3. Решите примеры: 1) 7/9 − 5/6 + 4/15; 2) (2/3 − 4/9) · 3/8; 3) 2/7 + 3/8 : 7/32; 4) 5/9 : (7/9 + 11/18); 5) 1 − 4/7 : 16/21; 6) 5/12 · (1/5 + 3/25); 7) 9/14 · (17/24 − 5/12); 8) 24/49 · 6/7 + 1/14.

Question

Вопрос:

Accepted Answer

1) Приводим к общему знаменателю 90: \(\frac{70}{90}-\frac{75}{90}+\frac{24}{90}=\frac{19}{90}\).

2) \(\left(\frac{2}{3}-\frac{4}{9}\right)\cdot\frac{3}{8}=\frac{2}{9}\cdot\frac{3}{8}=\frac{1}{12}\).

3) \(\frac{2}{7}+\frac{3}{8}:\frac{7}{32}=\frac{2}{7}+\frac{3}{8}\cdot\frac{32}{7}=\frac{2}{7}+\frac{12}{7}=2\).

4) \(\frac{5}{9}:\left(\frac{7}{9}+\frac{11}{18}\right)=\frac{5}{9}:\frac{25}{18}=\frac{5}{9}\cdot\frac{18}{25}=\frac{2}{5}\).

5) \(1-\frac{4}{7}:\frac{16}{21}=1-\frac{4}{7}\cdot\frac{21}{16}=1-\frac{3}{4}=\frac{1}{4}\).

6) \(\frac{5}{12}\cdot\left(\frac{1}{5}+\frac{3}{25}\right)=\frac{5}{12}\cdot\frac{8}{25}=\frac{2}{15}\).

7) \(\frac{9}{14}\cdot\left(\frac{17}{24}-\frac{5}{12}\right)=\frac{9}{14}\cdot\frac{7}{24}=\frac{3}{16}\).

8) \(\frac{24}{49}\cdot\frac{6}{7}+\frac{1}{14}=\frac{144}{343}+\frac{1}{14}=\frac{317}{686}\).

Ответ: 1) 19/90; 2) 1/12; 3) 2; 4) 2/5; 5) 1/4; 6) 2/15; 7) 3/16; 8) 317/686.