Сложите дроби: д) 2/9 + 1/12 = а) 7/10 + 1/10 = б) 7/12 + 1/4 = в) 5/5 + 1/15 = г) 5/6 + 1/9 = е) 7/24 + 1/60 = ж) 1/42 + 2/63 = з) 5/12 + 3/20 = 6. Вычислите разность. а) 7/8 - 3/4 = б) 9/10 - 2/5 = д) 7/12 - 8/15 = е) 25/39 - 15/26 =

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Сложение дробей

1. д) \(\frac{2}{9} + \frac{1}{12} = \frac{2 \cdot 4}{9 \cdot 4} + \frac{1 \cdot 3}{12 \cdot 3} = \frac{8}{36} + \frac{3}{36} = \frac{8+3}{36} = \frac{11}{36}\)
2. а) \(\frac{7}{10} + \frac{1}{10} = \frac{7+1}{10} = \frac{8}{10} = \frac{4}{5}\)
3. б) \(\frac{7}{12} + \frac{1}{4} = \frac{7}{12} + \frac{1 \cdot 3}{4 \cdot 3} = \frac{7}{12} + \frac{3}{12} = \frac{7+3}{12} = \frac{10}{12} = \frac{5}{6}\)
4. в) \(\frac{5}{5} + \frac{1}{15} = \frac{5 \cdot 3}{5 \cdot 3} + \frac{1}{15} = \frac{15}{15} + \frac{1}{15} = \frac{15+1}{15} = \frac{16}{15}\)
5. г) \(\frac{5}{6} + \frac{1}{9} = \frac{5 \cdot 3}{6 \cdot 3} + \frac{1 \cdot 2}{9 \cdot 2} = \frac{15}{18} + \frac{2}{18} = \frac{15+2}{18} = \frac{17}{18}\)
6. e) \(\frac{7}{24} + \frac{1}{60} = \frac{7 \cdot 5}{24 \cdot 5} + \frac{1 \cdot 2}{60 \cdot 2} = \frac{35}{120} + \frac{2}{120} = \frac{35+2}{120} = \frac{37}{120}\)
7. ж) \(\frac{1}{42} + \frac{2}{63} = \frac{1 \cdot 3}{42 \cdot 3} + \frac{2 \cdot 2}{63 \cdot 2} = \frac{3}{126} + \frac{4}{126} = \frac{3+4}{126} = \frac{7}{126} = \frac{1}{18}\)
8. з) \(\frac{5}{12} + \frac{3}{20} = \frac{5 \cdot 5}{12 \cdot 5} + \frac{3 \cdot 3}{20 \cdot 3} = \frac{25}{60} + \frac{9}{60} = \frac{25+9}{60} = \frac{34}{60} = \frac{17}{30}\)

Вычитание дробей

1. а) \(\frac{7}{8} - \frac{3}{4} = \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2} = \frac{7}{8} - \frac{6}{8} = \frac{7-6}{8} = \frac{1}{8}\)
2. б) \(\frac{9}{10} - \frac{2}{5} = \frac{9}{10} - \frac{2 \cdot 2}{5 \cdot 2} = \frac{9}{10} - \frac{4}{10} = \frac{9-4}{10} = \frac{5}{10} = \frac{1}{2}\)
3. д) \(\frac{7}{12} - \frac{8}{15} = \frac{7 \cdot 5}{12 \cdot 5} - \frac{8 \cdot 4}{15 \cdot 4} = \frac{35}{60} - \frac{32}{60} = \frac{35-32}{60} = \frac{3}{60} = \frac{1}{20}\)
4. e) \(\frac{25}{39} - \frac{15}{26} = \frac{25 \cdot 2}{39 \cdot 2} - \frac{15 \cdot 3}{26 \cdot 3} = \frac{50}{78} - \frac{45}{78} = \frac{50-45}{78} = \frac{5}{78}\)