 }$ | = | Turn the second fraction upside down (this is now as reciprocal), and change the operation to multiplication. | ||
| = | $\dfrac{ 9 }{ 2 } ~ \color{blue}{\cdot ~ \dfrac{ 3 }{ 8 } }$ | = | Multiply the numerators, and the denominators to get the result. | ||
| = | $\dfrac{ 27 }{ 16 }$ |
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