Bài 1. Thực hiện phép tính (Tính hợp lý nếu có thể):
a)1+1/5+8/7+4/5+6/7
b)5/7+7/13+19/13+6/5+9/7+9/5
c)15/16-3/8+9/16+7/8
Bài 2. Thực hiện phép tính:
a) 25/18 -7/5- 7/18+ 2/5
b) 31/19- 5 /11+33 /16+7 /19-6/11- 1 /16
c) (17 /12+9/7)- (8 /7 -7/12)
Bài 3. Tính giá trị biểu thức:
a) A= 1 /1×2 + 1 /2×3 + 1/ 3×4 + 1/ 4×5 + 1/ 5×6
b) B = 3 /2×5 + 3/ 5×8 + 3/ 8×11 + 3/ 11×14
Bài 4. Tính giá trị biểu thức:
a) 2000 /2001 × 2002/ 2003 × 2001/ 2002 × 2003 /2004 × 2006/ 2000
b) 2003 ×1999−2003×999 /2004×999+1004
Bài 3:
a: \(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=1-\dfrac{1}{6}=\dfrac{5}{6}\)
b: \(B=\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}\)
\(=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\)
\(=\dfrac{1}{2}-\dfrac{1}{14}=\dfrac{12}{28}=\dfrac{3}{7}\)
bài 4:
a: \(\dfrac{2000}{2001}\cdot\dfrac{2002}{2003}\cdot\dfrac{2001}{2002}\cdot\dfrac{2003}{2004}\cdot\dfrac{2006}{2000}\)
\(=\dfrac{2000}{2000}\cdot\dfrac{2001}{2001}\cdot\dfrac{2002}{2002}\cdot\dfrac{2003}{2003}\cdot\dfrac{2006}{2004}\)
\(=\dfrac{2006}{2004}=\dfrac{1003}{1002}\)
b: \(\dfrac{2003\cdot1999-2003\cdot999}{2004\cdot999+1004}\)
\(=\dfrac{2003\left(1999-999\right)}{999\left(1004+1000\right)+1004}\)
\(=\dfrac{2003\cdot1000}{1004\left(999+1\right)+1000\cdot999}\)
\(=\dfrac{2003\cdot1000}{999\cdot1000+1004\cdot1000}\)
\(=\dfrac{1000\cdot2003}{1000\left(1004+999\right)}=1\)
BÀI 1:
CÂU A:
\(1+\dfrac{1}{5}+\dfrac{8}{7}+\dfrac{4}{5}+\dfrac{6}{7}\\ =\left(\dfrac{6}{7}+\dfrac{8}{7}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+1\\ =2+1+1=4\)
CÂU B:
\(\dfrac{5}{7}+\dfrac{7}{13}+\dfrac{19}{13}+\dfrac{6}{5}+\dfrac{9}{7}+\dfrac{9}{5}\\ =\left(\dfrac{5}{7}+\dfrac{9}{7}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)+\left(\dfrac{6}{5}+\dfrac{9}{5}\right)\\ =2+2+3=7\)
CÂU C:
\(\dfrac{15}{16}-\dfrac{3}{8}+\dfrac{9}{16}+\dfrac{7}{8}\\ =\left(\dfrac{15}{16}+\dfrac{9}{16}\right)+\left(\dfrac{7}{8}-\dfrac{3}{8}\right)\\ =1,5+0,5=2\)
BÀI 2:
\(a.\dfrac{25}{18}-\dfrac{7}{5}-\dfrac{7}{18}+\dfrac{2}{5}\\ =\left(\dfrac{25}{18}-\dfrac{7}{18}\right)-\left(\dfrac{7}{5}-\dfrac{2}{5}\right)\\ =1-1=0\\ b.\dfrac{31}{19}-\dfrac{5}{11}+\dfrac{33}{16}+\dfrac{7}{19}-\dfrac{6}{11}-\dfrac{1}{16}\\ =\left(\dfrac{31}{19}+\dfrac{7}{19}\right)-\left(\dfrac{5}{11}+\dfrac{6}{11}\right)+\left(\dfrac{33}{16}-\dfrac{1}{16}\right)\\ =2-1+2=3\\ c.\left(\dfrac{17}{12}+\dfrac{9}{7}\right)-\left(\dfrac{8}{7}-\dfrac{7}{12}\right)\\ =\dfrac{17}{12}+\dfrac{9}{7}-\dfrac{8}{7}+\dfrac{7}{12}\\ =\left(\dfrac{17}{12}+\dfrac{7}{12}\right)+\left(\dfrac{9}{7}-\dfrac{8}{7}\right)\\ =2+\dfrac{1}{7}=\dfrac{15}{7}\)
