Explicație pas cu pas:
[tex] \bf a) \: \: \dfrac{5}{7} \cdot \bigg( \dfrac{3 \cdot5 + 1}{5} + \dfrac{17}{10} \bigg) = [/tex]
[tex] \bf \dfrac{5}{7} \cdot \bigg( \dfrac{16}{5} + \dfrac{17}{10} \bigg) = [/tex]
[tex] \bf \dfrac{5}{7} \cdot \dfrac{16}{5} + \dfrac{5}{7} \cdot \dfrac{17}{10} = [/tex]
[tex] \bf \dfrac{ \not5}{7} \cdot \dfrac{16}{ \not5} + \dfrac{ \not5}{7} \cdot \dfrac{17}{ \not10} = [/tex]
[tex] \bf \dfrac{16}{ 7} + \dfrac{ 17}{14} = [/tex]
[tex] \bf \dfrac{2 \cdot16}{ 14} + \dfrac{ 17}{14} = [/tex]
[tex]\bf \dfrac{32 + 17}{ 14} = [/tex]
[tex]\bf \dfrac{49}{ 14} = \dfrac{ \not49}{ \not14} = [/tex]
[tex] \large\boxed{ \boxed{\bf \dfrac{7}{ 2}}}[/tex]
[tex]\it~~~[/tex]
[tex]\bf b) \: \: \dfrac{2}{5} \cdot \bigg( \dfrac{2 \cdot4 + 3}{4} - \dfrac{13}{12} \bigg) =[/tex]
[tex]\bf \dfrac{2}{5} \cdot \bigg( \dfrac{11}{4} - \dfrac{13}{12} \bigg) =[/tex]
[tex]\bf \dfrac{2}{5} \cdot \dfrac{11}{4} - \dfrac{2}{5} \cdot\dfrac{13}{12} =[/tex]
[tex]\bf \dfrac{ \not2}{5} \cdot \dfrac{11}{\not4} - \dfrac{\not2}{5} \cdot\dfrac{13}{\not12} =[/tex]
[tex]\bf \dfrac{ 1}{5} \cdot \dfrac{11}{2} - \dfrac{1}{5} \cdot\dfrac{13}{6} =[/tex]
[tex]\bf \dfrac{ 11}{10} - \dfrac{13}{30}=[/tex]
[tex]\bf \dfrac{ 3 \cdot 11}{30} - \dfrac{13}{30}=[/tex]
[tex]\bf \dfrac{ 33 - 13}{30} =[/tex]
[tex]\bf \dfrac{ 20}{30} = \dfrac{ \not20}{ \not30} =[/tex]
[tex]\large \boxed{ \boxed{\bf \dfrac{ 2}{3}}}[/tex]
==pav38==
