Упр.1014 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 16-29+ 14 -48;
2) -3,2 — 7,8 — 5,4 + 4,6;
3) -4,28 — 1,53 — (-7,85) + (-9,06);
4) -5*3/8 + 4*5/6 — (-2*1/4);
5) -3*3/5 + (-2*1/3) + 4*8/15 — 1*5/6 — (-6*7/10) + 1/2.

1) $$16-29+14-48=(16+14)-29-48=30-29-48=1-48=-47.$$

2) $$-3{,}2-7{,}8-5{,}4+4{,}6=-(3{,}2+7{,}8)-5{,}4+4{,}6=-11-5{,}4+4{,}6=-16{,}4+4{,}6=-11{,}8.$$

3) $$-4{,}28-1{,}53-(-7{,}85)+(-9{,}06)=-4{,}28-1{,}53+7{,}85-9{,}06$$
$$=-(4{,}28+1{,}53)+7{,}85-9{,}06=-5{,}81+7{,}85-9{,}06=2{,}04-9{,}06=-7{,}02.$$

4) $$-5\frac{3}{8}+4\frac{5}{6}-\left(-2\frac{1}{4}\right)=-5\frac{3}{8}+4\frac{5}{6}+2\frac{1}{4}$$
$$=-\left(5\frac{3}{8}-2\frac{1}{4}\right)+4\frac{5}{6}=-\left(5\frac{3}{8}-2\frac{2}{8}\right)+4\frac{5}{6}$$
$$=-3\frac{1}{8}+4\frac{5}{6}=4\frac{20}{24}-3\frac{3}{24}=1\frac{17}{24}.$$

5) $$-3\frac{3}{5}+\left(-2\frac{1}{3}\right)+4\frac{8}{15}-1\frac{5}{6}-\left(-6\frac{7}{10}\right)+\frac{1}{2}$$
$$=-3\frac{3}{5}-2\frac{1}{3}+4\frac{8}{15}-1\frac{5}{6}+6\frac{7}{10}+\frac{1}{2}$$
$$=-\left(3\frac{3}{5}+2\frac{1}{3}-4\frac{8}{15}\right)+\left(6\frac{7}{10}+\frac{1}{2}\right)-1\frac{5}{6}$$
$$=-\left(3\frac{9}{15}+2\frac{5}{15}-4\frac{8}{15}\right)+\left(6\frac{7}{10}+\frac{5}{10}\right)-1\frac{5}{6}$$
$$=-\left(5\frac{14}{15}-4\frac{8}{15}\right)+6\frac{12}{10}-1\frac{5}{6}$$
$$=-1\frac{6}{15}+7\frac{2}{10}-1\frac{5}{6}=-1\frac{2}{5}+7\frac{1}{5}-1\frac{5}{6}$$
$$=6\frac{6}{5}-1\frac{2}{5}-1\frac{5}{6}=5\frac{4}{5}-1\frac{5}{6}=5\frac{24}{30}-1\frac{25}{30}=3\frac{29}{30}.$$

Ответ

1) $$-47$$; 2) $$-11{,}8$$; 3) $$-7{,}02$$; 4) $$1\frac{17}{24}$$; 5) $$3\frac{29}{30}$$.