Упр.92 ГДЗ Алимов 10-11 класс (Алгебра)

1) (0,645 : 0,3 — 1* 107/180) * (4:6,25 — 1: 5 + 1/7*1,96;
2) (1/2 -0,374): 0,125 + (5/6 -7/12): (0, 358 — 0,108).

1. $$\left(0{,}645:0{,}3-1\frac{107}{180}\right)\cdot\left(4:6{,}25-1:5+\frac17\cdot1{,}96\right)$$

   $$0{,}645:0{,}3=\frac{645}{1000}:\frac{3}{10}=\frac{645}{1000}\cdot\frac{10}{3}=\frac{43}{20}$$

   $$1\frac{107}{180}=\frac{287}{180}, \qquad 4:6{,}25=\frac{4}{6{,}25}=\frac{4}{625/100}=\frac{16}{25}$$

   $$1:5=\frac15, \qquad \frac17\cdot1{,}96=\frac17\cdot\frac{196}{100}=\frac{28}{100}=\frac{7}{25}$$

   $$\left(\frac{43}{20}-\frac{287}{180}\right)\cdot\left(\frac{16}{25}-\frac15+\frac{7}{25}\right) =\left(\frac{387}{180}-\frac{287}{180}\right)\cdot\left(\frac{16}{25}-\frac{5}{25}+\frac{7}{25}\right)$$

   $$=\frac{100}{180}\cdot\frac{18}{25}=\frac{5}{9}\cdot\frac{18}{25}=\frac{2}{5}=0{,}4$$

2. $$\left(\frac12-0{,}374\right):0{,}125+\left(\frac56-\frac{7}{12}\right):(0{,}358-0{,}108)$$

   $$\frac12-0{,}374=\frac12-\frac{374}{1000}=\frac{500-374}{1000}=\frac{126}{1000}=0{,}126$$

   $$0{,}126:0{,}125=\frac{126}{1000}:\frac{125}{1000}=\frac{126}{125}$$

   $$\frac56-\frac{7}{12}=\frac{10}{12}-\frac{7}{12}=\frac{3}{12}=\frac14$$

   $$0{,}358-0{,}108=0{,}25=\frac14$$

   $$\left(\frac56-\frac{7}{12}\right):(0{,}358-0{,}108)=\frac14:\frac14=1$$

   $$\frac{126}{125}+1=\frac{251}{125}=2{,}008$$

Ответ

1) $$0{,}4$$; 2) $$2{,}008$$.