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Find the sum of the fractions

Answer

$\dfrac { 46 } { 35 }$

Find the sum of the fractions

$\dfrac { 3 } { \color{#FF6800}{ 5 } } + \dfrac { 5 } { \color{#FF6800}{ 7 } }$

$ $ The smallest common multiple in denominator is $ 35$

$\dfrac { 3 } { \color{#FF6800}{ 5 } } + \dfrac { 5 } { \color{#FF6800}{ 7 } }$

$\dfrac { 3 } { 5 } + \dfrac { 5 } { 7 }$

$ $ Multiply the denominator and the numerator so that the denominator is the smallest common multiple $ $

$\dfrac { 3 \times \color{#FF6800}{ 7 } } { 5 \times \color{#FF6800}{ 7 } } + \dfrac { 5 \times \color{#FF6800}{ 5 } } { 7 \times \color{#FF6800}{ 5 } }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 7 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } } }$

$ $ Organize the expression $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 21 } } { \color{#FF6800}{ 35 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 25 } } { \color{#FF6800}{ 35 } } }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 21 } } { \color{#FF6800}{ 35 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 25 } } { \color{#FF6800}{ 35 } } }$

$ $ Since the denominator is the same as $ 35 $ , combine the fractions into one $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 21 } \color{#FF6800}{ + } \color{#FF6800}{ 25 } } { \color{#FF6800}{ 35 } } }$

$\dfrac { \color{#FF6800}{ 21 } \color{#FF6800}{ + } \color{#FF6800}{ 25 } } { 35 }$

$ $ Add $ 21 $ and $ 25$

$\dfrac { \color{#FF6800}{ 46 } } { 35 }$

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