Bài 4:

a; \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) = \(\dfrac{5}{20}\) - \(\dfrac{4}{20}\) = \(\dfrac{1}{20}\)

b; \(\dfrac{3}{5}\) - \(\dfrac{-1}{2}\) = \(\dfrac{6}{10}\) + \(\dfrac{5}{10}\) = \(\dfrac{11}{10}\)

c; \(\dfrac{3}{5}\) - \(\dfrac{-1}{3}\) = \(\dfrac{9}{15}\) + \(\dfrac{5}{15}\) = \(\dfrac{14}{15}\)

d; \(\dfrac{-5}{7}\) - \(\dfrac{1}{3}\)= \(\dfrac{-15}{21}\) - \(\dfrac{7}{21}\)= \(\dfrac{-22}{21}\)

Bài 5

a; 1 + \(\dfrac{3}{4}\) = \(\dfrac{4}{4}\) + \(\dfrac{3}{4}\) = \(\dfrac{7}{4}\)       b; 1 - \(\dfrac{1}{2}\) = \(\dfrac{2}{2}\) - \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\)

c; \(\dfrac{1}{5}\) - 2 = \(\dfrac{1}{5}\) - \(\dfrac{10}{5}\) = \(\dfrac{-9}{5}\)     d; -5 - \(\dfrac{1}{6}\) = \(\dfrac{-30}{6}\) - \(\dfrac{1}{6}\) = \(\dfrac{-31}{6}\)

e; - 3 - \(\dfrac{2}{7}\)= \(\dfrac{-21}{7}\) - \(\dfrac{2}{7}\)= \(\dfrac{-23}{7}\)     f; - 3 + \(\dfrac{2}{5}\) = \(\dfrac{-15}{5}\) + \(\dfrac{2}{5}\)= - \(\dfrac{13}{5}\)

g; - 3 - \(\dfrac{2}{3}\) = \(\dfrac{-9}{3}\) - \(\dfrac{2}{3}\) = \(\dfrac{-11}{3}\)     h; - 4 - \(\dfrac{-5}{7}\) = \(\dfrac{-28}{7}\)+ \(\dfrac{5}{7}\) = - \(\dfrac{23}{7}\)

Bài 6:

a; 2 - (\(\dfrac{-4}{5}\)) = 2 + \(\dfrac{4}{5}\) = \(\dfrac{10}{5}\) + \(\dfrac{4}{5}\) = \(\dfrac{14}{5}\)

b; - 2 + \(\dfrac{-5}{8}\) = \(\dfrac{-16}{8}\) - \(\dfrac{5}{8}\) = \(\dfrac{-21}{8}\)

c; \(\dfrac{3}{-4}\) - (-3) = \(\dfrac{-3}{4}\) + \(\dfrac{12}{4}\) = \(\dfrac{9}{4}\)

d; 6 - (- \(\dfrac{1}{20}\)) = \(\dfrac{120}{20}\) + \(\dfrac{1}{20}\) = \(\dfrac{121}{20}\)

Bài 7:

a; \(\dfrac{5}{12}\) + \(\dfrac{5}{2}\) + \(\dfrac{2}{12}\) + \(\dfrac{2}{3}\)

= (\(\dfrac{5}{12}+\dfrac{2}{12}\)) + (\(\dfrac{5}{3}+\dfrac{2}{3}\))

= \(\dfrac{7}{12}\) + \(\dfrac{7}{3}\)

= \(\dfrac{7}{12}\) + \(\dfrac{28}{12}\)
= \(\dfrac{35}{12}\)

b; -\(\dfrac{5}{8}\) + \(\dfrac{12}{7}\) + \(\dfrac{13}{8}\) + \(\dfrac{2}{7}\)

 = (\(\dfrac{-5}{8}\) + \(\dfrac{13}{8}\)) + (\(\dfrac{12}{7}\) + \(\dfrac{2}{7}\))

