Упр.181 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Найдите значение выражения:
   1) $$-27+68-56+61$$;
   2) $$4{,}17-9{,}42+0{,}2$$;
   3) $$3{,}1+(-4{,}72)+(-8{,}12)-(-0{,}96)$$;
   4) $$-18{,}31-6{,}27+(-8{,}44)-(-31{,}67)$$;
   5) $$6\frac{5}{12}-\left(-4\frac{2}{3}\right)+\left(-2\frac{3}{4}\right)$$;
   6) $$4\frac{1}{8}-6\frac{2}{9}+\left(-3\frac{1}{6}\right)-\left(-5\frac{3}{4}\right)$$.

1) $$-27+68-56+61=(68-27)+(61-56)=41+5=46$$

2) $$4{,}17-9{,}42+0{,}2=(4{,}17+0{,}2)-9{,}42=4{,}37-9{,}42=-5{,}05$$

3) $$3{,}1+(-4{,}72)+(-8{,}12)-(-0{,}96)=3{,}1-4{,}72-8{,}12+0{,}96$$

$$=(3{,}1+0{,}96)+(-4{,}72-8{,}12)=4{,}06-12{,}84=-8{,}78$$

4) $$-18{,}31-6{,}27+(-8{,}44)-(-31{,}67)=-18{,}31-6{,}27-8{,}44+31{,}67$$

$$=(-18{,}31-8{,}44)+(31{,}67-6{,}27)=-26{,}75+25{,}4=-1{,}35$$

5) $$6\frac{5}{12}-\left(-4\frac{2}{3}\right)+\left(-2\frac{3}{4}\right)=6\frac{5}{12}+4\frac{2}{3}-2\frac{3}{4}$$

$$=6\frac{5}{12}+4\frac{8}{12}-2\frac{9}{12}=10\frac{13}{12}-2\frac{9}{12}=8\frac{4}{12}=8\frac{1}{3}$$

6) $$4\frac{1}{8}-6\frac{2}{9}+\left(-3\frac{1}{6}\right)-\left(-5\frac{3}{4}\right)=4\frac{9}{72}-6\frac{16}{72}-3\frac{12}{72}+5\frac{54}{72}$$

$$=-2\frac{7}{72}-3\frac{12}{72}+5\frac{54}{72}=-5\frac{19}{72}+5\frac{54}{72}=\frac{35}{72}$$

Ответ: 1) 46; 2) $$-5{,}05$$; 3) $$-8{,}78$$; 4) $$-1{,}35$$; 5) $$8\frac{1}{3}$$; 6) $$\frac{35}{72}$$.