Вопрос:

243. Сократите дроби: a) $$ rac{22}{66}$$, $$ rac{125}{75}$$, $$ rac{75}{100}$$, $$ rac{24}{360}$$, $$ rac{125}{1000}$$, $$ rac{100}{250}$$, $$ rac{198}{126}$$. б) $$ rac{42}{720}$$, $$ rac{75}{300}$$, $$ rac{40}{64}$$, $$ rac{3}{243}$$, $$ rac{18}{300}$$, $$ rac{45}{900}$$, $$ rac{120}{180}$$.

Ответ:

Решение:

a)

  1. $$\frac{22}{66} = \frac{22 \cdot 1}{22 \cdot 3} = \frac{1}{3}$$
  2. $$\frac{125}{75} = \frac{25 \cdot 5}{25 \cdot 3} = \frac{5}{3}$$
  3. $$\frac{75}{100} = \frac{25 \cdot 3}{25 \cdot 4} = \frac{3}{4}$$
  4. $$\frac{24}{360} = \frac{12 \cdot 2}{12 \cdot 30} = \frac{2}{30} = \frac{1}{15}$$
  5. $$\frac{125}{1000} = \frac{125 \cdot 1}{125 \cdot 8} = \frac{1}{8}$$
  6. $$\frac{100}{250} = \frac{50 \cdot 2}{50 \cdot 5} = \frac{2}{5}$$
  7. $$\frac{198}{126} = \frac{18 \cdot 11}{18 \cdot 7} = \frac{11}{7}$$

б)

  1. $$\frac{42}{720} = \frac{6 \cdot 7}{6 \cdot 120} = \frac{7}{120}$$
  2. $$\frac{75}{300} = \frac{75 \cdot 1}{75 \cdot 4} = \frac{1}{4}$$
  3. $$\frac{40}{64} = \frac{8 \cdot 5}{8 \cdot 8} = \frac{5}{8}$$
  4. $$\frac{3}{243} = \frac{3 \cdot 1}{3 \cdot 81} = \frac{1}{81}$$
  5. $$\frac{18}{300} = \frac{6 \cdot 3}{6 \cdot 50} = \frac{3}{50}$$
  6. $$\frac{45}{900} = \frac{45 \cdot 1}{45 \cdot 20} = \frac{1}{20}$$
  7. $$\frac{120}{180} = \frac{60 \cdot 2}{60 \cdot 3} = \frac{2}{3}$$
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