= \(\dfrac{8}{8}\) + \(\dfrac{14}{7}\)

= 1 + 2

= 3

c; \(\dfrac{-2}{5}\) + \(\dfrac{3}{8}\) - \(\dfrac{3}{5}\) + \(\dfrac{13}{8}\)

= - (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + (\(\dfrac{3}{8}\) + \(\dfrac{13}{8}\))

= -1 + 2

=  1

Bài 7:

d; \(\dfrac{1}{5}-\dfrac{5}{19}+\dfrac{4}{5}+-\dfrac{14}{19}\)

= (\(\dfrac{1}{5}+\dfrac{4}{5}\)) - (\(\dfrac{5}{19}+\dfrac{14}{19}\))

= 1  - 1

= 0 

e; \(\dfrac{4}{13}\) + \(\dfrac{-11}{5}\) + \(\dfrac{9}{13}\) + \(\dfrac{6}{5}\)

= ( \(\dfrac{4}{13}+\dfrac{9}{13}\)) - (\(\dfrac{11}{5}-\dfrac{6}{5}\))

= 1 - 1

= 0 

f; \(-\dfrac{1}{9}+\dfrac{8}{7}+\dfrac{10}{9}-\dfrac{29}{7}\)

= (-\(\dfrac{1}{9}\) + \(\dfrac{10}{9}\)) + (\(\dfrac{8}{7}-\dfrac{29}{7}\))

= 1 -  3

= -2

Bài 8: a; \(\dfrac{2}{3}+\dfrac{5}{7}+-\dfrac{2}{3}\)

         = (\(\dfrac{2}{3}\) - \(\dfrac{2}{3}\)) + \(\dfrac{5}{7}\)

         =     \(\dfrac{5}{7}\)

b; \(-\dfrac{1}{4}+\dfrac{5}{8}-\dfrac{3}{8}\)

= \(-\dfrac{1}{4}+\left(\dfrac{5}{8}-\dfrac{3}{8}\right)\)

= - \(\dfrac{1}{4}+\dfrac{1}{4}\)

= 0 

Bài 8: 

c; \(\dfrac{-5}{9}\) + \(\dfrac{4}{11}\) + \(\dfrac{7}{11}\) 

       = \(\dfrac{-5}{9}+\left(\dfrac{4}{11}+\dfrac{7}{11}\right)\)

       = - \(\dfrac{5}{9}\) + 1

       = \(\dfrac{4}{9}\)

d; \(-\dfrac{11}{6}+\dfrac{2}{5}-\dfrac{1}{6}\) 

=    -(\(\dfrac{11}{6}+\dfrac{1}{6}\)) + \(\dfrac{2}{5}\)

= -2 + \(\dfrac{2}{5}\)

= \(-\dfrac{8}{5}\)

Bài 9:

a; \(\dfrac{12}{11}--\dfrac{7}{19}+\dfrac{12}{19}\)

= \(\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}\)

= \(\dfrac{12}{11}+\left(\dfrac{7}{19}+\dfrac{12}{19}\right)\)

= \(\dfrac{12}{11}\) + 1

= \(\dfrac{23}{11}\)

b; \(\dfrac{-5}{21}+-\dfrac{2}{21}+\dfrac{8}{24}\)

= -(\(\dfrac{5}{21}+\dfrac{2}{21}\)) + \(\dfrac{1}{3}\)

= - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\)

= 0

c; \(-\dfrac{15}{4}+\dfrac{-6}{17}+\dfrac{15}{4}\)

= (-\(\dfrac{15}{4}+\dfrac{15}{4}\)) + \(\dfrac{-6}{17}\)

= - \(\dfrac{6}{17}\)

Bài 10:

   \(\dfrac{5}{9}\) + (\(\dfrac{-4}{9}\) + 2)

