Нужно решить пример: (52:56- 2/7):2 1/7+ 17/20. Created by Demon412. matematika-ru

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$\displaystyle \bigg(52 \underset{_1}{:} 56 \underset{_2}{-} \frac{2}{7} \bigg)\underset{_3}{:}2\frac{1}{7} \underset{_4}{+}\frac{17}{20} =1,15\\\\\\1) \quad 52:56=\frac{52}{56} =\frac{13}{14} \\\\\\ 2)\quad \frac{13}{14}-\frac{2^{\backslash2}}{7}=\frac{13}{14}-\frac{4}{14}=\frac{9}{14} \\\\\\3)\quad \frac{9}{14}:2\frac{1}{7}=\frac{9}{14}:\frac{1+2\times7}{7}=\frac{9}{14}\times\frac{7}{15}=\frac{3}{2\times 5}=\frac{3}{10}$

$\displaystyle 4)\quad \frac{3}{10}+\frac{17}{20}=\frac{3\times2+17}{20}=\frac{23}{20} =1,15\\\\\\ O_{TBET}:\quad 1,15$

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Ответ:

$\displaystyle \tt 1\dfrac{3}{20}$

Пошаговое объяснение:

Вычислим значение выражения:

$\displaystyle \tt \left (52:56-\dfrac{2}{7} \right):2 \dfrac{1}{7}+\dfrac{17}{20}.$

$\displaystyle \tt 1) \; 52:56=\dfrac{52}{56}= \dfrac{4 \cdot 13}{4 \cdot 14}=\dfrac{13}{14};$

$\displaystyle \tt 2) \; \dfrac{13}{14}-\dfrac{2}{7}=\dfrac{13}{14}-\dfrac{2 \cdot 2}{7\cdot 2}=\dfrac{13}{14}-\dfrac{4}{14}=\dfrac{13-4}{14}=\dfrac{9}{14};$

$\displaystyle \tt 3) \; \dfrac{9}{14}:2\dfrac{1}{7}=\dfrac{9}{14}:\dfrac{2 \cdot 7+1}{7}=\dfrac{9}{14}:\dfrac{15}{7}=\dfrac{9}{14} \cdot \dfrac{7}{15}=\dfrac{3 \cdot 3}{2 \cdot 7} \cdot \dfrac{7}{3 \cdot 5}=\dfrac{3}{2 \cdot 5}=\dfrac{3}{10} ;$

$\displaystyle \tt 4) \; \dfrac{3}{10}+\dfrac{17}{20} =\dfrac{3 \cdot 2}{10 \cdot 2}+\dfrac{17}{20} =\dfrac{6}{20} +\dfrac{17}{20} =\dfrac{6+17}{20} =\dfrac{23}{20}=\dfrac{20+3}{20}=1\dfrac{3}{20}.$

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