Упр.253 ГДЗ Муравин 6 класс (Математика)

1) 28/135•225/616;
2) 52/105 :91/700;
3) 125/576•432/625;
4) 81/320 :729/80.

1) $$\frac{28}{135}\cdot\frac{225}{616}=\frac{28\cdot225}{135\cdot616}$$

Сократим дроби: $$\frac{28}{616}=\frac{1}{22},\quad \frac{225}{135}=\frac{5}{3}.$$ Тогда

$$\frac{28\cdot225}{135\cdot616}=\frac{1\cdot5}{3\cdot22}=\frac{5}{66}.$$

2) $$\frac{52}{105}:\frac{91}{700}=\frac{52}{105}\cdot\frac{700}{91}$$

Сократим: $$\frac{52}{91}=\frac{4}{7},\quad \frac{700}{105}=\frac{20}{3}.$$ Тогда

$$\frac{52}{105}\cdot\frac{700}{91}=\frac{4\cdot20}{3\cdot7}=\frac{80}{21}=3\frac{17}{21}.$$

3) $$\frac{125}{576}\cdot\frac{432}{625}=\frac{125\cdot432}{576\cdot625}$$

Сократим: $$\frac{125}{625}=\frac{1}{5},\quad \frac{432}{576}=\frac{3}{4}.$$ Тогда

$$\frac{125\cdot432}{576\cdot625}=\frac{1\cdot3}{4\cdot5}=\frac{3}{20}.$$

4) $$\frac{81}{320}:\frac{729}{80}=\frac{81}{320}\cdot\frac{80}{729}$$

Сократим: $$\frac{81}{729}=\frac{1}{9},\quad \frac{80}{320}=\frac{1}{4}.$$ Тогда

$$\frac{81\cdot80}{320\cdot729}=\frac{1\cdot1}{4\cdot9}=\frac{1}{36}.$$

Ответ

1) $$\frac{5}{66}$$; 2) $$3\frac{17}{21}$$; 3) $$\frac{3}{20}$$; 4) $$\frac{1}{36}$$.