Question
Find $ 1 ~ \dfrac{ 3 }{ 4 } + 1 ~ \dfrac{ 3 }{ 4 } $
Answer
$$ 1 ~ \dfrac{ 3 }{ 4 } + 1 ~ \dfrac{ 3 }{ 4 } = \dfrac{ 7 }{ 2 } $$
Explanation
| $1 ~ \dfrac{ 3 }{ 4 } + 1 ~ \dfrac{ 3 }{ 4 }$ | = | Convert mixed numbers to fractions.$$\color{blue}{ 1 } ~ \dfrac{ 3 }{ \color{red}{ 4 } } = \frac{ \color{red}{ 4 } \cdot \color{blue}{ 1 } + 3 }{ \color{red}{ 4 } } = \frac{ 7 }{ 4 }$$$$\color{blue}{ 1 } ~ \dfrac{ 3 }{ \color{red}{ 4 } } = \frac{ \color{red}{ 4 } \cdot \color{blue}{ 1 } + 3 }{ \color{red}{ 4 } } = \frac{ 7 }{ 4 }$$ | |||
| = | $\dfrac{ 7 }{ 4 } + \dfrac{ 7 }{ 4 }$ | = | Add the numerators to get the result | ||
| = | $\dfrac{ 14 }{ 4 }$ | = | Simplify $ \dfrac{ 14 }{ 4 } $ by dividing both 14 and 4 by their GCD, which is 2. GCD(14, 4) = 2. $$ \frac{ 14 }{ 4 } = \frac{ 14 : \color{blue}{ 2 } }{ 4 : \color{blue}{ 2 } } = \frac{ 7 }{ 2 } $$ |
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| = | $\dfrac{ 7 }{ 2 }$ |
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