Упр.256 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

1) 3 19/24 + (5 1/9 + 1 5/24); 3) 7 16/35 — (3 11/35 + 4 1/56);
2) (1 5/8 + 4 8/17) + (9/17 + 2 3/8); 4) (4 56/789 + 1 5/6) — 4 56/789.

1) $$3\frac{19}{24}+\left(5\frac{1}{9}+1\frac{5}{24}\right)=\left(3\frac{19}{24}+1\frac{5}{24}\right)+5\frac{1}{9}$$

$$=\left(3+1+\frac{19}{24}+\frac{5}{24}\right)+5\frac{1}{9}=4+\frac{24}{24}+5\frac{1}{9}=5+5\frac{1}{9}=10\frac{1}{9}$$

2) $$\left(1\frac{5}{8}+4\frac{8}{17}\right)+\left(\frac{9}{17}+2\frac{3}{8}\right)=\left(1\frac{5}{8}+2\frac{3}{8}\right)+\left(4\frac{8}{17}+\frac{9}{17}\right)$$

$$=\left(1+2+\frac{5}{8}+\frac{3}{8}\right)+\left(4+0+\frac{8}{17}+\frac{9}{17}\right)=3+\frac{8}{8}+4+\frac{17}{17}=4+5=9$$

3) $$7\frac{16}{35}-\left(3\frac{11}{35}+4\frac{1}{56}\right)=\left(7\frac{16}{35}-3\frac{11}{35}\right)-4\frac{1}{56}$$

$$=\left(7-3+\frac{16}{35}-\frac{11}{35}\right)-4\frac{1}{56}=4+\frac{5}{35}-4\frac{1}{56}$$

$$=4+\frac{1}{7}-4\frac{1}{56}=4+\frac{8}{56}-4\frac{1}{56}=(4-4)+\left(\frac{8}{56}-\frac{1}{56}\right)=\frac{7}{56}=\frac{1}{8}$$

4) $$\left(4\frac{56}{789}+1\frac{5}{6}\right)-4\frac{56}{789}=\left(4\frac{56}{789}-4\frac{56}{789}\right)+1\frac{5}{6}$$

$$=0+1\frac{5}{6}=1\frac{5}{6}$$

Ответ

1) $$10\frac{1}{9}$$; 2) $$9$$; 3) $$\frac{1}{8}$$; 4) $$1\frac{5}{6}$$.