a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)

\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)

b)\(5+\dfrac{3}{5}=\dfrac{25}{5}+\dfrac{3}{5}=\dfrac{28}{5};10-\dfrac{9}{16}=\dfrac{160}{16}-\dfrac{9}{16}=\dfrac{151}{16}\)

\(\dfrac{2}{3}-\left(\dfrac{1}{6}+\dfrac{1}{8}\right)=\dfrac{2}{3}-\left(\dfrac{8}{48}+\dfrac{6}{48}\right)=\dfrac{2}{3}-\dfrac{14}{48}=\dfrac{32}{48}-\dfrac{14}{48}=\dfrac{3}{8}\)

Câu 1:

A = (4/9 + 5/6) : (7/8 - 7/12)

A = (8/18 + 15/18) :(21/24 - 14/24)

A = 23/18 : 7/24

A = 23/18 x 24/7

A = 92/21

Câu B = 3/4.8/9.15/16...9999/10000

B = \(\frac{1.3}{2.2}\).\(\frac{2.4}{3.3}\)....\(\frac{99.101}{100.100}\)

B = \(\frac{1.2.3\ldots99}{2.3\ldots100}\). \(\frac{3.4.\ldots101}{2.3\ldots100}\)

B = \(\frac{1}{100}\) x \(\frac{101}{2}\)

B = \(\frac{101}{200}\)

a: \(=\left(-\dfrac{25}{140}+\dfrac{245}{140}+\dfrac{32}{140}\right)\cdot\dfrac{-69}{20}\)

\(=\dfrac{252}{140}\cdot\dfrac{-69}{20}\)

\(=\dfrac{9}{5}\cdot\dfrac{-69}{20}=\dfrac{-621}{100}\)

b: \(=\left(6-2-\dfrac{4}{5}\right)\cdot\dfrac{25}{8}-\dfrac{8}{5}\cdot4\)

\(=\dfrac{16}{5}\cdot\dfrac{25}{8}-\dfrac{32}{5}=\dfrac{18}{5}\)

c: \(=\left(\dfrac{2}{24}+\dfrac{18}{24}+\dfrac{14}{24}\right):\dfrac{-17}{8}\)

\(=\dfrac{34}{24}\cdot\dfrac{-8}{17}=\dfrac{-1}{3}\cdot2=-\dfrac{2}{3}\)

Câu a:

(4\(\frac{5}{37}\) - 3\(\frac45\) + 8\(\frac{15}{29}\)) - (3\(\frac{5}{37}\) - 6\(\frac{14}{29}\))

= 4\(\frac{5}{37}\) - 3\(\frac45\) + 8\(\frac{15}{29}\) - 3\(\frac{15}{37}\) + 6\(\frac{14}{29}\)

= (4 - 3) + (\(\frac{5}{37}-\frac{5}{37}\)) + (8 + 6) + (\(\frac{15}{29}\) + \(\frac{14}{29}\)) - 3 - \(\frac45\)

= 1 + 0 + 14 + 1 - 3 - \(\frac45\)

= 1 + 14 + 1 - 3 - \(\frac45\)

= 15 + 1 - 3 - \(\frac45\)

= 16 - 3 - \(\frac45\)

= 13 - \(\frac45\)

= \(\frac{61}{5}\)

Bạn Hương có 27 viên bi, bạn Hiền có số bi bằng 1/3 số bi của bạn Hương. Trung bình cộng số bi của hai bạn là bao nhiêu?

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\(\frac{1}{2}+\frac{5}{6}-\frac{3}{8}\)

\(=\frac{12}{24}+\frac{20}{24}-\frac{9}{24}\)

\(=\frac{23}{24}\)

\(\frac{10}{15}\cdot\frac{7}{4}+\frac{7}{4}\cdot\frac{9}{15}-\frac{4}{15}\cdot\frac{7}{4}\)

\(=\frac{7}{4}\cdot\left(\frac{10}{15}+\frac{9}{15}-\frac{4}{15}\right)\)

\(=\frac{7}{4}\cdot1=\frac{7}{4}\)

\(\left(\frac{4}{5}+\frac{1}{2}\right)\left(\frac{3}{13}-\frac{8}{13}\right)\)

\(=\left(\frac{8}{10}+\frac{5}{10}\right)\cdot\left(-\frac{5}{13}\right)\)

\(=\frac{13}{10}\cdot\left(-\frac{5}{13}\right)=-\frac{1}{2}\)

a,  3x-12 = 30 

=> 3x = 30 + 12

=> 3x = 42 

=> x = 42 : 3  = 14 

Vậy x = 14 

b, \(\frac{2}{3}x+\frac{1}{4}=\frac{7}{12}\)

\(\Rightarrow\frac{2}{3}x=\frac{7}{12}-\frac{1}{4}\)

\(\Rightarrow\frac{2}{3}x=\frac{7}{12}-\frac{3}{12}\)

\(\Rightarrow\frac{2}{3}x=\frac{1}{3}\)

\(\Rightarrow x=\frac{1}{3}\div\frac{2}{3}\Rightarrow\frac{1}{3}\cdot\frac{3}{2}=\frac{1}{2}\)

Vậy x = \(\frac{1}{2}\)

c, 2x² = 32 

=> x² = 32 : 2 

=> x² = 16

=> x² = 4² 

=> x = 4 

Vậy x = 4 

Câu a:

A = (1\(\frac16\) x \(\frac67\) x 6 : \(\frac35\)) : (4\(\frac15\) x \(\frac{10}{11}\) + 5\(\frac{2}{10}\))

A = (7/6 x 6/7 x 6 x 5/3) :(21/5 x 10/11 + 52/10)

A = (1 x 6 x 5/3) : (210/55 + 26/5)

A = 10 : (210/55 + 286/55)

A = 10 : (496/55)

A = 10 x 55/496

A = 275/248

Câu b:

B = \(1\)\(\frac{13}{15}\) x 25% x 3 + (8/15 - 79/60) : 1\(\frac{23}{4}\)

B = 28/15 x 1/4 x 3 + (32/60 - 79/60) : 27/4

B = 7/15 x 3 - 47/60 x 4/27

B = 7/5 - 47/405

B = 104/81