a) Ta có: \(4\cdot\left(13-16\right)-\left(3-5\right)\cdot\left(-3\right)^2\)

\(=4\cdot13-4\cdot16+2\cdot9\)

\(=52-64+18\)

=6

b) Ta có: \(-\dfrac{2}{5}+\dfrac{7}{11}+\dfrac{-11}{10}+\dfrac{7}{-11}\)

\(=-\left(\dfrac{2}{5}+\dfrac{11}{10}\right)+\left(\dfrac{7}{11}-\dfrac{7}{11}\right)\)

\(=-\left(\dfrac{4}{10}+\dfrac{11}{10}\right)\)

\(=\dfrac{-15}{10}=\dfrac{-3}{2}\)

Bài 1:

\(\frac{3}{5}+\frac{4}{15}=\frac{9}{15}+\frac{4}{15}=\frac{13}{15}\)

\(\frac{5}{6}:\frac{-7}{12}=\frac{5}{6}.\frac{-12}{7}=\frac{-60}{42}=\frac{-10}{7}\)

\(\frac{-21}{24}:\frac{-14}{8}=\frac{-21}{24}.\frac{-8}{14}=\frac{168}{336}=\frac{1}{2}\)

\(\frac{4}{5}:\frac{-8}{15}=\frac{4}{5}.\frac{-15}{8}=\frac{-60}{40}=\frac{-3}{2}\)

\(\frac{5}{12}-\frac{-7}{6}=\frac{5}{12}+\frac{7}{6}=\frac{5}{12}+\frac{14}{12}=\frac{19}{12}\)

\(\frac{-15}{16}.\frac{8}{25}=\frac{-120}{400}=\frac{-3}{10}\)

Bài 2 :

\(6\frac{4}{5}-\left(1\frac{2}{3}+3\frac{4}{5}\right)\)

\(=\frac{34}{5}-\left(\frac{5}{3}+\frac{19}{5}\right)\)

\(=\frac{34}{5}-\frac{5}{3}-\frac{19}{5}\)

\(=\left(\frac{34}{5}-\frac{19}{5}\right)-\frac{5}{3}\)

\(=3-\frac{5}{3}\)

\(=\frac{4}{3}\)

\(6\frac{5}{7}-\left(1\frac{2}{3}+2\frac{5}{7}\right)\)

\(=\frac{47}{7}-\left(\frac{5}{3}+\frac{19}{7}\right)\)

\(=\frac{47}{7}-\frac{5}{3}-\frac{19}{7}\)

\(=\left(\frac{47}{7}-\frac{19}{7}\right)-\frac{5}{3}\)

\(=4-\frac{5}{3}\)

\(=\frac{7}{3}\)

\(\frac{4}{19}.\frac{-3}{7}+\frac{-3}{7}.\frac{15}{19}+\frac{5}{7}\)

\(=\left(\frac{4}{19}+\frac{15}{19}\right).\frac{-3}{7}+\frac{5}{7}\)

\(=1.\frac{-3}{7}+\frac{5}{7}\)

\(=\frac{-3}{7}+\frac{5}{7}\)

\(=\frac{2}{7}\)

\(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

\(=\frac{5}{9}.\left(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\right)\)

\(=\frac{5}{9}.1\)

\(=\frac{5}{9}\)

Bài 3 :

\(\frac{x}{5}=\frac{2}{3}\)

\(\Rightarrow x.3=5.2\)

\(\Rightarrow x.3=10\)

\(\Rightarrow x=\frac{10}{3}\)

\(\frac{x}{3}-\frac{1}{2}=\frac{1}{5}\)

\(\frac{x}{3}=\frac{1}{5}+\frac{1}{2}\)

\(\frac{x}{3}=\frac{7}{10}\)

\(\Rightarrow x.10=3.7\)

\(\Rightarrow x.10=21\)

\(\Rightarrow x=\frac{21}{10}\)

\(\frac{4}{5}+x=\frac{2}{3}\)

\(x=\frac{2}{3}-\frac{4}{5}\)

\(x=\frac{-2}{15}\)

