2. Вычислите: 1) 1 - 7/15; 2) 3 - 9/23; 3) 4 - 1 2/3; 4) 10 - 5 4/11. 3. Найдите разность: 1) 7 5/6 - 3 2/3; 2) 8 5/12 - 6 7/20; 3) 11 11/12 - 5 7/9; 4) 9 17/24 - 8 11/36. 4. Выполните вычитание: 1) 3 1/16 - 1/8; 3) 4 2/7 - 1 4/9; 5) 9 7/9 - 4 5/6;

Question

Вопрос:

Ответ:

Accepted Answer

1) $$1 - \frac{7}{15} = \frac{15}{15} - \frac{7}{15} = \frac{8}{15}$$
2) $$3 - \frac{9}{23} = \frac{3 \cdot 23}{23} - \frac{9}{23} = \frac{69}{23} - \frac{9}{23} = \frac{60}{23} = 2\frac{14}{23}$$
3) $$4 - 1\frac{2}{3} = 4 - \frac{1 \cdot 3 + 2}{3} = 4 - \frac{5}{3} = \frac{4 \cdot 3}{3} - \frac{5}{3} = \frac{12}{3} - \frac{5}{3} = \frac{7}{3} = 2\frac{1}{3}$$
4) $$10 - 5\frac{4}{11} = 10 - \frac{5 \cdot 11 + 4}{11} = 10 - \frac{59}{11} = \frac{10 \cdot 11}{11} - \frac{59}{11} = \frac{110}{11} - \frac{59}{11} = \frac{51}{11} = 4\frac{7}{11}$$

1) $$7\frac{5}{6} - 3\frac{2}{3} = \frac{7 \cdot 6 + 5}{6} - \frac{3 \cdot 3 + 2}{3} = \frac{47}{6} - \frac{11}{3} = \frac{47}{6} - \frac{11 \cdot 2}{3 \cdot 2} = \frac{47}{6} - \frac{22}{6} = \frac{25}{6} = 4\frac{1}{6}$$
2) $$8\frac{5}{12} - 6\frac{7}{20} = \frac{8 \cdot 12 + 5}{12} - \frac{6 \cdot 20 + 7}{20} = \frac{101}{12} - \frac{127}{20} = \frac{101 \cdot 5}{12 \cdot 5} - \frac{127 \cdot 3}{20 \cdot 3} = \frac{505}{60} - \frac{381}{60} = \frac{124}{60} = \frac{31}{15} = 2\frac{1}{15}$$
3) $$11\frac{11}{12} - 5\frac{7}{9} = \frac{11 \cdot 12 + 11}{12} - \frac{5 \cdot 9 + 7}{9} = \frac{143}{12} - \frac{52}{9} = \frac{143 \cdot 3}{12 \cdot 3} - \frac{52 \cdot 4}{9 \cdot 4} = \frac{429}{36} - \frac{208}{36} = \frac{221}{36} = 6\frac{5}{36}$$
4) $$9\frac{17}{24} - 8\frac{11}{36} = \frac{9 \cdot 24 + 17}{24} - \frac{8 \cdot 36 + 11}{36} = \frac{233}{24} - \frac{299}{36} = \frac{233 \cdot 3}{24 \cdot 3} - \frac{299 \cdot 2}{36 \cdot 2} = \frac{699}{72} - \frac{598}{72} = \frac{101}{72} = 1\frac{29}{72}$$

1) $$3\frac{1}{16} - \frac{1}{8} = \frac{3 \cdot 16 + 1}{16} - \frac{1}{8} = \frac{49}{16} - \frac{1}{8} = \frac{49}{16} - \frac{1 \cdot 2}{8 \cdot 2} = \frac{49}{16} - \frac{2}{16} = \frac{47}{16} = 2\frac{15}{16}$$
3) $$4\frac{2}{7} - 1\frac{4}{9} = \frac{4 \cdot 7 + 2}{7} - \frac{1 \cdot 9 + 4}{9} = \frac{30}{7} - \frac{13}{9} = \frac{30 \cdot 9}{7 \cdot 9} - \frac{13 \cdot 7}{9 \cdot 7} = \frac{270}{63} - \frac{91}{63} = \frac{179}{63} = 2\frac{53}{63}$$
5) $$9\frac{7}{9} - 4\frac{5}{6} = \frac{9 \cdot 9 + 7}{9} - \frac{4 \cdot 6 + 5}{6} = \frac{88}{9} - \frac{29}{6} = \frac{88 \cdot 2}{9 \cdot 2} - \frac{29 \cdot 3}{6 \cdot 3} = \frac{176}{18} - \frac{87}{18} = \frac{89}{18} = 4\frac{17}{18}$$