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Hôm nay olm.vn sẽ hướng dẫn các em giải dạng toán nâng cao cấu trúc thi hsg, violympic  tính nhanh tổng các phân số mà tử số bằng tổng hai thừa số dưới mẫu:

Kiến thức cần nhớ:  \(\dfrac{a}{b.c}\)  trong đó a = b + c

+ Tách từng phân số thanh tổng hai phân số :

 \(\dfrac{a}{b.c}\) = \(\dfrac{b+c}{b.c}\) = \(\dfrac{1}{b}+\dfrac{1}{c}\)

+ Triệt tiêu các hạng tử giống nhau.

+ Thu gọn ta được tổng cần tính                               

  \(\dfrac{2}{6}+\dfrac{9}{20}-\dfrac{11}{30}+\dfrac{13}{42}-\dfrac{15}{56}+\dfrac{17}{72}-\dfrac{19}{90}+\dfrac{21}{110}-\dfrac{23}{132}\)

=\(\dfrac{1}{3}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{5}\)-(\(\dfrac{1}{5}+\dfrac{1}{6}\))+\(\dfrac{1}{6}\)+\(\dfrac{1}{7}\)-(\(\dfrac{1}{7}\)+\(\dfrac{1}{8}\))+\(\dfrac{1}{8}\) +\(\dfrac{1}{9}\)-(\(\dfrac{1}{9}\)+\(\dfrac{1}{10}\))+\(\dfrac{1}{10}\)+\(\dfrac{1}{11}\)-(\(\dfrac{1}{11}\)+\(\dfrac{1}{12}\))

= \(\dfrac{1}{3}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)+\(\dfrac{1}{10}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{11}\)-\(\dfrac{1}{12}\)

= \(\dfrac{1}{3}\)+\(\dfrac{1}{4}\) - \(\dfrac{1}{12}\)

= \(\dfrac{4}{12}+\dfrac{3}{12}-\dfrac{1}{12}\)

= \(\dfrac{1}{2}\)

A = 1 - \(\dfrac{5}{6}\)+\(\dfrac{7}{12}\)-\(\dfrac{9}{20}\)+\(\dfrac{11}{30}\)-\(\dfrac{13}{42}\)+\(\dfrac{15}{56}\) - \(\dfrac{17}{72}\)+\(\dfrac{19}{90}\)+\(\dfrac{23}{132}\)-\(\dfrac{25}{156}\)

A = 1 - \(\dfrac{5}{2.3}\)+\(\dfrac{7}{3.4}\)-\(\dfrac{9}{4.5}\)+\(\dfrac{11}{5.6}\)-\(\dfrac{13}{6.7}\)+\(\dfrac{15}{7.8}\)-\(\dfrac{17}{8.9}\)+\(\dfrac{19}{9.10}\)+\(\dfrac{23}{11.12}\)-\(\dfrac{25}{12.13}\)

A = 1 - \(\dfrac{1}{2}-\dfrac{1}{3}\)+\(\dfrac{1}{3}+\dfrac{1}{4}\)-\(\dfrac{1}{4}-\dfrac{1}{5}\)+...+\(\dfrac{1}{11}+\dfrac{1}{12}\)- \(\dfrac{1}{12}-\dfrac{1}{13}\)

A = 1 - \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\) 

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{11}{26}\) 

a. (+18) + (+2)= 20

b. (-3)+13= 11

c. (-12)+(-21)=-33

d. (-30)+(-23)=-53

e. -52+102=50

f. 88+(-23)=65

g. 13+|-13|=26

h. -43-26=-69

k. (-89)-9=-98

m. -56+|-32|=-24

n. 40 -|-14|=26

o. |-4|+|+15|=19

p. |30|-|-17|=13

1

a) \(\frac{14}{7}+\frac{5}{9}+\frac{4}{9}-2\)

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

\(=3-2=1\)

b) \(\frac{31}{25}+\left(\frac{15}{16}-\frac{6}{15}\right)+\frac{1}{16}\)

\(=\frac{31}{25}+\frac{43}{80}+\frac{1}{16}\)

\(=1\frac{311}{400}+\frac{1}{16}\)

\(=1\frac{21}{25}\)

Sr, câu 2   2/3   là    1/16

cau 4 kho the

9 x 9 = 81

3 x 12 = 36

56 x 23 = 1288

764 x 23 = 17664

9 x 9 = 81

 3 x 12 = 36

56 x 23 = 1288

764 x 23 = 17572

9 x 9 = 81

3 x 12 = 36

56 x 23 = 1288

764 x 23 = 17572

mik nhah nhất

k mik nha