a)
[tex]\frac{\frac{2}{7}-\left(-\frac{3}{4}\right)}{\frac{7}{8}}[/tex]
Aplicăm regula: [tex]-\left(-a\right)=a[/tex]
[tex]=\frac{\frac{2}{7}+\frac{3}{4}}{\frac{7}{8}}[/tex]
Aplicăm regula fracțiilor: [tex]\frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}[/tex]
[tex]=\frac{\left(\frac{2}{7}+\frac{3}{4}\right)\cdot \:8}{7}[/tex]
Adunăm:
[tex]\frac{2}{7}+\frac{3}{4}:\quad \frac{29}{28}[/tex]
[tex]=\frac{8\cdot \frac{29}{28}}{7}[/tex]
Înmulțim și calculăm:
[tex]\frac{29}{28}\cdot \:8 =\frac{29\cdot \:8}{28} =\frac{232}{28} =\frac{58}{7}[/tex]
[tex]=\frac{\frac{58}{7}}{7}[/tex]
Aplicăm regula fracțiilor:
[tex]\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
[tex]=\frac{58}{7\cdot \:7}[/tex]
[tex]=\frac{58}{49}[/tex]
b)
[tex]-\frac{1}{8}\times \frac{32}{3}-\frac{5}{6}\div \frac{5}{2}[/tex]
Aplicăm regula fracțiilor:
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=-\frac{1}{8}\times \frac{32}{3}-\frac{5}{6}\times \frac{2}{5}[/tex]
[tex]\frac{1}{8}\times \frac{32}{3}=\frac{4}{3}[/tex]
[tex]\frac{5}{6}\times \frac{2}{5}=\frac{1}{3}[/tex]
[tex]=-\frac{4}{3}-\frac{1}{3}[/tex]
Aplicăm regula:
[tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-4-1}{3}[/tex]
[tex]=\frac{-5}{3}[/tex]
[tex]=-\frac{5}{3}[/tex]
Sper că te-am ajutat!
Succes!