=  (\(\dfrac{5}{9}\) - \(\dfrac{4}{9}\)) + 2

=  \(\dfrac{1}{9}\) + 2

= \(\dfrac{19}{9}\) 

b; \(\dfrac{-5}{11}+\left(\dfrac{-6}{11}+1\right)\)

 = \(\dfrac{-5}{11}\) - \(\dfrac{6}{11}\) + 1

= -(\(\dfrac{5}{11}\) + \(\dfrac{6}{11}\)) + 1

= - 1 + 1

= 0

c; \(\dfrac{-6}{13}+\left(1+\dfrac{-7}{13}\right)\)

= \(-\dfrac{6}{13}+1-\dfrac{7}{13}\)

= -(\(\dfrac{6}{13}+\dfrac{7}{13}\)) + 1

= -1 + 1

= 0 

d; (\(\dfrac{3}{5}\) + \(\dfrac{-2}{7}\)) + \(-\dfrac{1}{5}\)

= (\(\dfrac{3}{5}-\dfrac{1}{5}\)) - \(\dfrac{2}{7}\)

= \(\dfrac{2}{5}-\dfrac{2}{7}\)

= \(\dfrac{4}{35}\)

e; (\(\dfrac{-2}{-5}\) + \(\dfrac{-5}{-6}\)) + \(\dfrac{4}{5}\)

= \(\dfrac{2}{5}\) + \(\dfrac{5}{6}\) + \(\dfrac{4}{5}\)

= (\(\dfrac{2}{5}+\dfrac{4}{5}\)) + \(\dfrac{5}{6}\)

= \(\dfrac{6}{5}\) + \(\dfrac{5}{6}\)

= \(\dfrac{61}{30}\)

f; \(\dfrac{14}{13}\) + (\(-\dfrac{1}{13}\) - \(\dfrac{19}{20}\))

= \(\dfrac{14}{13}-\dfrac{1}{13}\) - \(\dfrac{19}{20}\)

= (\(\dfrac{14}{13}\) - \(\dfrac{1}{13}\)) - \(\dfrac{19}{20}\)

= 1 - \(\dfrac{19}{20}\)

= \(\dfrac{1}{20}\)

Bài 11

a; \(\dfrac{-2}{49}\) - (\(\dfrac{47}{49}\) + \(\dfrac{5}{-3}\))

= \(-\dfrac{2}{49}\) - \(\dfrac{47}{49}\) + \(\dfrac{5}{3}\)

= - (\(\dfrac{2}{49}\) + \(\dfrac{47}{49}\)) + \(\dfrac{5}{3}\)

= - 1 + \(\dfrac{5}{3}\)

= \(\dfrac{2}{3}\)

b; \(\dfrac{-24}{17}\) - (\(\dfrac{-7}{17}-\dfrac{1}{16}\))

= - \(\dfrac{24}{17}\) + \(\dfrac{7}{17}\) + \(\dfrac{1}{16}\)

= - (\(\dfrac{24}{17}\) - \(\dfrac{7}{17}\)) + \(\dfrac{1}{16}\)

= - 1 + \(\dfrac{1}{16}\)

= \(-\dfrac{15}{16}\)

Bài 11

c; \(\dfrac{7}{-18}+\left(\dfrac{-5}{12}-\dfrac{13}{-18}\right)\)

= - \(\dfrac{7}{18}-\dfrac{5}{12}+\dfrac{13}{18}\)

=  (\(\dfrac{13}{18}-\dfrac{7}{18}\)) - \(\dfrac{5}{12}\)

= \(\dfrac{1}{3}\) - \(\dfrac{5}{12}\)

= \(-\dfrac{1}{12}\)

d; - \(\dfrac{13}{17}+\left(\dfrac{13}{-21}+\dfrac{-4}{17}\right)\)

=   - \(\dfrac{13}{17}\) - \(\dfrac{13}{21}-\dfrac{4}{17}\)

= - (\(\dfrac{13}{17}+\dfrac{4}{17}\)) - \(\dfrac{13}{21}\)

