1. Приведите к наименьшему общему знаменателю: 1) 1 2 и 1 6 ; 3 8 и 3 4 ; 2 9 и 5 36 ; 3 7 и 7 35 2) 1 15 и 1 5 ; 7 16 и 3 8 ; 11 14 и 13 140 ; 15 16 и 23 192 3) 7 10 и 2 9 ; 13 15 и 7 8 ; 3 10 и 17 9 ; 7 13 и 8 15 2. Приведите дроби к наименьшему общему знаменателю: 1-й уровень сложности 1. 1. 1. б) 1 1 1 a) B) 2' 3' 4 3' 4' 5' 3' 5' 30' 1. 1. 1. г) 2' 4' 16'

1. Приведите к наименьшему общему знаменателю:

1) \(\frac{1}{2}\) и \(\frac{1}{6}\); \(\frac{3}{8}\) и \(\frac{3}{4}\); \(\frac{2}{9}\) и \(\frac{5}{36}\); \(\frac{3}{7}\) и \(\frac{7}{35}\)

\(\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}\) \(\frac{3}{8}\) и \(\frac{3}{4} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}\) \(\frac{2}{9} = \frac{2 \cdot 4}{9 \cdot 4} = \frac{8}{36}\) и \(\frac{5}{36}\) \(\frac{3}{7} = \frac{3 \cdot 5}{7 \cdot 5} = \frac{15}{35}\) и \(\frac{7}{35}\)

2) \(\frac{1}{15}\) и \(\frac{1}{5}\); \(\frac{7}{16}\) и \(\frac{3}{8}\); \(\frac{11}{14}\) и \(\frac{13}{140}\); \(\frac{15}{16}\) и \(\frac{23}{192}\)

\(\frac{1}{15}\) и \(\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}\) \(\frac{7}{16}\) и \(\frac{3}{8} = \frac{3 \cdot 2}{8 \cdot 2} = \frac{6}{16}\) \(\frac{11}{14} = \frac{11 \cdot 10}{14 \cdot 10} = \frac{110}{140}\) и \(\frac{13}{140}\) \(\frac{15}{16} = \frac{15 \cdot 12}{16 \cdot 12} = \frac{180}{192}\) и \(\frac{23}{192}\)

3) \(\frac{7}{10}\) и \(\frac{2}{9}\); \(\frac{13}{15}\) и \(\frac{7}{8}\); \(\frac{3}{10}\) и \(\frac{17}{9}\); \(\frac{7}{13}\) и \(\frac{8}{15}\)

\(\frac{7}{10} = \frac{7 \cdot 9}{10 \cdot 9} = \frac{63}{90}\) и \(\frac{2}{9} = \frac{2 \cdot 10}{9 \cdot 10} = \frac{20}{90}\) \(\frac{13}{15} = \frac{13 \cdot 8}{15 \cdot 8} = \frac{104}{120}\) и \(\frac{7}{8} = \frac{7 \cdot 15}{8 \cdot 15} = \frac{105}{120}\) \(\frac{3}{10} = \frac{3 \cdot 9}{10 \cdot 9} = \frac{27}{90}\) и \(\frac{17}{9} = \frac{17 \cdot 10}{9 \cdot 10} = \frac{170}{90}\) \(\frac{7}{13} = \frac{7 \cdot 15}{13 \cdot 15} = \frac{105}{195}\) и \(\frac{8}{15} = \frac{8 \cdot 13}{15 \cdot 13} = \frac{104}{195}\)

2. Приведите дроби к наименьшему общему знаменателю:

а) \(\frac{1}{2}\); \(\frac{1}{3}\); \(\frac{1}{4}\)

\(\frac{1}{2} = \frac{1 \cdot 6}{2 \cdot 6} = \frac{6}{12}\) \(\frac{1}{3} = \frac{1 \cdot 4}{3 \cdot 4} = \frac{4}{12}\) \(\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}\)

б) \(\frac{1}{3}\); \(\frac{1}{4}\); \(\frac{1}{5}\)

\(\frac{1}{3} = \frac{1 \cdot 20}{3 \cdot 20} = \frac{20}{60}\) \(\frac{1}{4} = \frac{1 \cdot 15}{4 \cdot 15} = \frac{15}{60}\) \(\frac{1}{5} = \frac{1 \cdot 12}{5 \cdot 12} = \frac{12}{60}\)

в) \(\frac{1}{3}\); \(\frac{1}{5}\); \(\frac{1}{30}\)

\(\frac{1}{3} = \frac{1 \cdot 10}{3 \cdot 10} = \frac{10}{30}\) \(\frac{1}{5} = \frac{1 \cdot 6}{5 \cdot 6} = \frac{6}{30}\) \(\frac{1}{30}\)

г) \(\frac{1}{2}\); \(\frac{1}{4}\); \(\frac{1}{16}\)

\(\frac{1}{2} = \frac{1 \cdot 8}{2 \cdot 8} = \frac{8}{16}\) \(\frac{1}{4} = \frac{1 \cdot 4}{4 \cdot 4} = \frac{4}{16}\) \(\frac{1}{16}\)

Ответ: смотри решение выше

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