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đặt bt trên là A
\(\frac{1}{2}\)A=\(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\)
\(\frac{1}{2}\)A=\(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-....+\frac{1}{87}-\frac{1}{90}\)
\(\frac{1}{2}A=\frac{1}{15}-\frac{1}{90}\)
..... tự tính nhé
B=5/18*21+5/21*24+5/24*27+...+5/123*126
3/5B=3/5(5/18*21+5/21*24+...+5/123*126)
3/5B=3/5*5/18*21+3/5*5/21*24+...+3/5*5/123*126
3/5B=3/18*21+3/21*24+...+3/123*126
3/5B=1/18-1/21+1/21-1/24+...+1/123-1/126
3/5B=1/18-1/126
3/5B=126/2268-18/2268
3/5B=108/2268
3/5B=21
B=21÷3/5
B=21*5/3
B=35
a) A = 1/3 - 1/7 + 1/7 - 1/11 +......+1/107 - 1/111
A = 1/3 - 1/111
A = ..............Bạn tự tính nhé!
b) B = 2.(3/15.18 + 3/18.21 +........+3/87.90)
B = 2.(1/15 - 1/18 + 1/18 - 1/21 +........+1/87 - 1/90)
B = 2.(1/15 - 1/90)
B = 2.5/90
B =......Tự tính nhé!
C ; D làm tương tự nhé!
\(A=2\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+......+\frac{1}{87}-\frac{1}{90}\right)\)
\(\Rightarrow A=2\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(\Rightarrow A=2.\frac{1}{18}=\frac{1}{9}\)
\(A=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
\(=6.\frac{1}{3}.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(=2.\frac{1}{18}\)
\(=\frac{1}{9}\)
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{5.7}+...+\frac{2}{15.16}\)
\(=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(=2.\frac{3}{16}\)
\(=\frac{3}{8}\)
\(\dfrac{7}{21}+\dfrac{-9}{36}=\dfrac{1}{3}+\dfrac{-1}{4}=\dfrac{4}{12}+\dfrac{-3}{12}=\dfrac{1}{12}\)
\(\dfrac{-12}{18}+\dfrac{-21}{35}=\dfrac{-2}{3}+\dfrac{-3}{5}=\dfrac{-10}{15}+\dfrac{-9}{15}=\dfrac{-19}{15}\)
\(\dfrac{-18}{14}+\dfrac{15}{-21}=\dfrac{-9}{7}+\dfrac{-5}{7}=\dfrac{-14}{7}=-2\)
\(\dfrac{3}{21}+\dfrac{-6}{42}=\dfrac{1}{7}+\dfrac{-1}{7}=0\)
Tính các tổng dưới đây sau khi đã rút gọn phân số :
a)\(\dfrac{7}{21}\) + \(\dfrac{9}{-36}\) = \(\dfrac{7}{21}\)+\(\dfrac{-9}{36}\)=\(\dfrac{1}{3}\)+\(\dfrac{-1}{4}\)=\(\dfrac{4}{12}\)+\(\dfrac{-3}{12}\)=\(\dfrac{1}{12}\)
b) \(\dfrac{-12}{18}\)+\(\dfrac{-21}{35}\)=\(\dfrac{-2}{3}\)+\(\dfrac{-3}{5}\)=\(\dfrac{-10}{15}\)+\(\dfrac{-9}{15}\)=\(\dfrac{-19}{15}\)
c) \(\dfrac{-3}{21}\)+\(\dfrac{6}{42}\)=\(\dfrac{-1}{7}\)+\(\dfrac{1}{7}\)=0
d) \(\dfrac{-18}{24}\)+\(\dfrac{15}{-21}\)=\(\dfrac{-18}{24}\)+\(\dfrac{-15}{21}\)=\(\dfrac{-3}{4}\)+\(\dfrac{-5}{7}\)=\(\dfrac{-21}{28}\)+\(\dfrac{-20}{28}\)=\(\dfrac{-41}{28}\)
a) `6/18+ (-14)/21 = 1/3 - 2/3=-1/3`
b) `3/5 - (-1/2) = 3/5+1/2=11/10`
c) `2/7 : 3/4 = 2/7 . 4/3 = 8/21`
d) `(-28)/33 . (-3)/4 = 28/33 . 3/4=7/11`
a) \(\dfrac{6}{18}+\dfrac{-14}{21}=\dfrac{1}{3}-\dfrac{2}{3}=\dfrac{-1}{3}\)
b) \(\dfrac{3}{5}-\dfrac{-1}{2}=\dfrac{3}{5}+\dfrac{1}{2}=\dfrac{6}{10}+\dfrac{5}{10}=\dfrac{11}{10}\)
c) \(\dfrac{2}{7}:\dfrac{3}{4}=\dfrac{2}{7}\cdot\dfrac{4}{3}=\dfrac{8}{21}\)
d) \(\dfrac{-28}{33}\cdot\dfrac{-3}{4}=\dfrac{28}{4}\cdot\dfrac{3}{33}=7\cdot\dfrac{1}{11}=\dfrac{7}{11}\)
Theo đề bài, ta có:
A = \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\)
A = \(2.\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90}\right)\)
A =\(2.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
A = \(2.\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)= \(\dfrac{1}{8}\)
A= \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+...+\dfrac{6}{87.90}\)
A= \(2\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+...+\dfrac{3}{87.90}\right)\)
A= \(2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
A= \(2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)
A= 2. \(\dfrac{1}{16}\)
A= \(\dfrac{1}{8}\)