Question
Find $ 1 ~ \dfrac{ 1 }{ 8 } + 1 ~ \dfrac{ 3 }{ 8 } $
Answer
$$ 1 ~ \dfrac{ 1 }{ 8 } + 1 ~ \dfrac{ 3 }{ 8 } = \dfrac{ 5 }{ 2 } $$
Explanation
| $1 ~ \dfrac{ 1 }{ 8 } + 1 ~ \dfrac{ 3 }{ 8 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 1 } ~ \dfrac{ 1 }{ \color{red}{ 8 } } = \frac{ \color{red}{ 8 } \cdot \color{blue}{ 1 } + 1 }{ \color{red}{ 8 } } = \frac{ 9 }{ 8 }$$$$\color{blue}{ 1 } ~ \dfrac{ 3 }{ \color{red}{ 8 } } = \frac{ \color{red}{ 8 } \cdot \color{blue}{ 1 } + 3 }{ \color{red}{ 8 } } = \frac{ 11 }{ 8 }$$ | |||
| = | $\dfrac{ 9 }{ 8 } + \dfrac{ 11 }{ 8 }$ | = | Add the numerators to get the result | ||
| = | $\dfrac{ 20 }{ 8 }$ | = | Simplify $ \dfrac{ 20 }{ 8 } $ by dividing both 20 and 8 by their GCD, which is 4. GCD(20, 8) = 4. $$ \frac{ 20 }{ 8 } = \frac{ 20 : \color{blue}{ 4 } }{ 8 : \color{blue}{ 4 } } = \frac{ 5 }{ 2 } $$ |
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| = | $\dfrac{ 5 }{ 2 }$ |
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