a: =-21/36-3/36=-24/36=-2/3

b: =43/12*1/2+5/24=43/24+5/24=2

c: =8/9+1/9=1

e: =1-1/4+1/4-1/7+...+1/97-1/100

=1-1/100=99/100

a)6

b,-7

c)15

d)-4

e)20

a) \(\dfrac{1}{2}\)=\(\dfrac{6}{12}\)       b) \(\dfrac{-7}{8}\)=\(\dfrac{-28}{32}\)      c)\(\dfrac{3}{4}\)=\(\dfrac{15}{20}\)       d) \(\dfrac{-4}{9}\)=\(\dfrac{-16}{36}\)

e) \(\dfrac{3}{4}\)=\(\dfrac{15}{20}\)

HỌC TỐT

Cách 1

\(2\dfrac{3}{4}\)+ \(5\dfrac{7}{9}\)= \(\dfrac{11}{4}+\dfrac{47}{9}\)

= \(\dfrac{99}{36}+\dfrac{188}{36}\)

= \(\dfrac{287}{36}\)= 7,9722...

Cách 2

\(2\dfrac{3}{4}+5\dfrac{7}{8}=2\dfrac{55}{36}+5\dfrac{55}{36}\)

= \(7\dfrac{55}{36}=8\dfrac{19}{36}\)

Cách 1 mình làm nhầm bài đúng phải là

\(2\dfrac{3}{4}+5\dfrac{7}{9}=\dfrac{11}{4}+\dfrac{52}{9}=\dfrac{99}{36}+\dfrac{208}{36}\)

=\(\dfrac{307}{36}\)=8,527777778

a. 7/9 - 16/9 = -9/9 = -1

b. 2/-15 + 7/10 = 17/30

c. (4 2/3 - 4 3/4) : -5/12 - 4/5 

= (14/3 - 19/4) : (-5/12) - 4/5

= -1/12 : (-5/12) - 4/5

= 1/5 - 4/5

= -3/5

a)\(\dfrac{7}{-25}+-\dfrac{8}{25}=-\dfrac{15}{25}=-\dfrac{3}{5}\)
b)\(\dfrac{7}{21}-\dfrac{9}{-36}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}\)
\(=\dfrac{4}{12}+\dfrac{3}{12}=\dfrac{7}{12}\)
c)\(-\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{1}{4}+\dfrac{5}{7}\)
\(=\left(-\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)
\(=-\dfrac{1}{2}+1\)
\(=\dfrac{2}{2}-\dfrac{1}{2}=\dfrac{1}{2}\)

\(a,\dfrac{7}{-25}+\dfrac{-8}{25}=\dfrac{-7}{25}+\dfrac{-8}{25}=\dfrac{-15}{25}=\dfrac{-3}{5}\\ b,\dfrac{7}{21}-\dfrac{9}{-36}=\dfrac{7}{21}+\dfrac{9}{36}=\dfrac{7}{12}\\ c,\dfrac{-3}{4}+\dfrac{2}{7}+\dfrac{1}{4}+\dfrac{5}{7}\\ =\left(\dfrac{-3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\\ =-\dfrac{1}{2}+1\\ =\dfrac{1}{2}\)

c)5/15- (-4/20)-9/36

Rút gọn

=1/3- (-1/5)-1/4

=8/15-1/4

=17/60

d)-2/1/4.(3/5/12-1/2/9)

=-7/4.(41/12-11/9)

=-7/4.2

=7/2

a) \(\dfrac{2}{5}=\dfrac{2\times5}{5\times2}=\dfrac{10}{25}\)

\(\dfrac{4}{7}=\dfrac{4\times2}{7\times2}=\dfrac{8}{14}\)

b) \(\dfrac{36}{40}=\dfrac{36:4}{40:4}=\dfrac{9}{10}\)

\(\dfrac{24}{32}=\dfrac{24:8}{32:8}=\dfrac{3}{4}\)

Bài 1 :

Câu a : \(\sqrt{\dfrac{1,44}{3,61}}=\sqrt{\dfrac{144}{361}}=\dfrac{\sqrt{144}}{\sqrt{361}}=\dfrac{12}{19}\)

Câu b : \(\sqrt{\dfrac{0,25}{9}}=\sqrt{\dfrac{25}{900}}=\dfrac{\sqrt{25}}{\sqrt{900}}=\dfrac{5}{30}=\dfrac{1}{6}\)

Câu c : \(\sqrt{1\dfrac{13}{36}}.\sqrt{3\dfrac{13}{36}}=\sqrt{\dfrac{49}{36}}.\sqrt{\dfrac{121}{46}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{121}}{36}=\dfrac{7}{6}.\dfrac{11}{6}=\dfrac{77}{36}\)

Câu d : \(\sqrt{\dfrac{1}{121}.3\dfrac{6}{25}}=\sqrt{\dfrac{1}{121}.\dfrac{81}{25}}=\dfrac{1}{\sqrt{121}}.\dfrac{\sqrt{81}}{\sqrt{25}}=\dfrac{1}{11}.\dfrac{9}{5}=\dfrac{9}{55}\)

Câu e : \(\sqrt{1\dfrac{13}{36}.2\dfrac{2}{49}.2\dfrac{7}{9}}=\sqrt{\dfrac{49}{36}.\dfrac{100}{49}.\dfrac{25}{9}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{100}}{\sqrt{49}}.\dfrac{\sqrt{25}}{\sqrt{9}}=\dfrac{7}{6}.\dfrac{10}{7}.\dfrac{5}{3}=\dfrac{25}{9}\)

Bài 2 :

Câu a : \(\dfrac{\sqrt{245}}{\sqrt{5}}=\sqrt{\dfrac{245}{5}}=\sqrt{49}=7\)

Câu b : \(\dfrac{\sqrt{3}}{\sqrt{75}}=\sqrt{\dfrac{3}{75}}=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)

Câu c : \(\dfrac{\sqrt{10,8}}{\sqrt{0,3}}=\sqrt{\dfrac{10,8}{0,3}}=\sqrt{\dfrac{108}{3}}=\sqrt{36}=6\)

Câu d : \(\dfrac{\sqrt{6,5}}{\sqrt{58,5}}=\sqrt{\dfrac{6,5}{58,5}}=\sqrt{\dfrac{65}{585}}=\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}\)

Bài 3 :

Câu a : \(\sqrt{\dfrac{61^2-60^2}{81}}=\sqrt{\dfrac{\left(61-60\right)\left(61+60\right)}{81}}=\sqrt{\dfrac{121}{81}}=\dfrac{\sqrt{121}}{81}=\dfrac{11}{9}\)

Câu b : \(\sqrt{\dfrac{74^2-24^2}{121}}=\sqrt{\dfrac{\left(74+24\right)\left(74-24\right)}{121}}=\sqrt{\dfrac{98.50}{121}}=\dfrac{\sqrt{4900}}{\sqrt{121}}=\dfrac{70}{11}\)

Bài 4 :

Câu a : \(9-4\sqrt{x}=1\Leftrightarrow4\sqrt{x}=8\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\)

Câu b : \(\sqrt{\dfrac{x}{5}}=4\Leftrightarrow\dfrac{x}{5}=16\Leftrightarrow x=80\)

Câu c : \(\sqrt{7x}< 9\Leftrightarrow7x< 81\Leftrightarrow x< \dfrac{81}{7}\)