Упр.510 ГДЗ Муравин 6 класс (Математика)

Задача

1) 2-15+23-11;
2)-31+14+5-17;
3) 24,8+35,6-14,8-55,6;
4) 3 1/3-2 3/5+1 2/3-2 2/5-3 2/15;
5) 6 1/2+4 1/6-7 5/9-5 1/3-4 1/9;
6)-13,57+25,43+11,27-23,13;
7) 11,269+5,427-7,169-6,527;
8) 34,8-15,39+27,5-47,91;
9)-0,037+1/4+7/8+5/16-1,4;
10) 0,4-1/2+0,75-5/6+0,85-2/3.

Подробный ответ

Сгруппируем положительные и отрицательные слагаемые.

1) $$2-15+23-11=(2+23)-(15+11)=25-26=-1.$$

2) $$-31+14+5-17=(14+5)-(31+17)=19-48=-29.$$

3) $$24{,}8+35{,}6-14{,}8-55{,}6=(24{,}8+35{,}6)-(14{,}8+55{,}6)=60{,}4-70{,}4=-10.$$

4) $$3\frac{1}{3}-2\frac{3}{5}+1\frac{2}{3}-2\frac{2}{5}-3\frac{2}{15}$$
$$=\left(3\frac{1}{3}+1\frac{2}{3}\right)-\left(2\frac{3}{5}+2\frac{2}{5}+3\frac{2}{15}\right)$$
$$=5-\left(4+\frac{5}{5}+3\frac{2}{15}\right)=5-8\frac{2}{15}=-3\frac{2}{15}.$$

5) $$6\frac{1}{2}+4\frac{1}{6}-7\frac{5}{9}-5\frac{1}{3}-4\frac{1}{9}$$
$$=\left(6\frac{1}{2}+4\frac{1}{6}\right)-\left(7\frac{5}{9}+5\frac{1}{3}+4\frac{1}{9}\right)$$
$$=10\frac{2}{3}-16\frac{1}{3}=-6\frac{2}{3}.$$

6) $$-13{,}57+25{,}43+11{,}27-23{,}13=(25{,}43+11{,}27)-(13{,}57+23{,}13)$$
$$=36{,}7-36{,}7=0.$$

7) $$11{,}269+5{,}427-7{,}169-6{,}527=(11{,}269+5{,}427)-(7{,}169+6{,}527)$$
$$=16{,}696-13{,}696=3.$$

8) $$34{,}8-15{,}39+27{,}5-47{,}91=(34{,}8+27{,}5)-(15{,}39+47{,}91)$$
$$=62{,}3-63{,}3=-1.$$

9) $$-0{,}037+\frac{1}{4}+\frac{7}{8}+\frac{5}{16}-1{,}4$$
$$=\left(\frac{1}{4}+\frac{7}{8}+\frac{5}{16}\right)-\left(0{,}037+1{,}4\right)$$
$$=\frac{4}{16}+\frac{14}{16}+\frac{5}{16}-1{,}437=\frac{23}{16}-1{,}437$$
$$=1{,}4375-1{,}437=0{,}0005.$$

10) $$0{,}4-\frac{1}{2}+0{,}75-\frac{5}{6}+0{,}85-\frac{2}{3}$$
$$=(0{,}4+0{,}75+0{,}85)-\left(\frac{1}{2}+\frac{5}{6}+\frac{2}{3}\right)$$
$$=2-\left(\frac{3}{6}+\frac{5}{6}+\frac{4}{6}\right)=2-\frac{12}{6}=2-2=0.$$