5) Представьте выражение \(\frac{3}{4}-\frac{8}{11}\) в виде дроби со знаменателем 88. В ответ запишите числитель полученной дроби. 6) Представьте выражение \(\frac{2}{3}-\frac{7}{13}\) в виде дроби со знаменателем 78. В ответ запишите числитель полученной дроби. Задание 4. Найдите значение выражения 1) \(\frac{1}{30}+\frac{1}{42}\) 2) \(\frac{1}{36}-\frac{1}{44}\) 3) \(\frac{1}{36}+\frac{1}{45}\) 4) \(\frac{1}{35}-\frac{1}{60}\) 5) \(\frac{1}{21}+\frac{1}{28}\) 6) \(\frac{1}{72}-\frac{1}{99}\) О6. Дроби и степени Блок 2. ФИПИ. Расширенная версия Задание 1. Найдите значение выражения 1) \((\frac{17}{10}-\frac{1}{20}):\frac{2}{15}\) 2) \((\frac{5}{22}-\frac{8}{11}):\frac{11}{5}\) 3) \((\frac{5}{26}-\frac{3}{25}):\frac{13}{2}\) 4) \((\frac{10}{13}+\frac{15}{4}):\frac{26}{5}\) 5) \((\frac{17}{26}+\frac{11}{13}):\frac{17}{6}\) 6) \((\frac{11}{12}+\frac{11}{20}):\frac{15}{8}\) 7) \((\frac{3}{4}-\frac{1}{6}):3\) 8) \((\frac{2}{5}+\frac{13}{15}):6\) 9) \((\frac{3}{8}-\frac{1}{20}):10\) 10) \((\frac{2}{20}+\frac{7}{30}):15\) 11) \((\frac{9}{10}-\frac{7}{15}):3\) 12) \((\frac{1}{6}+\frac{1}{4}):9\) Задание 2. Найдите значение выражения 1) \((\frac{9}{16}+2\frac{3}{8}):4\) 2) \((\frac{4}{9}-3\frac{1}{15}):9\) 3) \((2\frac{3}{4}+2\frac{1}{16}):16\) 4) \((1\frac{11}{16}-3\frac{7}{8}):4\) 5) \((1\frac{3}{4}+2\frac{4}{5}):30\) 6) \((1\frac{1}{13}-2\frac{3}{4}):26\) 7) \((1\frac{12}{17}+2\frac{7}{11}):17\) 8) \(3\frac{4}{9}:(\frac{1}{5}-\frac{4}{7})\) 9) \(4\frac{7}{8}:(2\frac{3}{4}+\frac{10}{19})\) 10) \(1\frac{1}{12}:(\frac{13}{18}-\frac{2}{5}\frac{9}{9})\) 11) \(3\frac{1}{2}:(1\frac{4}{15}+2\frac{9}{10})\) 12) \(4\frac{1}{4}:(\frac{2}{10}-3\frac{1}{8})\)

Задание 5:

Чтобы представить \(\frac{3}{4}-\frac{8}{11}\) со знаменателем 88, нужно привести дроби к общему знаменателю.

\(\frac{3}{4} = \frac{3 \times 22}{4 \times 22} = \frac{66}{88}\)

\(\frac{8}{11} = \frac{8 \times 8}{11 \times 8} = \frac{64}{88}\)

Теперь вычитаем: \(\frac{66}{88} - \frac{64}{88} = \frac{66-64}{88} = \frac{2}{88}\)

Числитель полученной дроби равен 2.

Ответ: 2

Задание 6:

Чтобы представить \(\frac{2}{3}-\frac{7}{13}\) со знаменателем 78, нужно привести дроби к общему знаменателю.

\(\frac{2}{3} = \frac{2 \times 26}{3 \times 26} = \frac{52}{78}\)

\(\frac{7}{13} = \frac{7 \times 6}{13 \times 6} = \frac{42}{78}\)

Теперь вычитаем: \(\frac{52}{78} - \frac{42}{78} = \frac{52-42}{78} = \frac{10}{78}\)

Числитель полученной дроби равен 10.

