Question
$$ \text{ Which is bigger } 2 ~ \dfrac{ 5 }{ 3 } \text{ or } 3 ~ \dfrac{ 1 }{ 5 } \text{ ? }$$
Answer
$$ 2 ~ \dfrac{ 5 }{ 3 } > 3 ~ \dfrac{ 1 }{ 5 } $$
Explanation
| $2 ~ \dfrac{ 5 }{ 3 } \bigcirc 3 ~ \dfrac{ 1 }{ 5 }$ | Convert mixed numbers to fractions.$$\color{blue}{ 2 } ~ \dfrac{ 5 }{ \color{red}{ 3 } } = \frac{ \color{red}{ 3 } \cdot \color{blue}{ 2 } + 5 }{ \color{red}{ 3 } } = \frac{ 11 }{ 3 }$$$$\color{blue}{ 3 } ~ \dfrac{ 1 }{ \color{red}{ 5 } } = \frac{ \color{red}{ 5 } \cdot \color{blue}{ 3 } + 1 }{ \color{red}{ 5 } } = \frac{ 16 }{ 5 }$$ |
| $\dfrac{ 11 }{ 3 } \bigcirc \dfrac{ 16 }{ 5 }$ | Make denominators the same by multiplying the first fraction by 5 and, the second fraction by 3.$$\dfrac{ 11 }{ 3 } = \frac{ 11 \color{blue}{\cdot 5 } }{ 3 \color{blue}{ \cdot 5 }} = \frac{ 55 }{ 15 }$$$$\dfrac{ 16 }{ 5 } = \frac{ 16 \color{blue}{\cdot 3 } }{ 5 \color{blue}{ \cdot 3 }} = \frac{ 48 }{ 15 }$$ |
| $\dfrac{ 55 }{ 15 } \bigcirc \dfrac{ 48 }{ 15 }$ | $ \dfrac{ 55 }{ 15 } $ and $ \dfrac{ 48 }{ 15 } $ have the same denominator (15), so we will compare their numerators.Since $ 55 > 48 $, we conclude that $ \dfrac{ 55 }{ 15 } > \dfrac{ 48 }{ 15 } $. |
| $\dfrac{ 55 }{ 15 } > \dfrac{ 48 }{ 15 }$ |
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