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Find the sum or difference of the fractions
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$\dfrac { 2 } { 3 }$
Find the sum or difference of the fractions
$\dfrac { 4 } { \color{#FF6800}{ 3 } } - \dfrac { 1 } { \color{#FF6800}{ 2 } } + \dfrac { 3 } { \color{#FF6800}{ 2 } } - \dfrac { 5 } { \color{#FF6800}{ 3 } }$
$ $ The smallest common multiple in denominator is $ 6$
$\dfrac { 4 } { \color{#FF6800}{ 3 } } - \dfrac { 1 } { \color{#FF6800}{ 2 } } + \dfrac { 3 } { \color{#FF6800}{ 2 } } - \dfrac { 5 } { \color{#FF6800}{ 3 } }$
$\dfrac { 4 } { 3 } - \dfrac { 1 } { 2 } + \dfrac { 3 } { 2 } - \dfrac { 5 } { 3 }$
$ $ Multiply the denominator and the numerator so that the denominator is the smallest common multiple $ $
$\dfrac { 4 \times \color{#FF6800}{ 2 } } { 3 \times \color{#FF6800}{ 2 } } - \dfrac { 1 \times \color{#FF6800}{ 3 } } { 2 \times \color{#FF6800}{ 3 } } + \dfrac { 3 \times \color{#FF6800}{ 3 } } { 2 \times \color{#FF6800}{ 3 } } - \dfrac { 5 \times \color{#FF6800}{ 2 } } { 3 \times \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } } { \color{#FF6800}{ 6 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 9 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 10 } } { \color{#FF6800}{ 6 } } }$
$ $ Since the denominator is the same as $ 6 $ , combine the fractions into one $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 6 } } }$
$\dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { 6 }$
$ $ Calculate the sum or the difference $ $
$\dfrac { \color{#FF6800}{ 4 } } { 6 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 6 } } }$
$ $ Reduce the fraction to the lowest term $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } }$
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