a) \(\dfrac{1}{3}\)của 45 = \(45.\dfrac{1}{3}=15\)

b) \(\dfrac{2}{7}\)của \(\dfrac{63}{91}\)= \(\dfrac{63}{91}.\dfrac{2}{7}=\dfrac{18}{91}\)

c) 23% của 200 = 200 . \(\dfrac{23}{100}\)= 46

d) \(1\dfrac{2}{3}\)của \(3\dfrac{1}{4}\)= \(3\dfrac{1}{4}.1\dfrac{2}{3}=\dfrac{65}{12}\)

Bn phân lại các phần đc k ? Nhìn hơi rối mắt.

\(\dfrac{51}{53}+\dfrac{55}{57}+\dfrac{61}{63}+\dfrac{69}{71}+\dfrac{79}{81}+\dfrac{91}{93}\) 

\(=\left(\dfrac{52}{53}-\dfrac{1}{53}\right)+\left(\dfrac{56}{57}-\dfrac{1}{57}\right)+\left(\dfrac{62}{63}-\dfrac{1}{63}\right)+\left(\dfrac{70}{71}-\dfrac{1}{71}\right)+\left(\dfrac{80}{81}-\dfrac{1}{81}\right)+\left(\dfrac{92}{93}-\dfrac{1}{93}\right)\)

\(=\left(1-\dfrac{1}{53}-\dfrac{1}{53}\right)+\left(1-\dfrac{1}{57}-\dfrac{1}{57}\right)+\left(1-\dfrac{1}{63}-\dfrac{1}{63}\right)+\left(1-\dfrac{1}{71}-\dfrac{1}{71}\right)+\left(1-\dfrac{1}{81}-\dfrac{1}{81}\right)+\left(1-\dfrac{1}{93}-\dfrac{1}{93}\right)\)

\(=\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)\) 

\(=1+1+1+1+1+1\) 

\(=6\)

f, \(\dfrac{165}{270}\) = \(\dfrac{165:15}{270:15}\) = \(\dfrac{11}{18}\) = \(\dfrac{11\times6}{18\times6}\) = \(\dfrac{66}{108}\)

 \(\dfrac{91}{156}\) = \(\dfrac{91:13}{156:13}\) = \(\dfrac{7}{12}\) = \(\dfrac{7\times9}{12\times9}\) = \(\dfrac{63}{108}\)

\(\dfrac{210}{1134}\) = \(\dfrac{210:42}{1134:42}\) = \(\dfrac{5}{27}\) =  \(\dfrac{5\times4}{27\times4}\) = \(\dfrac{20}{108}\)

g, \(\dfrac{21}{9}\) = \(\dfrac{21:3}{9:3}\) = \(\dfrac{7}{3}\) = \(\dfrac{7\times10}{3\times10}\) = \(\dfrac{70}{30}\)

     \(\dfrac{120}{50}\) =  \(\dfrac{120:10}{50:10}\) = \(\dfrac{12}{5}\) = \(\dfrac{12\times6}{5\times6}\) = \(\dfrac{72}{30}\)

       \(\dfrac{63}{54}\) = \(\dfrac{63:9}{54:9}\) = \(\dfrac{7}{6}\)  = \(\dfrac{7\times5}{6\times5}\) = \(\dfrac{35}{30}\)

h, \(\dfrac{75}{100}\) = \(\dfrac{75:25}{100:4}\) = \(\dfrac{3}{4}\) = \(\dfrac{3\times9}{4\times6}\) = \(\dfrac{27}{36}\)

      \(\dfrac{150}{90}\) = \(\dfrac{150:30}{90:30}\) =  \(\dfrac{5}{3}\) = \(\dfrac{5\times12}{3\times12}\) = \(\dfrac{60}{36}\)

       \(\dfrac{250}{900}\) = \(\dfrac{250:50}{900:50}\) = \(\dfrac{5}{18}\)  = \(\dfrac{5\times2}{18\times2}\) = \(\dfrac{10}{36}\)

\(A=\left(-\dfrac{5}{7}+\dfrac{8}{5}\right):\dfrac{91}{8}+\left(-\dfrac{2}{7}-\dfrac{3}{5}\right):\dfrac{91}{8}\)

\(=\dfrac{31}{35}:\dfrac{91}{8}+\dfrac{-31}{35}:\dfrac{91}{8}\)

\(=\dfrac{248}{3185}+\dfrac{-248}{3185}\)

= 0

\(B=\dfrac{13}{15}:\left(\dfrac{4}{5}-\dfrac{3}{7}\right)+\dfrac{13}{15}:\left(\dfrac{2}{5}-\dfrac{1}{9}\right)\)

