Odpowiedź :
Odpowiedź
[tex]\large\begin{aligned} 7\dfrac 4 8 \,\cdot\: 3 \dfrac 2 3 = \end[/tex]
[tex]\displaystyle = \left( 7 + \dfrac 4 8 \right) \,\cdot\: \left( 3 + \dfrac 2 3 \right) =\\\\\\=\left( \dfrac {7 \cdot 8} 8 + \dfrac 4 8 \right) \,\cdot\: \left( \dfrac {3 \cdot 3} 3+ \dfrac 2 3 \right) =\\\\\\=\left( \dfrac {56} 8 + \dfrac 4 8 \right) \,\cdot\: \left( \dfrac {9} 3+ \dfrac 2 3 \right) =\\\\\\=\left( \dfrac {56 + 4} 8 \right) \,\cdot\: \left( \dfrac {9 + 2} 3 \right) =[/tex]
[tex]= \dfrac {60} 8 \,\cdot\: \dfrac {11} 3 = \dfrac {60 \cdot 11} {8 \cdot 3} = \dfrac {20 \cdot 11} 8 = \dfrac {5 \cdot 11} 2 = \\\\\\\large \boxed { ~~ = \dfrac {55} 2 = 27\dfrac 1 2 ~~ }[/tex]
[tex]\large\begin{aligned} 4\dfrac 1 5 \,+\: 3 \dfrac 2 7 = \end[/tex]
[tex]\displaystyle =\left( 4 + \dfrac 1 5 \right) \,+\: \left( 3 + \dfrac 2 7 \right) =\\\\\\= \dfrac {21} 5 \,+\: \dfrac {23} 7 =\\\\\\= \dfrac {21 \cdot 7} {5 \cdot 7} \,+\: \dfrac {23 \cdot 5} {7 \cdot 5} =\\\\\\= \dfrac {147} {35} \,+\: \dfrac {115} {35} =\\\\\\= \dfrac {147 + 115} {35} =\\\\\\\large\boxed { ~~ = \dfrac {262} {35} = 7 \dfrac {17} {35} ~~ }[/tex]
[tex]\displaystyle ~~\: 3\dfrac 1 9 \,:\: \dfrac 7 8 =\\\\\\= 3\dfrac 1 9 \,\cdot\: \dfrac 8 7 =\\\\\\= \left( 3 + \dfrac 1 9 \right) \,\cdot\: \dfrac 8 7 =\\\\\\= \dfrac {28} 9 \,\cdot\: \dfrac 8 7 =\\\\\\= \dfrac {4} 9 \,\cdot\: \dfrac 8 1 =\\\\\\\large\boxed{ ~~ = \dfrac {32} 9 = 3\dfrac 5 9 ~~ }[/tex]
[tex]\large\begin{aligned} 4\dfrac 1 {12} \,-\: 2 \dfrac 4 6 = \end[/tex]
[tex]\displaystyle = \dfrac {49} {12} \,-\: \dfrac {16} 6 =\\\\\\= \dfrac {49} {12} \,-\: \dfrac {16 \cdot 2} {6 \cdot 2} =\\\\\\= \dfrac {49 - 32} {12} =\\\\\\\large\boxed { ~~ = \dfrac {17} {12} = 1 \dfrac 5 {12}~~ }[/tex]
[tex]\displaystyle ~~~ \dfrac { \left( 5\dfrac 1 4 \:+\: 2 \dfrac 1 7\right)^2 \:\cdot\:\, \left( 1 \dfrac 4 3 \:-\: \dfrac 7 5 \right)^3} {5\dfrac 3 2 \:+\: 3 \dfrac 3 9 \cdot \dfrac 2 7} =\\\\\\\\ = \dfrac { \left( 5\dfrac 1 4 \:+\: 2 \dfrac 1 7\right)^2 \:\cdot\:\, \left( 1 \dfrac 4 3 \:-\: \dfrac 7 5 \right)^3} {5\dfrac 3 2 \:+\: 3 \dfrac 1 3 \cdot \dfrac 2 7} =\\\\~~~~~~~~~~~~~~~~~~~~~~~~\_\_\_[/tex]
[tex]\displaystyle = \dfrac { \left( \dfrac {207} {28}\right)^2 \:\cdot\:\, \left( \dfrac {14} {15} \right)^3} { \dfrac {13} 2 \:+\: \dfrac {10} 3 \cdot \dfrac 2 7} =\\\\\\\\= \dfrac { \left( \dfrac {207} {28}\right)^2 \:\cdot\:\, \left( \dfrac {14} {15} \right)^3} { \dfrac {13} 2 \:+\: \dfrac {20} {21} } =\\\\\\\\= \dfrac { \left( \dfrac {9 \cdot 23} {2 \cdot 14}\right)^2 \:\cdot\:\, \left( \dfrac {14} {3 \cdot 5} \right)^3} { \dfrac {313} {42} } =[/tex]
[tex]\displaystyle = \left( \dfrac {9 \cdot 23} {2 \cdot 14}\right)^2 \:\cdot\:\, \left( \dfrac {14} {3 \cdot 5} \right)^3} \:\cdot\:\, \dfrac {42} {313} =\\\\\\= \left( \dfrac {9 \cdot 23} {2 \cdot 14}\right)^2 \:\cdot\:\, \left( \dfrac {14} {3 \cdot 5} \right)^3} \:\cdot\:\, \dfrac { 3 \cdot 14 } {313} =\\\\\\= \dfrac {9^2 \cdot 23^2 \cdot 14^3 \cdot 3 \cdot 14} {2^2 \cdot 14^2 \cdot 3^3 \cdot 5^3 \cdot 313} =[/tex]
[tex]\displaystyle = \dfrac {9 \cdot 23^2 \cdot 14^2} {2^2 \cdot 5^3 \cdot 313} =\\\\\\= \dfrac {9 \cdot 23^2 \cdot 7^2} { 5^3 \cdot 313 } =\\\\\\\large\boxed { ~~ = \dfrac {233289} {39125} = 5 \dfrac {37664} {39125} ~~ }[/tex]
Sprawdzone... :-)