Задание №3. Вычислите выражения и сократите: 8/12 · 4/5 − 1/9 · 3/5; 1/12 · 4/5 + 1/3 · 5/4; 13/20 · 1/26 − 1/32 · 4/5; 15/22 · 11/13 + 2/13 · 5/4; (9/17 : 5/11) · 17/24; 14/23 · (3/4 : 7/23); (27/100 : 2/5) · 20/27.

Question

Вопрос:

Accepted Answer

\(\frac{8}{12}\cdot\frac{4}{5}-\frac{1}{9}\cdot\frac{3}{5}=\frac{8}{15}-\frac{1}{15}=\frac{7}{15}\).
\(\frac{1}{12}\cdot\frac{4}{5}+\frac{1}{3}\cdot\frac{5}{4}=\frac{1}{15}+\frac{5}{12}=\frac{4}{60}+\frac{25}{60}=\frac{29}{60}\).
\(\frac{13}{20}\cdot\frac{1}{26}-\frac{1}{32}\cdot\frac{4}{5}=\frac{1}{40}-\frac{1}{40}=0\).
\(\frac{15}{22}\cdot\frac{11}{13}+\frac{2}{13}\cdot\frac{5}{4}=\frac{15}{26}+\frac{5}{26}=\frac{10}{13}\).
\(\left(\frac{9}{17}:\frac{5}{11}\right)\cdot\frac{17}{24}=\frac{9}{17}\cdot\frac{11}{5}\cdot\frac{17}{24}=\frac{33}{40}\).
\(\frac{14}{23}\cdot\left(\frac{3}{4}:\frac{7}{23}\right)=\frac{14}{23}\cdot\frac{3}{4}\cdot\frac{23}{7}=\frac{3}{2}\).
\(\left(\frac{27}{100}:\frac{2}{5}\right)\cdot\frac{20}{27}=\frac{27}{100}\cdot\frac{5}{2}\cdot\frac{20}{27}=\frac{1}{2}\).

Ответ: 1) 7/15; 2) 29/60; 3) 0; 4) 10/13; 5) 33/40; 6) 3/2; 7) 1/2.