1. Выполните действия: 1) 7 7/9 − 4 1/12 + 2 3/4; 2) 17 2/3 − 6 1/36 + 4 3/8; 3) 10 9/16 − (3 11/12 + 4 4/9); 4) (20 − 7 23/36) − (14 4/27 − 6 1/18).

Question

Вопрос:

Accepted Answer

\(7\dfrac{7}{9}-4\dfrac{1}{12}+2\dfrac{3}{4}=\dfrac{70}{9}-\dfrac{49}{12}+\dfrac{11}{4}=\dfrac{280-147+99}{36}=\dfrac{232}{36}=\dfrac{58}{9}=6\dfrac{4}{9}\). Ответ: \(6\dfrac{4}{9}\).
\(17\dfrac{2}{3}-6\dfrac{1}{36}+4\dfrac{3}{8}=\dfrac{53}{3}-\dfrac{217}{36}+\dfrac{35}{8}=\dfrac{1272-434+315}{72}=\dfrac{1153}{72}=16\dfrac{1}{72}\). Ответ: \(16\dfrac{1}{72}\).
\(10\dfrac{9}{16}-\left(3\dfrac{11}{12}+4\dfrac{4}{9}\right)=\dfrac{169}{16}-\left(\dfrac{47}{12}+\dfrac{40}{9}\right)=\dfrac{169}{16}-\dfrac{301}{36}=\dfrac{1521-1204}{144}=\dfrac{317}{144}=2\dfrac{29}{144}\). Ответ: \(2\dfrac{29}{144}\).
\(\left(20-7\dfrac{23}{36}\right)-\left(14\dfrac{4}{27}-6\dfrac{1}{18}\right)=\left(\dfrac{720}{36}-\dfrac{275}{36}\right)-\left(\dfrac{382}{27}-\dfrac{109}{18}\right)=\dfrac{445}{36}-\dfrac{437}{54}=\dfrac{1335-874}{108}=\dfrac{461}{108}=4\dfrac{29}{108}\). Ответ: \(4\dfrac{29}{108}\).

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