Упр.5.6 ГДЗ Рабочая тетрадь Зубарева 6 класс Мнемозина (Математика)

Задача

3 8/21 + 5 5/21 + 9 11/21;
2 7/42 + 10 17/42 + 5 10/21;
6 19/21 + 7 3/7 + 4 5/21;
8 4/7 + 7 11/2 + 1 13/42.

Подробный ответ

Вычислим суммы, отдельно складывая целые и дробные части.

$$ 3\frac{8}{21}+5\frac{5}{21}+9\frac{11}{21} =(3+5+9)+\left(\frac{8}{21}+\frac{5}{21}+\frac{11}{21}\right) =17+\frac{24}{21} =17+1\frac{3}{21} =18\frac{1}{7}. $$

$$ 2\frac{7}{42}+10\frac{17}{42}+5\frac{10}{21} =(2+10)+\left(\frac{7}{42}+\frac{17}{42}\right)+5\frac{10}{21} =12+\frac{24}{42}+5\frac{10}{21} =12+\frac{12}{21}+5\frac{10}{21} $$
$$ =(12+5)+\left(\frac{12}{21}+\frac{10}{21}\right) =17+\frac{22}{21} =17+1\frac{1}{21} =18\frac{1}{21}. $$

$$ 6\frac{19}{21}+7\frac{3}{7}+4\frac{5}{21} =(6+4)+\left(\frac{19}{21}+\frac{5}{21}\right)+7\frac{3}{7} =10+\frac{24}{21}+7\frac{3}{7} $$
$$ =10+1\frac{3}{21}+7\frac{3}{7} =11\frac{1}{7}+7\frac{3}{7} =(11+7)+\left(\frac{1}{7}+\frac{3}{7}\right) =18\frac{4}{7}. $$

$$ 8\frac{4}{7}+7\frac{11}{42}+1\frac{13}{42} =\left(8+7+1\right)+\left(\frac{4}{7}+\frac{11}{42}+\frac{13}{42}\right) =16+\left(\frac{24}{42}+\frac{11}{42}+\frac{13}{42}\right) $$
$$ =16+\frac{48}{42} =16+\frac{8}{7} =16+1\frac{1}{7} =17\frac{1}{7}. $$