Упр.5.7 ГДЗ Виленкин Жохов 6 класс Часть 2, Просвещение (Математика)

а) $$\frac{5}{9}+\left(\frac{4}{9}-\frac{7}{11}\right)=\frac{5}{9}+\frac{4}{9}-\frac{7}{11}=1-\frac{7}{11}=\frac{11}{11}-\frac{7}{11}=\frac{4}{11}$$

б) $$5\frac{3}{7}+\left(-\frac{3}{7}-\frac{8}{9}\right)=5\frac{3}{7}-\frac{3}{7}-\frac{8}{9}=5-\frac{8}{9}=4\frac{1}{9}$$

в) $$4{,}32+\left(\frac{12}{13}-3{,}32\right)=4{,}32+\frac{12}{13}-3{,}32=(4{,}32-3{,}32)+\frac{12}{13}=1+\frac{12}{13}=1\frac{12}{13}$$

г) $$\frac{7}{15}-\left(\frac{4}{15}-\frac{4}{5}\right)=\frac{7}{15}-\frac{4}{15}+\frac{4}{5}=\frac{3}{15}+\frac{4}{5}=\frac{1}{5}+\frac{4}{5}=1$$

д) $$6\frac{7}{9}-\left(3\frac{4}{9}+2\frac{1}{3}\right)=6\frac{7}{9}-3\frac{4}{9}-2\frac{1}{3}=3+\frac{3}{9}-2\frac{1}{3}=3\frac{1}{3}-2\frac{1}{3}=1$$

е) $$-9\frac{11}{12}-\left(\frac{1}{4}-\frac{5}{12}\right)=-9\frac{11}{12}-\frac{1}{4}+\frac{5}{12}=-9\frac{11}{12}-\frac{3}{12}+\frac{5}{12}=-9\frac{11}{12}+\frac{2}{12}=-9\frac{9}{12}=-9\frac{3}{4}$$

ж) $$\left(4\frac{1}{4}-6\frac{8}{11}\right)+\left(6{,}75-3\frac{3}{11}\right)=4\frac{1}{4}-6\frac{8}{11}+6{,}75-3\frac{3}{11}$$

$$=\left(4\frac{1}{4}+6{,}75\right)-\left(6\frac{8}{11}+3\frac{3}{11}\right)=11-\left(9+\frac{11}{11}\right)=11-10=1$$

з) $$\left(9\frac{7}{18}-2{,}7\right)-\left(4\frac{1}{18}+2{,}3\right)=9\frac{7}{18}-2{,}7-4\frac{1}{18}-2{,}3$$

$$=\left(9\frac{7}{18}-4\frac{1}{18}\right)-\left(2{,}7+2{,}3\right)=5\frac{6}{18}-5=5\frac{1}{3}-5=\frac{1}{3}$$

Ответ

а) $$\frac{4}{11}$$; б) $$4\frac{1}{9}$$; в) $$1\frac{12}{13}$$; г) $$1$$; д) $$1$$; е) $$-9\frac{3}{4}$$; ж) $$1$$; з) $$\frac{1}{3}$$.