03.02 Умножение обыкновенных дробей.pdf

Предмет: Математика

Класс: 6

Привет! Давай выполним умножение обыкновенных дробей и смешанных чисел.

№1

Образец:

\[\frac{2}{3} \cdot \frac{5}{7} = \frac{2 \cdot 5}{3 \cdot 7} = \frac{10}{21}\]

Решите:

1. \[\frac{2}{5} \cdot \frac{3}{7} = \frac{2 \cdot 3}{5 \cdot 7} = \frac{6}{35}\]

2. \[\frac{1}{2} \cdot \frac{5}{6} = \frac{1 \cdot 5}{2 \cdot 6} = \frac{5}{12}\]

3. \[\frac{7}{2} \cdot \frac{2}{11} = \frac{7 \cdot 2}{2 \cdot 11} = \frac{14}{22} = \frac{7}{11}\]

4. \[\frac{10}{2} \cdot \frac{2}{11} = \frac{10 \cdot 2}{2 \cdot 11} = \frac{20}{22} = \frac{10}{11}\]

5. \[\frac{1}{4} \cdot \frac{4}{15} = \frac{1 \cdot 4}{4 \cdot 15} = \frac{4}{60} = \frac{1}{15}\]

№2

Образец:

\[4 \cdot \frac{5}{7} = \frac{4}{1} \cdot \frac{5}{7} = \frac{4 \cdot 5}{1 \cdot 7} = \frac{20}{7} = 2\frac{6}{7}\]

Решите:

1. \[8 \cdot \frac{2}{3} = \frac{8}{1} \cdot \frac{2}{3} = \frac{8 \cdot 2}{1 \cdot 3} = \frac{16}{3} = 5\frac{1}{3}\]

2. \[\frac{3}{2} \cdot 5 = \frac{3}{2} \cdot \frac{5}{1} = \frac{3 \cdot 5}{2 \cdot 1} = \frac{15}{2} = 7\frac{1}{2}\]

3. \[\frac{12}{13} \cdot 2 = \frac{12}{13} \cdot \frac{2}{1} = \frac{12 \cdot 2}{13 \cdot 1} = \frac{24}{13} = 1\frac{11}{13}\]

4. \[11 \cdot \frac{1}{2} = \frac{11}{1} \cdot \frac{1}{2} = \frac{11 \cdot 1}{1 \cdot 2} = \frac{11}{2} = 5\frac{1}{2}\]

5. \[6 \cdot \frac{10}{11} = \frac{6}{1} \cdot \frac{10}{11} = \frac{6 \cdot 10}{1 \cdot 11} = \frac{60}{11} = 5\frac{5}{11}\]

№3

Образец:

\[\frac{12}{15} \cdot \frac{5}{24} = \frac{12^1 \cdot 5^1}{15^3 \cdot 24^2} = \frac{1 \cdot 1}{3 \cdot 2} = \frac{1}{6}\]

Решите:

1. \[\frac{12}{15} \cdot \frac{3}{4} = \frac{12^3 \cdot 3}{15^5 \cdot 4^1} = \frac{3 \cdot 3}{5 \cdot 1} = \frac{9}{5} = 1\frac{4}{5}\]

2. \[\frac{11}{16} \cdot \frac{4}{33} = \frac{11^1 \cdot 4^1}{16^4 \cdot 33^3} = \frac{1 \cdot 1}{4 \cdot 3} = \frac{1}{12}\]

3. \[\frac{7}{10} \cdot \frac{5}{21} = \frac{7^1 \cdot 5^1}{10^2 \cdot 21^3} = \frac{1 \cdot 1}{2 \cdot 3} = \frac{1}{6}\]

4. \[\frac{12}{100} \cdot \frac{50}{12} = \frac{12^1 \cdot 50^1}{100^2 \cdot 12^1} = \frac{1 \cdot 1}{2 \cdot 1} = \frac{1}{2}\]

5. \[\frac{14}{32} \cdot \frac{64}{7} = \frac{14^2 \cdot 64^2}{32^1 \cdot 7^1} = \frac{2 \cdot 2}{1 \cdot 1} = 4\]

№4

Образец:

\[1\frac{1}{3} \cdot \frac{1}{5} = \frac{2 \cdot 1}{3 \cdot 5} = \frac{5 \cdot 6^2}{3^1 \cdot 21^7} = \frac{1 \cdot 2}{1 \cdot 1} = 2\]

Решите:

1. \[2\frac{1}{2} \cdot \frac{2}{5} = \frac{5}{2} \cdot \frac{2}{5} = \frac{5 \cdot 2}{2 \cdot 5} = 1\]

2. \[3\frac{1}{2} \cdot 1\frac{1}{7} = \frac{7}{2} \cdot \frac{8}{7} = \frac{7 \cdot 8}{2 \cdot 7} = \frac{56}{14} = 4\]

3. \[1\frac{1}{2} \cdot 2\frac{1}{4} = \frac{3}{2} \cdot \frac{9}{4} = \frac{3 \cdot 9}{2 \cdot 4} = \frac{27}{8} = 3\frac{3}{8}\]

4. \[1\frac{1}{3} \cdot \frac{2}{11} = \frac{4}{3} \cdot \frac{2}{11} = \frac{4 \cdot 2}{3 \cdot 11} = \frac{8}{33}\]

5. \[2\frac{1}{2} \cdot 2\frac{2}{11} = \frac{5}{2} \cdot \frac{24}{11} = \frac{5 \cdot 24}{2 \cdot 11} = \frac{120}{22} = \frac{60}{11} = 5\frac{5}{11}\]

Ответ: Решения выше