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МатематикаВопрос:
798. Приведите дроби к общему знаменателю, равному произведению знаменателей дробей: a) \(\frac{1}{2}\) и \(\frac{1}{3}\); б) \(\frac{1}{2}\) и \(\frac{1}{5}\); в) \(\frac{1}{2}\) и \(\frac{1}{7}\); г) \(\frac{1}{2}\) и \(\frac{1}{9}\); д) \(\frac{1}{2}\) и \(\frac{2}{3}\); е) \(\frac{1}{2}\) и \(\frac{3}{5}\); ж) \(\frac{1}{6}\) и \(\frac{1}{7}\); з) \(\frac{1}{7}\) и \(\frac{2}{9}\); и) \(\frac{1}{7}\) и \(\frac{1}{8}\); к) \(\frac{3}{7}\) и \(\frac{5}{8}\); л) \(\frac{1}{10}\) и \(\frac{1}{11}\); м) \(\frac{3}{10}\) и \(\frac{10}{11}\); н) \(\frac{1}{10}\) и \(\frac{1}{13}\); о) \(\frac{2}{10}\) и \(\frac{1}{13}\); п) \(\frac{3}{10}\) и \(\frac{4}{13}\); р) \(\frac{9}{10}\) и \(\frac{12}{13}\).
Ответ:
Чтобы привести дроби к общему знаменателю, равному произведению знаменателей, нужно умножить числитель и знаменатель каждой дроби на знаменатель другой дроби.
a) \(\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}\); \(\frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}\)
б) \(\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}\); \(\frac{1}{5} = \frac{1 \cdot 2}{5 \cdot 2} = \frac{2}{10}\)
в) \(\frac{1}{2} = \frac{1 \cdot 7}{2 \cdot 7} = \frac{7}{14}\); \(\frac{1}{7} = \frac{1 \cdot 2}{7 \cdot 2} = \frac{2}{14}\)
г) \(\frac{1}{2} = \frac{1 \cdot 9}{2 \cdot 9} = \frac{9}{18}\); \(\frac{1}{9} = \frac{1 \cdot 2}{9 \cdot 2} = \frac{2}{18}\)
д) \(\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}\); \(\frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6}\)
е) \(\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}\); \(\frac{3}{5} = \frac{3 \cdot 2}{5 \cdot 2} = \frac{6}{10}\)
ж) \(\frac{1}{6} = \frac{1 \cdot 7}{6 \cdot 7} = \frac{7}{42}\); \(\frac{1}{7} = \frac{1 \cdot 6}{7 \cdot 6} = \frac{6}{42}\)
з) \(\frac{1}{7} = \frac{1 \cdot 9}{7 \cdot 9} = \frac{9}{63}\); \(\frac{2}{9} = \frac{2 \cdot 7}{9 \cdot 7} = \frac{14}{63}\)
и) \(\frac{1}{7} = \frac{1 \cdot 8}{7 \cdot 8} = \frac{8}{56}\); \(\frac{1}{8} = \frac{1 \cdot 7}{8 \cdot 7} = \frac{7}{56}\)
к) \(\frac{3}{7} = \frac{3 \cdot 8}{7 \cdot 8} = \frac{24}{56}\); \(\frac{5}{8} = \frac{5 \cdot 7}{8 \cdot 7} = \frac{35}{56}\)
л) \(\frac{1}{10} = \frac{1 \cdot 11}{10 \cdot 11} = \frac{11}{110}\); \(\frac{1}{11} = \frac{1 \cdot 10}{11 \cdot 10} = \frac{10}{110}\)
м) \(\frac{3}{10} = \frac{3 \cdot 11}{10 \cdot 11} = \frac{33}{110}\); \(\frac{10}{11} = \frac{10 \cdot 10}{11 \cdot 10} = \frac{100}{110}\)
н) \(\frac{1}{10} = \frac{1 \cdot 13}{10 \cdot 13} = \frac{13}{130}\); \(\frac{1}{13} = \frac{1 \cdot 10}{13 \cdot 10} = \frac{10}{130}\)
о) \(\frac{2}{10} = \frac{2 \cdot 13}{10 \cdot 13} = \frac{26}{130}\); \(\frac{1}{13} = \frac{1 \cdot 10}{13 \cdot 10} = \frac{10}{130}\)
п) \(\frac{3}{10} = \frac{3 \cdot 13}{10 \cdot 13} = \frac{39}{130}\); \(\frac{4}{13} = \frac{4 \cdot 10}{13 \cdot 10} = \frac{40}{130}\)
р) \(\frac{9}{10} = \frac{9 \cdot 13}{10 \cdot 13} = \frac{117}{130}\); \(\frac{12}{13} = \frac{12 \cdot 10}{13 \cdot 10} = \frac{120}{130}\)
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