5.334 Сократите дробь: 33 150 25 14 150 1000 264 a) 99 , 125 , 100 , 210 , 1000 , 2500 , 148 ; 45 30 125 7 12 75 140 б) 630, 64 , 500 , 217, 600, 300, 210

а)

• $$ \frac{33}{99} = \frac{3 \cdot 11}{9 \cdot 11} = \frac{3}{9} = \frac{1 \cdot 3}{3 \cdot 3} = \frac{1}{3} $$
• $$\frac{150}{125} = \frac{25 \cdot 6}{25 \cdot 5} = \frac{6}{5}$$
• $$\frac{25}{100} = \frac{25 \cdot 1}{25 \cdot 4} = \frac{1}{4}$$
• $$\frac{14}{210} = \frac{7 \cdot 2}{7 \cdot 30} = \frac{2}{30} = \frac{2 \cdot 1}{2 \cdot 15} = \frac{1}{15}$$
• $$\frac{150}{1000} = \frac{15 \cdot 10}{100 \cdot 10} = \frac{15}{100} = \frac{5 \cdot 3}{5 \cdot 20} = \frac{3}{20}$$
• $$\frac{1000}{2500} = \frac{10 \cdot 100}{25 \cdot 100} = \frac{10}{25} = \frac{5 \cdot 2}{5 \cdot 5} = \frac{2}{5}$$
• $$\frac{264}{148} = \frac{4 \cdot 66}{4 \cdot 37} = \frac{66}{37}$$

б)

• $$\frac{45}{630} = \frac{5 \cdot 9}{70 \cdot 9} = \frac{5}{70} = \frac{5 \cdot 1}{5 \cdot 14} = \frac{1}{14}$$
• $$\frac{30}{64} = \frac{2 \cdot 15}{2 \cdot 32} = \frac{15}{32}$$
• $$\frac{125}{500} = \frac{125 \cdot 1}{125 \cdot 4} = \frac{1}{4}$$
• $$\frac{7}{217} = \frac{7 \cdot 1}{7 \cdot 31} = \frac{1}{31}$$
• $$\frac{12}{600} = \frac{12 \cdot 1}{12 \cdot 50} = \frac{1}{50}$$
• $$\frac{75}{300} = \frac{75 \cdot 1}{75 \cdot 4} = \frac{1}{4}$$
• $$\frac{140}{210} = \frac{14 \cdot 10}{21 \cdot 10} = \frac{14}{21} = \frac{7 \cdot 2}{7 \cdot 3} = \frac{2}{3}$$

Ответ: а) 1/3, 6/5, 1/4, 1/15, 3/20, 2/5, 66/37; б) 1/14, 15/32, 1/4, 1/31, 1/50, 1/4, 2/3.