\(=\dfrac{13}{15}:\dfrac{13}{35}+\dfrac{13}{15}:\dfrac{13}{45}\)

\(=\dfrac{7}{3}+3\)

\(=\dfrac{16}{3}\)

a)\(\sqrt{\dfrac{3^2}{7^2}}=\sqrt{\dfrac{9}{49}}=\sqrt{\dfrac{3}{7}}\)

b)\(\dfrac{\sqrt{3^2}+\sqrt{39^2}}{\sqrt{7^2}+\sqrt{91^2}}=\dfrac{\sqrt{9}+\sqrt{1521}}{\sqrt{49}+\sqrt{8281}}=\dfrac{3+39}{7+91}=\dfrac{42}{98}\)

c)Tương tự câu b, ta đc:

\(\dfrac{\sqrt{3^2}-\sqrt{39^2}}{\sqrt{7^2}-\sqrt{91^2}}=\dfrac{3-39}{7-91}=\dfrac{-36}{86}=\dfrac{3}{7}\)

d)Tương tự câu a, ta đc:

\(\dfrac{\sqrt{39^2}}{\sqrt{91^2}}=\dfrac{39}{91}\)

Chúc Bạn Học Tốt!!!

a) \(\sqrt{\dfrac{3^2}{7^2}}=\sqrt{\left(\dfrac{3}{7}\right)^2}=\left|\dfrac{3}{7}\right|=\dfrac{3}{7}\)

b) \(\dfrac{\sqrt{3}^2+\sqrt{39}^2}{\sqrt{7}^2+\sqrt{91}^2}=\dfrac{\left|3\right|+\left|39\right|}{\left|7\right|+\left|91\right|}=\dfrac{3+39}{7+91}=\dfrac{42}{98}=\dfrac{3}{7}\)

c) \(\dfrac{\sqrt{3}^2-\sqrt{39}^2}{\sqrt{7}^2-\sqrt{91}^2}=\dfrac{\left|3\right|- \left|39\right|}{\left|7\right|-\left|91\right|}=\dfrac{3-39}{7-91}=\dfrac{-36}{-84}=\dfrac{3}{7}\)

d) \(\sqrt{\dfrac{39^2}{91^2}}=\sqrt{\left(\dfrac{39}{91}\right)^2}=\left|\dfrac{39}{91}\right|=\dfrac{39}{91}=\dfrac{3}{7}\)

\(2\dfrac{3}{7}.63=152\)

152

`2 3/7xx63=17/7xx63=17xx9=153`

\(\dfrac{14}{7}>\dfrac{9}{7}\)

\(\dfrac{6}{13}< 1\)

\(\dfrac{7}{9}=\dfrac{14}{18}\)

\(\dfrac{4}{9}=\dfrac{20}{45}< \dfrac{26}{45}\)

\(\dfrac{11}{24}>\dfrac{9}{24}=\dfrac{3}{8}\)

\(\dfrac{42}{91}=\dfrac{42:7}{91:7}=\dfrac{6}{13}< \dfrac{7}{13}\)

\(\dfrac{34}{64}< \dfrac{52}{64}=\dfrac{13}{16}\)

\(\dfrac{17}{30}>\dfrac{16}{30}=\dfrac{8}{15}\)

a/ \(x-\dfrac{3}{7}=\dfrac{2}{5}\cdot\dfrac{1}{4}\)

\(x-\dfrac{3}{7}=\dfrac{1}{10}\)

\(x=\dfrac{1}{10}+\dfrac{3}{7}=\dfrac{37}{70}\)

Vậy....

b/ \(x+\dfrac{4}{5}=-\dfrac{5}{12}\cdot\dfrac{3}{25}\)

\(x+\dfrac{4}{5}=-\dfrac{1}{20}\)

\(x=-\dfrac{1}{20}-\dfrac{4}{5}=-\dfrac{17}{20}\)

Vậy....

c/ \(\dfrac{x}{182}=-\dfrac{6}{12}\cdot\dfrac{35}{91}\)

\(\dfrac{x}{182}=-\dfrac{5}{26}\)

\(=>x\cdot26=-5\cdot182\)

\(26x=-910\)

\(x=-910:26=-35\)

Vậy....

a) Ta có: \(x-\dfrac{3}{7}=\dfrac{2}{5}\cdot\dfrac{1}{4}\)

\(\Leftrightarrow x-\dfrac{3}{7}=\dfrac{1}{10}\)

\(\Leftrightarrow x=\dfrac{1}{10}+\dfrac{3}{7}=\dfrac{7}{70}+\dfrac{30}{70}\)

hay \(x=\dfrac{37}{70}\)

Vậy: \(x=\dfrac{37}{70}\)