\(\frac{3}{4}-x=\frac{1}{3}\)

\(x=\frac{3}{4}-\frac{1}{3}\)

\(x=\frac{5}{12}\)

\(x-\frac{5}{9}=\frac{-2}{3}\)

\(x=\frac{-2}{3}+\frac{5}{9}\)

\(x=\frac{-1}{9}\)

\(\frac{1}{2}x+\frac{1}{2}=\frac{5}{2}\)

\(\frac{1}{2}x=\frac{5}{2}-\frac{1}{2}\)

\(\frac{1}{2}x=2\)

\(x=2:\frac{1}{2}\)

\(x=4\)

\(\frac{-2}{3}-\frac{1}{3}.\left(2x-5\right)=\frac{3}{2}\)

\(\frac{1}{3}.\left(2x-5\right)=\frac{-2}{3}-\frac{3}{2}\)

\(\frac{1}{3}.\left(2x-5\right)=\frac{-19}{10}\)

\(2x-5=\frac{-19}{10}:\frac{1}{3}\)

\(2x-5=\frac{-57}{10}\)

\(2x=\frac{-57}{10}+5\)

\(2x=\frac{-7}{10}\)

\(x=\frac{-7}{10}:2\)

\(x=\frac{-7}{20}\)

\(3\frac{1}{3}+\frac{5}{6}x=3\frac{2}{1}\)

\(\frac{10}{3}+\frac{5}{6}x=5\)

\(\frac{5}{6}x=5-\frac{10}{3}\)

\(\frac{5}{6}x=\frac{5}{3}\)

\(x=\frac{5}{3}:\frac{5}{6}\)

\(x=2\)

\(\frac{3}{8}-\frac{1}{6}x=\frac{1}{4}\)

\(\frac{1}{6}x=\frac{3}{8}-\frac{1}{4}\)

\(\frac{1}{6}x=\frac{1}{8}\)

\(x=\frac{1}{8}:\frac{1}{6}\)

\(x=\frac{3}{4}\)

Các bài toán này bn bấm máy thì sẽ ra nha.

Bài 7 có quy tắc tính trong ngoặc trước, ngoài ngoặc sau.

7b bn nhóm 2/3 +1/18 lại vào một chỗ và để cho chúng dấu ngoặc

tíc mình nha

\(\frac{1}{2}+-\frac{1}{5}+-\frac{5}{7}+\frac{1}{6}-\frac{3}{35}+\frac{1}{3}+\frac{1}{41}=\frac{1}{41}\)

1/41 giai ra dai nam cu rut gon roi quy dong

\(\frac{1}{2}+\left(-\frac{1}{5}\right)+\left(-\frac{5}{7}\right)+\frac{1}{6}+\left(-\frac{3}{35}\right)+\frac{1}{3}+\frac{1}{41}\)

\(=\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{3}\right)+\left[\left(\frac{-1}{5}\right)+\left(-\frac{5}{7}\right)+\left(-\frac{3}{35}\right)\right]+\frac{1}{41}\)

\(=1+\left(-1\right)+\frac{1}{41}\)

=0+1/41=1/41

\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)

\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)

\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)

\(A=1+2+3+...+7+8=\dfrac{\left(8+1\right).\left(\dfrac{8-1}{1}+1\right)}{2}=36\)

\(B=3+4+5+...+10+11=\dfrac{\left(11+3\right).\left(\dfrac{11-3}{1}+1\right)}{2}=63\)

\(C=1+3+5+...+13+15=\dfrac{\left(15+1\right).\left(\dfrac{15-1}{2}+1\right)}{2}=64\)

\(D=2+4+6+...+18+20=\dfrac{\left(20+2\right).\left(\dfrac{20-2}{2}+1\right)}{2}=110\)

\(E=1+4+7+...+22+25=\dfrac{\left(25+1\right).\left(\dfrac{25-1}{3}+1\right)}{2}=117\)

\(G=1+5+9+...+33+37+41=\dfrac{\left(41+1\right).\left(\dfrac{41-1}{4}+1\right)}{2}=231\)