Ответ: 10

Задание 4. Найдите значение выражения:

1. \(\frac{1}{30}+\frac{1}{42} = \frac{7+5}{210} = \frac{12}{210} = \frac{2}{35}\)
2. \(\frac{1}{36}-\frac{1}{44} = \frac{11-9}{396} = \frac{2}{396} = \frac{1}{198}\)
3. \(\frac{1}{36}+\frac{1}{45} = \frac{5+4}{180} = \frac{9}{180} = \frac{1}{20}\)
4. \(\frac{1}{35}-\frac{1}{60} = \frac{12-7}{420} = \frac{5}{420} = \frac{1}{84}\)
5. \(\frac{1}{21}+\frac{1}{28} = \frac{4+3}{84} = \frac{7}{84} = \frac{1}{12}\)
6. \(\frac{1}{72}-\frac{1}{99} = \frac{11-8}{792} = \frac{3}{792} = \frac{1}{264}\)

Задание 1. Найдите значение выражения:

1. \((\frac{17}{10}-\frac{1}{20}):\frac{2}{15} = (\frac{34-1}{20}):\frac{2}{15} = \frac{33}{20} \times \frac{15}{2} = \frac{33 \times 3}{4 \times 2} = \frac{99}{8}\)
2. \((\frac{5}{22}-\frac{8}{11}):\frac{11}{5} = (\frac{5-16}{22}):\frac{11}{5} = \frac{-11}{22} \times \frac{5}{11} = \frac{-1}{2} \times \frac{5}{1} = -\frac{5}{2}\)
3. \((\frac{5}{26}-\frac{3}{25}):\frac{13}{2} = (\frac{125-78}{650}):\frac{13}{2} = \frac{47}{650} \times \frac{2}{13} = \frac{47}{325 \times 13} = \frac{47}{4225}\)
4. \((\frac{10}{13}+\frac{15}{4}):\frac{26}{5} = (\frac{40+195}{52}):\frac{26}{5} = \frac{235}{52} \times \frac{5}{26} = \frac{1175}{1352}\)
5. \((\frac{17}{26}+\frac{11}{13}):\frac{17}{6} = (\frac{17+22}{26}):\frac{17}{6} = \frac{39}{26} \times \frac{6}{17} = \frac{3}{2} \times \frac{6}{17} = \frac{9}{17}\)
6. \((\frac{11}{12}+\frac{11}{20}):\frac{15}{8} = (\frac{55+33}{60}):\frac{15}{8} = \frac{88}{60} \times \frac{8}{15} = \frac{22}{15} \times \frac{8}{15} = \frac{176}{225}\)
7. \((\frac{3}{4}-\frac{1}{6}):3 = (\frac{9-2}{12}):3 = \frac{7}{12} \times \frac{1}{3} = \frac{7}{36}\)
8. \((\frac{2}{5}+\frac{13}{15}):6 = (\frac{6+13}{15}):6 = \frac{19}{15} \times \frac{1}{6} = \frac{19}{90}\)
9. \((\frac{3}{8}-\frac{1}{20}):10 = (\frac{15-2}{40}):10 = \frac{13}{40} \times \frac{1}{10} = \frac{13}{400}\)
10. \((\frac{2}{20}+\frac{7}{30}):15 = (\frac{6+14}{60}):15 = \frac{20}{60} \times \frac{1}{15} = \frac{1}{3} \times \frac{1}{15} = \frac{1}{45}\)
11. \((\frac{9}{10}-\frac{7}{15}):3 = (\frac{27-14}{30}):3 = \frac{13}{30} \times \frac{1}{3} = \frac{13}{90}\)
12. \((\frac{1}{6}+\frac{1}{4}):9 = (\frac{2+3}{12}):9 = \frac{5}{12} \times \frac{1}{9} = \frac{5}{108}\)