= - 1 - \(\dfrac{13}{21}\)

= - \(\dfrac{34}{21}\)

Bài 11

e; (\(\dfrac{13}{-10}-\dfrac{-4}{13})+\dfrac{11}{-10}\)

= - \(\dfrac{13}{10}\) + \(\dfrac{4}{13}\) - \(\dfrac{11}{10}\)

= - (\(\dfrac{13}{10}+\dfrac{11}{10}\)) + \(\dfrac{4}{13}\)

= - \(\dfrac{12}{5}\) + \(\dfrac{4}{13}\)

= - \(\dfrac{136}{65}\)

Cô Hoài giải nhiều quá ạ, nghỉ ngơi đi cô ơi.

Bài 12:

a; \(-\dfrac{3}{4}\) + \(\dfrac{2}{7}\) - \(\dfrac{1}{4}\) + \(\dfrac{3}{5}\) + \(\dfrac{5}{7}\)

= - (\(\dfrac{3}{4}\) + \(\dfrac{1}{4}\)) + (\(\dfrac{2}{7}\)+ \(\dfrac{5}{7}\)) + \(\dfrac{3}{5}\)

= -1 + 1 + \(\dfrac{3}{5}\)

= \(\dfrac{3}{5}\)

b; \(\dfrac{-2}{5}+\dfrac{3}{-4}+\dfrac{6}{7}+\dfrac{3}{4}+\dfrac{2}{5}\)

= (\(-\dfrac{2}{5}+\dfrac{2}{5}\)) + (-\(\dfrac{3}{4}+\dfrac{3}{4}\)) + \(\dfrac{6}{7}\)

= 0 + 0 + \(\dfrac{6}{7}\)

= \(\dfrac{6}{7}\)

c; \(-\dfrac{1}{8}+\dfrac{7}{9}+\dfrac{-7}{9}+\dfrac{6}{7}+\dfrac{2}{14}\)

= - \(\dfrac{1}{8}\) + (\(\dfrac{7}{9}\) - \(\dfrac{7}{9}\)) + (\(\dfrac{6}{7}\) + \(\dfrac{2}{14}\))

= - \(\dfrac{1}{8}\) + 0 + (\(\dfrac{6}{7}\) + \(\dfrac{1}{7}\))

= -  \(\dfrac{1}{8}\) + 1

= \(\dfrac{7}{8}\)

Bài 13:

a; A = \(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\)

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\)

A = \(\dfrac{1}{3}-\dfrac{1}{9}\)

A =  \(\dfrac{2}{9}\)

Bài 13

B = \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{24.25}\)

B = \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{24}-\dfrac{1}{25}\)

B = \(\dfrac{1}{5}-\dfrac{1}{25}\)

B = \(\dfrac{4}{25}\)

Bài 13

C = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

C = \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

C = \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\)

C = \(\dfrac{99}{100}\)

Bài 13

D  = \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)

D = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\)

D = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)

D = \(\dfrac{1}{1}\) - \(\dfrac{1}{6}\)

D = \(\dfrac{5}{6}\)

Bài 14:

A = \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{97.99}+\dfrac{2}{99.101}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + ... + \(\dfrac{1}{97}\) - \(\dfrac{1}{99}\) + \(\dfrac{1}{99}\) - \(\dfrac{1}{101}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{101}\)

A = \(\dfrac{100}{101}\)

Bài 14

B = \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\) + ...+ \(\dfrac{2}{46.48}\) + \(\dfrac{2}{48.50}\)

B  =  \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) -  \(\dfrac{1}{6}\) + ... + \(\dfrac{1}{46}\) - \(\dfrac{1}{48}\) +  \(\dfrac{1}{48}-\dfrac{1}{50}\)

B = \(\dfrac{1}{2}\) - \(\dfrac{1}{50}\)

B = \(\dfrac{12}{25}\)

lớp 5 à