Упр.854 ГДЗ Никольский Потапов 5 класс (Математика)

Задача

а) 1/27 + 5/9 + 1/3; б) 2/9 + 5/6 + 1/18; в) 2/15 + 1/5 + 3/10;
г) 3/8 + 5/12 + 1/24; д) 1/4 + 3/8 + 5/16; е) 5/7 + 3/14 + 1/21.

Подробный ответ

Приведём дроби к общему знаменателю и воспользуемся переместительным и сочетательным законами сложения.

а)

$$ \frac{1}{27}+\frac{5}{9}+\frac{1}{3} = \frac{1}{27}+\frac{15}{27}+\frac{9}{27} = \left(\frac{1}{27}+\frac{9}{27}\right)+\frac{15}{27} = \frac{10}{27}+\frac{15}{27} = \frac{25}{27} $$

б)

$$ \frac{2}{9}+\frac{5}{6}+\frac{1}{18} = \frac{4}{18}+\frac{15}{18}+\frac{1}{18} = \left(\frac{4}{18}+\frac{1}{18}\right)+\frac{15}{18} = \frac{5}{18}+\frac{15}{18} = \frac{20}{18} = \frac{10}{9} $$

в)

$$ \frac{2}{15}+\frac{1}{5}+\frac{3}{10} = \frac{4}{30}+\frac{6}{30}+\frac{9}{30} = \left(\frac{4}{30}+\frac{6}{30}\right)+\frac{9}{30} = \frac{10}{30}+\frac{9}{30} = \frac{19}{30} $$

г)

$$ \frac{3}{8}+\frac{5}{12}+\frac{1}{24} = \frac{9}{24}+\frac{10}{24}+\frac{1}{24} = \left(\frac{9}{24}+\frac{1}{24}\right)+\frac{10}{24} = \frac{10}{24}+\frac{10}{24} = \frac{20}{24} = \frac{5}{6} $$

д)

$$ \frac{1}{4}+\frac{3}{8}+\frac{5}{16} = \frac{4}{16}+\frac{6}{16}+\frac{5}{16} = \left(\frac{4}{16}+\frac{6}{16}\right)+\frac{5}{16} = \frac{10}{16}+\frac{5}{16} = \frac{15}{16} $$

е)

$$ \frac{5}{7}+\frac{3}{14}+\frac{1}{21} = \frac{30}{42}+\frac{9}{42}+\frac{2}{42} = \left(\frac{30}{42}+\frac{9}{42}\right)+\frac{2}{42} = \frac{39}{42}+\frac{2}{42} = \frac{41}{42} $$