Выполните действия: а) 27/35 · 7/9 − 9/24 · 6/45; б) 1 41/44 · 11/17 − 27/40 · 5/18; в) 12 1/10 · 2 4/11 + 2 24/31 · 7 3/4; г) 13 2/7 − 5 5/8 · (1 2/9 − 39/45); д) (3/5)^3; е) (7/8)^2.

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Вопрос:

Accepted Answer

а) \[\frac{27}{35}\cdot\frac79-\frac9{24}\cdot\frac6{45}=\frac35-\frac1{20}=\frac{11}{20}.\]
б) \[1\frac{41}{44}\cdot\frac{11}{17}-\frac{27}{40}\cdot\frac5{18}=\frac{85}{44}\cdot\frac{11}{17}-\frac3{16}=\frac54-\frac3{16}=\frac{17}{16}=1\frac1{16}.\]
в) \[12\frac1{10}\cdot2\frac4{11}+2\frac{24}{31}\cdot7\frac34=\frac{121}{10}\cdot\frac{26}{11}+\frac{86}{31}\cdot\frac{31}{4}=\frac{286}{10}+\frac{86}{4}=\frac{143}{5}+\frac{43}{2}=\frac{381}{10}=38\frac1{10}.\]
г) \[13\frac27-5\frac58\left(1\frac29-\frac{39}{45}\right)=\frac{93}{7}-\frac{45}{8}\left(\frac{11}{9}-\frac{13}{15}\right)=\frac{93}{7}-\frac{45}{8}\cdot\frac{16}{45}=\frac{93}{7}-2=\frac{79}{7}=11\frac27.\]
д) \[\left(\frac35\right)^3=\frac{27}{125}.\]
е) \[\left(\frac78\right)^2=\frac{49}{64}.\]

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