1. Найдите сумму или разность: 1) a) 1/3 + 5/6; 2) a) 8/11 - 1/13; 3) a) 5/34 - 41/51; 1) б) 5/7 - 1/14; 2) б) 7/20 + 2/3; 3) б) 3 1/30 - 5 7/90; 1) в) 2 2/3 + 5/12; 2) в) 3 2/15 - 1 1/7; 3) в) 6 1/7 - 10 5/14.

1. Найдите сумму или разность:

Разбираемся с каждым примером по порядку:

1) a) \(\frac{1}{3} + \frac{5}{6}\)

• \(\frac{1}{3} + \frac{5}{6} = \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}\)

Ответ: \(1 \frac{1}{6}\)

1) б) \(\frac{5}{7} - \frac{1}{14}\)

• \(\frac{5}{7} - \frac{1}{14} = \frac{10}{14} - \frac{1}{14} = \frac{9}{14}\)

Ответ: \(\frac{9}{14}\)

1) в) \(2 \frac{2}{3} + \frac{5}{12}\)

• \(2 \frac{2}{3} + \frac{5}{12} = \frac{8}{3} + \frac{5}{12} = \frac{32}{12} + \frac{5}{12} = \frac{37}{12} = 3 \frac{1}{12}\)

Ответ: \(3 \frac{1}{12}\)

2) a) \(\frac{8}{11} - \frac{1}{13}\)

• \(\frac{8}{11} - \frac{1}{13} = \frac{104}{143} - \frac{11}{143} = \frac{93}{143}\)

Ответ: \(\frac{93}{143}\)

2) б) \(\frac{7}{20} + \frac{2}{3}\)

• \(\frac{7}{20} + \frac{2}{3} = \frac{21}{60} + \frac{40}{60} = \frac{61}{60} = 1 \frac{1}{60}\)

Ответ: \(1 \frac{1}{60}\)

2) в) \(3 \frac{2}{15} - 1 \frac{1}{7}\)

• \(3 \frac{2}{15} - 1 \frac{1}{7} = \frac{47}{15} - \frac{8}{7} = \frac{329}{105} - \frac{120}{105} = \frac{209}{105} = 1 \frac{104}{105}\)

Ответ: \(1 \frac{104}{105}\)

3) a) \(\frac{5}{34} - \frac{41}{51}\)

• \(\frac{5}{34} - \frac{41}{51} = \frac{15}{102} - \frac{82}{102} = -\frac{67}{102}\)

Ответ: \(-\frac{67}{102}\)

3) б) \(3 \frac{1}{30} - 5 \frac{7}{90}\)

• \(3 \frac{1}{30} - 5 \frac{7}{90} = \frac{91}{30} - \frac{457}{90} = \frac{273}{90} - \frac{457}{90} = -\frac{184}{90} = -2 \frac{4}{90} = -2 \frac{2}{45}\)

Ответ: \(-2 \frac{2}{45}\)

3) в) \(6 \frac{1}{7} - 10 \frac{5}{14}\)

• \(6 \frac{1}{7} - 10 \frac{5}{14} = \frac{43}{7} - \frac{145}{14} = \frac{86}{14} - \frac{145}{14} = -\frac{59}{14} = -4 \frac{3}{14}\)

Ответ: \(-4 \frac{3}{14}\)