Question

-37/16+33/28×1 13/22+3÷5 1/7​

Answer 1

Ответ:

$\dfrac{7}{48}$

Пошаговое объяснение:

$-\dfrac{37}{16} +\dfrac{33}{28} \cdot 1\dfrac{13}{22} +3: 5\dfrac{1}{7}$

Установим порядок действий.

$-\dfrac{37}{16}\stackrel{(3)}{\; +}\dfrac{33}{28}\stackrel{(1)}{\; \cdot} 1\dfrac{13}{22} \stackrel{(4)}{\;+}3\stackrel{(2)}{\;:} 5\dfrac{1}{7}$

$1) \dfrac{33}{28} \cdot 1\dfrac{13}{22} =\dfrac{33}{28} \cdot \dfrac{35}{22}=\dfrac{33\cdot 35}{28\cdot 22} =\dfrac{3\cdot11\cdot5\cdot7}{4\cdot7\cdot2\cdot11} =\dfrac{15}{8} =1\dfrac{7}{8}$

$2)3:5\dfrac{1}{7} =3:\dfrac{36}{7} =3\cdot \dfrac{7}{36} =\dfrac{3\cdot7}{3\cdot12} =\dfrac{7}{12}$

$3) -\dfrac{37}{16} +1\dfrac{7}{8} =-2\dfrac{5}{16} +1\dfrac{7}{8} =-\left(2\dfrac{5}{16} -1\dfrac{7}{8} \right)= - 1\dfrac{5-14}{16} =-\dfrac{16+5-14}{16} =-\dfrac{7}{16}$

$4) -\dfrac{7}{16} +\dfrac{7}{12} =\dfrac{7}{12}^{\backslash4}-\dfrac{7}{16}^{\backslash3}=\dfrac{28-21}{48} =\dfrac{7}{48}$