Упр.1.1 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 18 5/12-7/12·1 19/21-17/72·2/3;
2) (6 3/4-5 1/8 :1 9/32)·5/11;
3) (-1,42-(-3,22)) :(-0,4)+(-6)·(-0,7);
4) (-7/18+11/12) :(-19/48);
5) (-3 1/12-2 1/15) :(-5 3/20).

1. $$18\frac{5}{12}-\frac{7}{12}\cdot 1\frac{19}{21}-\frac{17}{72}\cdot \frac{2}{3}$$
   $$=18\frac{5}{12}-\frac{7}{12}\cdot \frac{40}{21}-\frac{17}{72}\cdot \frac{2}{3}$$
   $$=18\frac{5}{12}-\frac{10}{9}-\frac{17}{108}$$
   $$=18\frac{45}{108}-1\frac{1}{9}-\frac{17}{108}$$
   $$=18\frac{28}{108}-1\frac{1}{9}=18\frac{7}{27}-1\frac{3}{27}=17\frac{4}{27}.$$
2. $$\left(6\frac{3}{4}-5\frac{1}{8}:1\frac{9}{32}\right)\cdot \frac{5}{11}$$
   $$=\left(6\frac{3}{4}-\frac{41}{8}:\frac{41}{32}\right)\cdot \frac{5}{11}$$
   $$=\left(6\frac{3}{4}-4\right)\cdot \frac{5}{11}$$
   $$=2\frac{3}{4}\cdot \frac{5}{11}=\frac{11}{4}\cdot \frac{5}{11}=\frac{5}{4}=1\frac{1}{4}.$$
3. $$(-1{,}42-(-3{,}22)):(-0{,}4)+(-6)\cdot(-0{,}7)$$
   $$=(-1{,}42+3{,}22):(-0{,}4)+4{,}2$$
   $$=1{,}8:(-0{,}4)+4{,}2$$
   $$=-4{,}5+4{,}2=-0{,}3.$$
4. $$\left(-\frac{7}{18}+\frac{11}{12}\right):\left(-\frac{19}{48}\right)$$
   $$=\frac{-14+33}{36}:\left(-\frac{19}{48}\right)$$
   $$=\frac{19}{36}\cdot \left(-\frac{48}{19}\right)$$
   $$=-\frac{48}{36}=-\frac{4}{3}=-1\frac{1}{3}.$$
5. $$\left(-3\frac{1}{12}-2\frac{1}{15}\right):\left(-5\frac{3}{20}\right)$$
   $$=\left(-3\frac{5}{60}-2\frac{4}{60}\right):\left(-\frac{103}{20}\right)$$
   $$=-5\frac{9}{60}:\left(-\frac{103}{20}\right)$$
   $$=-\frac{103}{20}:\left(-\frac{103}{20}\right)=1.$$

Ответ

1) $$17\frac{4}{27}$$; 2) $$1\frac{1}{4}$$; 3) $$-0{,}3$$; 4) $$-1\frac{1}{3}$$; 5) $$1$$.