Упр.534 ГДЗ Муравин 6 класс (Математика)
Вычислите:
- 1) $$\left(\frac{55}{57}-\frac{51}{95}\right)\mathbin{\colon}\left(-\frac{122}{133}\right)$$;
2) $$\left(-\frac{60}{259}\right)\mathbin{\colon}\left(-\frac{45}{148}+\frac{75}{222}\right)$$;
3) $$\left(\frac{8}{225}-\frac{4}{105}\right)\mathbin{\colon}\left(\frac{6}{35}-\frac{2}{45}\right)$$;
4) $$\left(\frac{4}{51}-\frac{1}{136}\right)\mathbin{\colon}\left(-\frac{5}{34}-\frac{7}{51}\right)$$.
1) $$\left(\frac{55}{57}-\frac{51}{95}\right):\left(-\frac{122}{133}\right)$$
$$\frac{55}{57}-\frac{51}{95}=\frac{55\cdot 5-51\cdot 3}{285}=\frac{275-153}{285}=\frac{122}{285}$$
$$\frac{122}{285}:\left(-\frac{122}{133}\right)=\frac{122}{285}\cdot\left(-\frac{133}{122}\right)=-\frac{133}{285}=-\frac{7}{15}$$
2) $$\left(-\frac{60}{259}\right):\left(-\frac{45}{148}+\frac{75}{222}\right)$$
$$-\frac{45}{148}+\frac{75}{222}=\frac{-45\cdot 3+75\cdot 2}{444}=\frac{-135+150}{444}=\frac{15}{444}=\frac{5}{148}$$
$$-\frac{60}{259}:\frac{5}{148}=-\frac{60}{259}\cdot\frac{148}{5}$$
Сократим:
$$\frac{60}{5}=12,\qquad \frac{148}{259}=\frac{4}{7}$$
Тогда
$$-\frac{60}{259}\cdot\frac{148}{5}=-12\cdot\frac{4}{7}=-\frac{48}{7}=-6\frac{6}{7}$$
3) $$\left(\frac{8}{225}-\frac{4}{105}\right):\left(\frac{6}{35}-\frac{2}{45}\right)$$
$$\frac{8}{225}-\frac{4}{105}=\frac{8\cdot 7-4\cdot 15}{1575}=\frac{56-60}{1575}=-\frac{4}{1575}$$
$$\frac{6}{35}-\frac{2}{45}=\frac{6\cdot 9-2\cdot 7}{315}=\frac{54-14}{315}=\frac{40}{315}=\frac{8}{63}$$
Тогда
$$-\frac{4}{1575}:\frac{8}{63}=-\frac{4}{1575}\cdot\frac{63}{8}$$
Сократим:
$$\frac{63}{1575}=\frac{1}{25},\qquad \frac{4}{8}=\frac{1}{2}$$
Получаем
$$-\frac{1}{25}\cdot\frac{1}{2}=-\frac{1}{50}$$
4) $$\left(\frac{4}{51}-\frac{1}{136}\right):\left(-\frac{5}{34}-\frac{7}{51}\right)$$
$$\frac{4}{51}-\frac{1}{136}=\frac{4\cdot 8-1\cdot 3}{408}=\frac{32-3}{408}=\frac{29}{408}$$
$$-\frac{5}{34}-\frac{7}{51}=\frac{-5\cdot 3-7\cdot 2}{102}=\frac{-15-14}{102}=-\frac{29}{102}$$
Тогда
$$\frac{29}{408}:\left(-\frac{29}{102}\right)=\frac{29}{408}\cdot\left(-\frac{102}{29}\right)=-\frac{102}{408}=-\frac{1}{4}$$
Ответ
$$1)\ -\frac{7}{15};\quad 2)\ -6\frac{6}{7};\quad 3)\ -\frac{1}{50};\quad 4)\ -\frac{1}{4}$$