Задание 2. Найдите значение выражения:

1. \((\frac{9}{16}+2\frac{3}{8}):4 = (\frac{9}{16}+\frac{19}{8}):4 = (\frac{9+38}{16}):4 = \frac{47}{16} \times \frac{1}{4} = \frac{47}{64}\)
2. \((\frac{4}{9}-3\frac{1}{15}):9 = (\frac{4}{9}-\frac{46}{15}):9 = (\frac{20-138}{45}):9 = \frac{-118}{45} \times \frac{1}{9} = \frac{-118}{405}\)
3. \((2\frac{3}{4}+2\frac{1}{16}):16 = (\frac{11}{4}+\frac{33}{16}):16 = (\frac{44+33}{16}):16 = \frac{77}{16} \times \frac{1}{16} = \frac{77}{256}\)
4. \((1\frac{11}{16}-3\frac{7}{8}):4 = (\frac{27}{16}-\frac{31}{8}):4 = (\frac{27-62}{16}):4 = \frac{-35}{16} \times \frac{1}{4} = \frac{-35}{64}\)
5. \((1\frac{3}{4}+2\frac{4}{5}):30 = (\frac{7}{4}+\frac{14}{5}):30 = (\frac{35+56}{20}):30 = \frac{91}{20} \times \frac{1}{30} = \frac{91}{600}\)
6. \((1\frac{1}{13}-2\frac{3}{4}):26 = (\frac{14}{13}-\frac{11}{4}):26 = (\frac{56-143}{52}):26 = \frac{-87}{52} \times \frac{1}{26} = \frac{-87}{1352}\)
7. \((1\frac{12}{17}+2\frac{7}{11}):17 = (\frac{29}{17}+\frac{29}{11}):17 = (\frac{319+493}{187}):17 = \frac{812}{187} \times \frac{1}{17} = \frac{812}{3179}\)
8. \(3\frac{4}{9}:(\frac{1}{5}-\frac{4}{7}) = \frac{31}{9}:(\frac{7-20}{35}) = \frac{31}{9}:\frac{-13}{35} = \frac{31}{9} \times \frac{-35}{13} = \frac{-1085}{117}\)
9. \(4\frac{7}{8}:(2\frac{3}{4}+\frac{10}{19}) = \frac{39}{8}:(\frac{11}{4}+\frac{10}{19}) = \frac{39}{8}:(\frac{209+40}{76}) = \frac{39}{8}:\frac{249}{76} = \frac{39}{8} \times \frac{76}{249} = \frac{39}{1} \times \frac{19}{249} = \frac{741}{249} = \frac{247}{83}\)
10. \(1\frac{1}{12}:(\frac{13}{18}-\frac{2}{5}\frac{9}{9}) = \frac{13}{12}:(\frac{13}{18}-\frac{2}{5}) = \frac{13}{12}:(\frac{65-36}{90}) = \frac{13}{12}:\frac{29}{90} = \frac{13}{12} \times \frac{90}{29} = \frac{13}{2} \times \frac{15}{29} = \frac{195}{58}\)
11. \(3\frac{1}{2}:(1\frac{4}{15}+2\frac{9}{10}) = \frac{7}{2}:(\frac{19}{15}+\frac{29}{10}) = \frac{7}{2}:(\frac{38+87}{30}) = \frac{7}{2}:\frac{125}{30} = \frac{7}{2} \times \frac{30}{125} = \frac{7}{1} \times \frac{15}{125} = \frac{105}{125} = \frac{21}{25}\)
12. \(4\frac{1}{4}:(\frac{2}{10}-3\frac{1}{8}) = \frac{17}{4}:(\frac{1}{5}-\frac{25}{8}) = \frac{17}{4}:(\frac{8-125}{40}) = \frac{17}{4}:\frac{-117}{40} = \frac{17}{4} \times \frac{-40}{117} = 17 \times \frac{-10}{117} = \frac{-170}{117}\)