Упр.16.7 ГДЗ Рабочая тетрадь Зубарева Мордкович 6 класс Экзамен (Математика)

Задача

а) (15 5/6-9 25/27)-(2/3-5/18)+7/27+13/18;
б) (20 8/15•7 1/2-54 3/5•2/5) :(3 13/21•8 2/5-29 2/5)-5/6•1 1/5+21/25.

Подробный ответ

а) Преобразуем смешанные числа в неправильные дроби и выполним действия по порядку:

$$ \left(15\frac{5}{6}-9\frac{25}{27}\right)-\left(\frac{2}{3}-\frac{5}{18}\right)+\frac{7}{27}+\frac{13}{18} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)-\left(\frac{12}{18}-\frac{5}{18}\right)+\frac{7}{27}+\frac{13}{18} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)-\frac{7}{18}+\frac{7}{27}+\frac{13}{18} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)+\left(-\frac{7}{18}+\frac{13}{18}\right)+\frac{7}{27} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)+\frac{1}{3}+\frac{7}{27} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)+\frac{9}{27}+\frac{7}{27} $$
$$ = \left(15\frac{5}{6}-9\frac{25}{27}\right)+\frac{16}{27} $$
$$ = 15\frac{5}{6}-9\frac{9}{27} = 15\frac{5}{6}-9\frac{1}{3} = 6\frac{1}{2}. $$

б) Сначала вычислим произведения и разности в скобках:

$$ \left(20\frac{8}{15}\cdot 7\frac{1}{2}-54\frac{3}{5}\cdot \frac{2}{5}\right):\left(3\frac{13}{21}\cdot 8\frac{2}{5}-29\frac{2}{5}\right)-\frac{5}{6}\cdot 1\frac{1}{5}+\frac{21}{25} $$
$$ = \left(\frac{308}{15}\cdot \frac{15}{2}-\frac{273}{5}\cdot \frac{2}{5}\right):\left(\frac{76}{21}\cdot \frac{42}{5}-29\frac{2}{5}\right)-\frac{5}{6}\cdot \frac{6}{5}+\frac{21}{25} $$
$$ = \left(154-\frac{546}{25}\right):\left(76\cdot \frac{2}{5}-29\frac{2}{5}\right)-1+\frac{21}{25} $$
$$ = \left(154-21\frac{21}{25}\right):\left(30\frac{2}{5}-29\frac{2}{5}\right)-1+\frac{21}{25} $$
$$ = 132\frac{4}{25}:1-1+\frac{21}{25} $$
$$ = 132\frac{4}{25}-1+\frac{21}{25} $$
$$ = 132\frac{4}{25}-\frac{25}{25}+\frac{21}{25} = 132. $$