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МатематикаВопрос:
3. Выполните деление: a) 1:\frac{1}{7}= 5:\frac{5}{8}= 4:\frac{8}{9}= 120:\frac{1}{10}= B) 12:\frac{5}{8}= \frac{1}{3}:3= \frac{5}{7}:10= \frac{10}{11}:5= б) \frac{3}{7}:\frac{9}{14}= \frac{3}{10}:\frac{8}{11}= \frac{7}{12}:\frac{5}{6}= \frac{7}{8}:\frac{3}{4}= г) \frac{1}{200}:200= \frac{9}{16}:6= \frac{84}{121}:\frac{63}{110}=
Ответ:
Краткое пояснение: Чтобы разделить дробь на дробь, нужно первую дробь умножить на дробь, обратную второй.
а)
- 1 : \(\frac{1}{7}\) = 1 ⋅ \(\frac{7}{1}\) = 7
- 5 : \(\frac{5}{8}\) = \(\frac{5}{1}\) ⋅ \(\frac{8}{5}\) = \(\frac{5⋅8}{1⋅5}\) = \(\frac{40}{5}\) = 8
- 4 : \(\frac{8}{9}\) = \(\frac{4}{1}\) ⋅ \(\frac{9}{8}\) = \(\frac{4⋅9}{1⋅8}\) = \(\frac{36}{8}\) = \(\frac{9}{2}\) = 4\(\frac{1}{2}\)
- 120 : \(\frac{1}{10}\) = 120 ⋅ \(\frac{10}{1}\) = 120 ⋅ 10 = 1200
- 12 : \(\frac{5}{8}\) = \(\frac{12}{1}\) ⋅ \(\frac{8}{5}\) = \(\frac{12⋅8}{1⋅5}\) = \(\frac{96}{5}\) = 19\(\frac{1}{5}\)
- \(\frac{1}{3}\) : 3 = \(\frac{1}{3}\) : \(\frac{3}{1}\) = \(\frac{1}{3}\) ⋅ \(\frac{1}{3}\) = \(\frac{1⋅1}{3⋅3}\) = \(\frac{1}{9}\)
- \(\frac{5}{7}\) : 10 = \(\frac{5}{7}\) : \(\frac{10}{1}\) = \(\frac{5}{7}\) ⋅ \(\frac{1}{10}\) = \(\frac{5⋅1}{7⋅10}\) = \(\frac{5}{70}\) = \(\frac{1}{14}\)
- \(\frac{10}{11}\) : 5 = \(\frac{10}{11}\) : \(\frac{5}{1}\) = \(\frac{10}{11}\) ⋅ \(\frac{1}{5}\) = \(\frac{10⋅1}{11⋅5}\) = \(\frac{10}{55}\) = \(\frac{2}{11}\)
- \(\frac{3}{7}\) : \(\frac{9}{14}\) = \(\frac{3}{7}\) ⋅ \(\frac{14}{9}\) = \(\frac{3⋅14}{7⋅9}\) = \(\frac{42}{63}\) = \(\frac{2}{3}\)
- \(\frac{3}{10}\) : \(\frac{8}{11}\) = \(\frac{3}{10}\) ⋅ \(\frac{11}{8}\) = \(\frac{3⋅11}{10⋅8}\) = \(\frac{33}{80}\)
- \(\frac{7}{12}\) : \(\frac{5}{6}\) = \(\frac{7}{12}\) ⋅ \(\frac{6}{5}\) = \(\frac{7⋅6}{12⋅5}\) = \(\frac{42}{60}\) = \(\frac{7}{10}\)
- \(\frac{7}{8}\) : \(\frac{3}{4}\) = \(\frac{7}{8}\) ⋅ \(\frac{4}{3}\) = \(\frac{7⋅4}{8⋅3}\) = \(\frac{28}{24}\) = 1\(\frac{1}{6}\)
- \(\frac{1}{200}\) : 200 = \(\frac{1}{200}\) : \(\frac{200}{1}\) = \(\frac{1}{200}\) ⋅ \(\frac{1}{200}\) = \(\frac{1⋅1}{200⋅200}\) = \(\frac{1}{40000}\)
- \(\frac{9}{16}\) : 6 = \(\frac{9}{16}\) : \(\frac{6}{1}\) = \(\frac{9}{16}\) ⋅ \(\frac{1}{6}\) = \(\frac{9⋅1}{16⋅6}\) = \(\frac{9}{96}\) = \(\frac{3}{32}\)
- \(\frac{84}{121}\) : \(\frac{63}{110}\) = \(\frac{84}{121}\) ⋅ \(\frac{110}{63}\) = \(\frac{84⋅110}{121⋅63}\) = \(\frac{9240}{7623}\) = \(\frac{80}{63}\) = 1\(\frac{17}{63}\)
Ответ: См. решение
