445. Найдите значение выражения: а) (5/12 + 3/8) · 12/19; б) 6/7 · (11/18 − 5/12); в) (3 1/14 − 2 5/7) · (7 − 6 3/5); г) (3 1/12 − 2 3/4) · (1 1/6 − 5/12); д) (6 7/12 − 5 11/15) · (1 3/17 − 10/17); е) 2/3 · 9/16 − 5/24 · 2/5 − 1/6.

Question

Вопрос:

Accepted Answer

\(\left(\frac{5}{12}+\frac{3}{8}\right)\cdot\frac{12}{19}=\left(\frac{10}{24}+\frac{9}{24}\right)\cdot\frac{12}{19}=\frac{19}{24}\cdot\frac{12}{19}=\frac12\).
\(\frac67\cdot\left(\frac{11}{18}-\frac{5}{12}\right)=\frac67\cdot\left(\frac{22}{36}-\frac{15}{36}\right)=\frac67\cdot\frac7{36}=\frac16\).
\(\left(3\frac1{14}-2\frac57\right)\cdot\left(7-6\frac35\right)=\left(\frac{43}{14}-\frac{19}{7}\right)\cdot\frac25=\left(\frac{43}{14}-\frac{38}{14}\right)\cdot\frac25=\frac5{14}\cdot\frac25=\frac17\).
\(\left(3\frac1{12}-2\frac34\right)\cdot\left(1\frac16-\frac5{12}\right)=\left(\frac{37}{12}-\frac{33}{12}\right)\cdot\left(\frac76-\frac5{12}\right)=\frac13\cdot\frac34=\frac14\).
\(\left(6\frac7{12}-5\frac{11}{15}\right)\cdot\left(1\frac3{17}-\frac{10}{17}\right)=\left(\frac{79}{12}-\frac{86}{15}\right)\cdot\left(\frac{20}{17}-\frac{10}{17}\right)=\left(\frac{395}{60}-\frac{344}{60}\right)\cdot\frac{10}{17}=\frac{17}{20}\cdot\frac{10}{17}=\frac12\).
\(\frac23\cdot\frac9{16}-\frac5{24}\cdot\frac25-\frac16=\frac38-\frac1{12}-\frac16=\frac38-\frac14=\frac18\).

Ответ: а) \(\frac12\); б) \(\frac16\); в) \(\frac17\); г) \(\frac14\); д) \(\frac12\); е) \(\frac18\).