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Find the sum of the fractions
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$\dfrac { 31 } { 24 }$
Find the sum of the fractions
$\dfrac { 3 } { \color{#FF6800}{ 8 } } + \dfrac { 11 } { \color{#FF6800}{ 12 } }$
$ $ The smallest common multiple in denominator is $ 24$
$\dfrac { 3 } { \color{#FF6800}{ 8 } } + \dfrac { 11 } { \color{#FF6800}{ 12 } }$
$\dfrac { 3 } { 8 } + \dfrac { 11 } { 12 }$
$ $ Multiply the denominator and the numerator so that the denominator is the smallest common multiple $ $
$\dfrac { 3 \times \color{#FF6800}{ 3 } } { 8 \times \color{#FF6800}{ 3 } } + \dfrac { 11 \times \color{#FF6800}{ 2 } } { 12 \times \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { \color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 11 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 12 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 24 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 22 } } { \color{#FF6800}{ 24 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 24 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 22 } } { \color{#FF6800}{ 24 } } }$
$ $ Since the denominator is the same as $ 24 $ , combine the fractions into one $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ + } \color{#FF6800}{ 22 } } { \color{#FF6800}{ 24 } } }$
$\dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ + } \color{#FF6800}{ 22 } } { 24 }$
$ $ Add $ 9 $ and $ 22$
$\dfrac { \color{#FF6800}{ 31 } } { 24 }$
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