Упр.609 ГДЗ Ткачёва 6 класс (Математика)

1) |5 3/4| + |-1 3/8|; 2) |-2 11/12| + |1 5/6|;
3) |3 1/12| — |-1 5/18|; 4) |-4 3/8| — |-2 17/20|;
5) |-2 1/3| · |-1 9/14|; 6) |-1 3/5| · |1 1/24|;
7) |3 1/7| : |-1 1/35|; 8) |-2 1/12| : |-3 1/18|.

Используем свойство модуля: $$|a|$$ равно числу $$a$$ без знака.

1) $$|5\tfrac{3}{4}|+|-1\tfrac{3}{8}|=5\tfrac{3}{4}+1\tfrac{3}{8}=5\tfrac{6}{8}+1\tfrac{3}{8}=6\tfrac{9}{8}=7\tfrac{1}{8}.$$

2) $$|-2\tfrac{11}{12}|+|1\tfrac{5}{6}|=2\tfrac{11}{12}+1\tfrac{5}{6}=2\tfrac{11}{12}+1\tfrac{10}{12}=3\tfrac{21}{12}=4\tfrac{9}{12}=4\tfrac{3}{4}.$$

3) $$|3\tfrac{1}{12}|-|-1\tfrac{5}{18}|=3\tfrac{1}{12}-1\tfrac{5}{18}=3\tfrac{3}{36}-1\tfrac{10}{36}=2\tfrac{39}{36}-1\tfrac{10}{36}=1\tfrac{29}{36}.$$

4) $$|-4\tfrac{3}{8}|-|-2\tfrac{17}{20}|=4\tfrac{3}{8}-2\tfrac{17}{20}=4\tfrac{15}{40}-2\tfrac{34}{40}=3\tfrac{55}{40}-2\tfrac{34}{40}=1\tfrac{21}{40}.$$

5) $$|-2\tfrac{1}{3}|\cdot|-1\tfrac{9}{14}|=2\tfrac{1}{3}\cdot1\tfrac{9}{14}=\frac{7}{3}\cdot\frac{23}{14}=\frac{7\cdot23}{3\cdot14}=\frac{23}{6}=3\tfrac{5}{6}.$$

6) $$|-1\tfrac{3}{5}|\cdot|1\tfrac{1}{24}|=1\tfrac{3}{5}\cdot1\tfrac{1}{24}=\frac{8}{5}\cdot\frac{25}{24}=\frac{8\cdot25}{5\cdot24}=\frac{5}{3}=1\tfrac{2}{3}.$$

7) $$|3\tfrac{1}{7}|:|-1\tfrac{1}{35}|=3\tfrac{1}{7}:1\tfrac{1}{35}=\frac{22}{7}:\frac{36}{35}=\frac{22}{7}\cdot\frac{35}{36}=\frac{11\cdot5}{18}=\frac{55}{18}=3\tfrac{1}{18}.$$

8) $$|-2\tfrac{1}{12}|:|-3\tfrac{1}{18}|=2\tfrac{1}{12}:3\tfrac{1}{18}=\frac{25}{12}:\frac{55}{18}=\frac{25}{12}\cdot\frac{18}{55}=\frac{5\cdot3}{2\cdot11}=\frac{15}{22}.$$

Ответ

1) $$7\tfrac{1}{8}$$; 2) $$4\tfrac{3}{4}$$; 3) $$1\tfrac{29}{36}$$; 4) $$1\tfrac{21}{40}$$; 5) $$3\tfrac{5}{6}$$; 6) $$1\tfrac{2}{3}$$; 7) $$3\tfrac{1}{18}$$; 8) $$\frac{15}{22}$$.