Упр.540 ГДЗ Муравин 6 класс (Математика)

1. Выполните действия:
   1) $$19{,}6\cdot2{,}5-\left(2{,}0625-1\frac{5}{12}\right)\div\frac{1}{8}$$;
   2) $$\left(\left(\frac{15}{28}-\frac{11}{36}\right)\cdot\frac{21}{29}-6\frac{6}{7}\div\left(-\frac{16}{21}\right)\right)\div(-16{,}5)$$;
   3) $$\left(5{,}05\div\frac{1}{40}-2{,}8\cdot\frac{5}{6}\right)\cdot3+(-16)\cdot(-0{,}1875)$$;
   4) $$\left(9\frac{3}{20}-1{,}24\right)\div2\frac{1}{3}-\left(\frac{3}{4}+2\frac{5}{8}\right)\div(-0{,}625)$$.

1) $$19{,}6\cdot 2{,}5-(2{,}0625-1\frac{5}{12}):\frac18$$

$$19{,}6\cdot 2{,}5=49$$

$$2{,}0625=2\frac{1}{16}$$

$$2\frac{1}{16}-1\frac{5}{12}=1+\frac{1}{16}-\frac{5}{12}=1+\frac{3-20}{48}=1-\frac{17}{48}=\frac{31}{48}$$

$$\frac{31}{48}:\frac18=\frac{31}{48}\cdot 8=\frac{31}{6}=5\frac16$$

$$49-5\frac16=43\frac56$$

2) $$\left(\left(\frac{15}{28}-\frac{11}{36}\right)\cdot\frac{21}{29}-6\frac67:\left(-\frac{16}{21}\right)\right):(-16{,}5)$$

$$\frac{15}{28}-\frac{11}{36}=\frac{135-77}{252}=\frac{58}{252}=\frac{29}{126}$$

$$\frac{29}{126}\cdot\frac{21}{29}=\frac{1}{6}$$

$$6\frac67=\frac{48}{7},\qquad \frac{48}{7}:\left(-\frac{16}{21}\right)=\frac{48}{7}\cdot\frac{21}{-16}=-9$$

$$\frac16-(-9)=\frac16+9=\frac{55}{6}$$

$$-16{,}5=-\frac{33}{2}$$

$$\frac{55}{6}:\left(-\frac{33}{2}\right)=\frac{55}{6}\cdot\frac{2}{-33}=-\frac{5}{9}$$

3) $$\left(5{,}05:\frac{1}{40}-2{,}8\cdot\frac56\right)\cdot 3+(-16)\cdot(-0{,}1875)$$

$$5{,}05:\frac{1}{40}=5{,}05\cdot 40=202$$

$$2{,}8\cdot\frac56=\frac{14}{5}\cdot\frac56=\frac73$$

$$202-\frac73=201\frac23$$

$$201\frac23\cdot 3=605$$

$$(-16)\cdot(-0{,}1875)=3$$

$$605+3=608$$

4) $$\left(9\frac{3}{20}-1{,}24\right):2\frac13-\left(\frac34+2\frac58\right):(-0{,}625)$$

$$9\frac{3}{20}-1{,}24=9\frac{15}{100}-1\frac{24}{100}=8\frac{91}{100}$$

$$2\frac13=\frac73,\qquad 8\frac{91}{100}:\frac73=8\frac{91}{100}\cdot\frac37=\frac{2673}{700}$$

$$\frac34+2\frac58=\frac34+2\frac58=\frac{6}{8}+\frac{21}{8}=\frac{27}{8}$$

$$-0{,}625=-\frac58,\qquad \frac{27}{8}:\left(-\frac58\right)=\frac{27}{8}\cdot\frac{8}{-5}=-\frac{27}{5}$$

$$\frac{2673}{700}-\left(-\frac{27}{5}\right)=\frac{2673}{700}+\frac{3780}{700}=\frac{6453}{700}=9\frac{153}{700}$$

Ответ

1) $$43\frac56$$; 2) $$-\frac59$$; 3) $$608$$; 4) $$9\frac{153}{700}$$.