14. Вычисления: Действия с обыкновенными дробями

$$\frac{12}{7} : \left( \frac{6}{7}-\frac{3}{4} \right) = \frac{12}{7} : \frac{3}{28} $$ $$ \frac{12}{7} \cdot \frac{28}{3} = 16$$

$$\frac{8}{15} : \left( \frac{2}{3}-\frac{3}{5} \right)=\frac{8}{15} : \frac{1}{15} $$ $$ \frac{8}{15} \cdot \frac{15}{1} = 8$$

$$\left( \frac{1}{13}-2\frac{3}{4} \right) \cdot 26 = \frac{1}{13} \cdot 26-2\frac{3}{4} \cdot 26$$ $$ \frac{1}{13} \cdot 26-2\frac{3}{4}\cdot 26= 2-\frac{11 \cdot 26}{4}$$ $$2-\frac{11 \cdot 26}{4}= 2-\frac{143}{2} = -69.5$$

$$\frac{13}{7} : \left( \frac{1}{3} + \frac{2}{7} \right) = \frac{13}{7} : \left( \frac{7}{21} + \frac{6}{21} \right)$$ $$\frac{13}{7} : \left( \frac{7}{21} + \frac{6}{21} \right) = \frac{13}{7} : \frac{13}{21}$$ $$\frac{13}{7} : \frac{13}{21} = \frac{13 \cdot 21}{7 \cdot 13} = 3$$

$$\frac{7}{2}\cdot\frac{5}{4}-\frac{3}{8}=\frac{35}{8}-\frac{3}{8}$$$$\frac{35}{8}-\frac{3}{8}=\frac{32}{8}=4$$

$$\frac{5}{4}+\frac{7}{6}:\frac{2}{3}=\frac{5}{4}+\frac{7}{6}\cdot\frac{3}{2}$$ $$\frac{5}{4}+\frac{7}{{}^{2}\cancel{6}}\cdot\frac{{}^{1}\cancel{3}}{2}=\frac{5}{4}+\frac{7}{4}=\frac{12}{4}=3$$

$$\frac{12}{7}:\Big(\frac{6}{7}-\frac{3}{4}\Big)=\frac{12}{7}:\Big(\frac{24}{28}-\frac{21}{28}\Big)$$$$\frac{12}{7}:\Big(\frac{24}{28}-\frac{21}{28}\Big)=\frac{12}{7}:\frac{3}{28}$$$$\frac{12}{7}:\frac{3}{28}=\frac{{}^{4}\cancel{12}}{7}\cdot\frac{28}{{}^{1}\cancel{3}}=16$$

$$\frac{7}{18}+\frac{5}{2}\cdot\frac{4}{9}=\frac{7}{18}+\frac{5\cdot4}{2\cdot9}$$ $$\frac{7}{18}+\frac{20}{18}=\frac{27}{18}=1.5$$

$$\Big(-2\frac{3}{4}-\frac{3}{8}\Big)\cdot160=\Big(-\frac{22}{8}-\frac{3}{8}\Big)\cdot160$$ $$\Big(-\frac{22}{8}-\frac{3}{8}\Big)\cdot160=-\frac{25\cdot160}{8}$$ $$-\frac{25\cdot{}^{20}\cancel{160}}{{}^{1}\cancel{8}}=-500$$

$$\frac{2}{5}+\frac{1}{4}+2=0.4+0.25+2=2.65$$

$$\frac{29}{7}:\Big(\frac{2}{7}+\frac{3}{4}\Big)=\frac{29}{7}:\frac{8+21}{28}$$ $$\frac{29}{7}:\frac{8+21}{28}=\frac{29}{7}:\frac{29}{28}$$ $$\frac{29}{7}:\frac{29}{28}=\frac{29\cdot28}{7\cdot29}$$ $$\frac{{}^{}\cancel{29}\cdot28}{7\cdot{}^{}\cancel{29}}=4$$

$$\Big(\frac{7}{8}-\frac{17}{12}\Big):\frac{5}{12}=\Big(\frac{21-34}{24}\Big):\frac{5}{12}$$ $$\Big(\frac{21-34}{24}\Big):\frac{5}{12}=-\frac{13}{24}:\frac{5}{12}$$ $$-\frac{13}{24}:\frac{5}{12}=-\frac{13\cdot12}{24\cdot5}$$ $$-\frac{13\cdot{}^{1}\cancel{12}}{{}^{2}\cancel{24}\cdot5}=-1.3$$

$$\frac{4}{11}:\Big(-\frac{16}{33}\Big)+5\frac{3}{4}=-\frac{4\cdot33}{11\cdot16}+5\frac{3}{4}$$ $$-\frac{{}^{1}\cancel{4}\cdot33}{11\cdot{}^{4}\cancel{16}}+5\frac{3}{4}=-\frac{3}{4}+5\frac{3}{4}=5$$

$$\Big(\frac{11}{12}+\frac{11}{20}\Big)\cdot\frac{15}{8}=\Big(\frac{55+33}{60}\Big)\cdot\frac{15}{8}$$ $$\Big(\frac{55+33}{60}\Big)\cdot\frac{15}{8}=\frac{88}{60}\cdot\frac{15}{8}$$ $$\frac{88}{60}\cdot\frac{15}{8}=\frac{88\cdot15}{60\cdot8}$$ $$\frac{{}^{11}\cancel{88}\cdot{}^{1}\cancel{15}}{{}^{4}\cancel{60}\cdot{}^{1}\cancel{8}}=2.75$$

$$\frac{18}{4}\cdot\frac{14}{3}:\frac{4}{5}=\frac{18}{4}\cdot\frac{14}{3}\cdot\frac{5}{4}$$ $$\frac{18}{4}\cdot\frac{14}{3}\cdot\frac{5}{4}=\frac{6}{2}\cdot\frac{7}{1}\cdot\frac{5}{4}$$ $$\frac{6\cdot7\cdot5}{2\cdot1\cdot4}=\frac{210}{8}=26.25$$