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Formula
Find the sum or difference of the fractions
$\left( + \dfrac{ 4 }{ 3 } \right) + \left( - \dfrac{ 1 }{ 2 } \right) + \left( + \dfrac{ 3 }{ 2 } \right) + \left( - \dfrac{ 5 }{ 3 } \right)$
$\dfrac { 2 } { 3 }$
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 
$\dfrac { 4 \times \color{#FF6800}{ 2 } } { 3 \times \color{#FF6800}{ 2 } } - \dfrac { 1 \times \color{#FF6800}{ 3 } } { 2 \times \color{#FF6800}{ 3 } } + \dfrac { 3 \times \color{#FF6800}{ 3 } } { 2 \times \color{#FF6800}{ 3 } } - \dfrac { 5 \times \color{#FF6800}{ 2 } } { 3 \times \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ \dfrac { 4 \times 2 } { 3 \times 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 \times 3 } { 2 \times 3 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 \times 3 } { 2 \times 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 \times 2 } { 3 \times 2 } }$
 Organize the expression 
$\color{#FF6800}{ \dfrac { 8 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 6 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 9 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 10 } { 6 } }$
$\color{#FF6800}{ \dfrac { 8 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 6 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 9 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 10 } { 6 } }$
 Since the denominator is the same as $6$ , combine the fractions into one 
$\color{#FF6800}{ \dfrac { 8 - 3 + 9 - 10 } { 6 } }$
$\dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { 6 }$
 Calculate the sum or the difference 
$\dfrac { \color{#FF6800}{ 4 } } { 6 }$
$\color{#FF6800}{ \dfrac { 4 } { 6 } }$
 Reduce the fraction to the lowest term 
$\color{#FF6800}{ \dfrac { 2 } { 3 } }$
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