№1. Приведите дроби к новым знаменателям: а) = = = = ; б) = = = = в) = = = =

Ответ: a) 10/12, 15/18, 20/24, 40/48; б) 9/15, 15/25, 27/45, 84/140; в) 8/18, 16/36, 24/54, 40/90

Решение:

• а) \(\frac{5}{6} = \frac{5 \cdot 2}{6 \cdot 2} = \frac{10}{12}; \frac{5}{6} = \frac{5 \cdot 3}{6 \cdot 3} = \frac{15}{18}; \frac{5}{6} = \frac{5 \cdot 4}{6 \cdot 4} = \frac{20}{24}; \frac{5}{6} = \frac{5 \cdot 8}{6 \cdot 8} = \frac{40}{48}\)
• б) \(\frac{3}{5} = \frac{3 \cdot 3}{5 \cdot 3} = \frac{9}{15}; \frac{3}{5} = \frac{3 \cdot 5}{5 \cdot 5} = \frac{15}{25}; \frac{3}{5} = \frac{3 \cdot 9}{5 \cdot 9} = \frac{27}{45}; \frac{3}{5} = \frac{3 \cdot 28}{5 \cdot 28} = \frac{84}{140}\)
• в) \(\frac{4}{9} = \frac{4 \cdot 2}{9 \cdot 2} = \frac{8}{18}; \frac{4}{9} = \frac{4 \cdot 4}{9 \cdot 4} = \frac{16}{36}; \frac{4}{9} = \frac{4 \cdot 6}{9 \cdot 6} = \frac{24}{54}; \frac{4}{9} = \frac{4 \cdot 100}{9 \cdot 100} = \frac{400}{900}\)

Ответ: a) 10/12, 15/18, 20/24, 40/48; б) 9/15, 15/25, 27/45, 84/140; в) 8/18, 16/36, 24/54, 40/90