Các dạng bài tập cơ bản về phân số

 

Bài 1.     Tính:

a)  A = \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}

b) B=\displaystyle 6\frac{2}{3}+7\frac{5}{8}+3\frac{1}{3}-4\frac{5}{8}

b) C =\displaystyle \left( 4\frac{2}{5}+2\frac{3}{7} \right)-\left( 2\frac{2}{5}-1\frac{4}{7} \right)

c) D =\displaystyle \frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}

d) E=\displaystyle \,\,\frac{6}{7}+\frac{1}{7}\times \frac{2}{7}+\frac{1}{7}\times \frac{5}{7}

e) F=\displaystyle 1\frac{4}{5}+\frac{1}{5}\times \frac{1}{5}+\frac{1}{5}\times \frac{4}{5}

Bài 2.     Tìm số x, biết:

a)  \displaystyle \frac{x}{15}=\frac{2}{5} ..

b) \displaystyle \frac{3}{x-7}=\frac{27}{135}

c)  \displaystyle x-(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63})=\frac{1}{9}

d) \displaystyle 9=\left( \frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{5}{6}+\frac{7}{12} \right)\times \frac{3}{10}+x

Bài 3.     Tính nhanh giá trị các biểu thức sau:

a)  A =\displaystyle 5\frac{3}{5}+1\frac{3}{4}+6\frac{1}{8}+4\frac{1}{4}+3\frac{7}{8}+3\frac{2}{5}

b) B =\displaystyle \frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}

c)  C =\displaystyle 4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}

d) D =\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}

e) E =\displaystyle \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}

f)  \displaystyle F=\frac{1}{1000}+\frac{13}{1000}+\frac{25}{1000}+\frac{37}{1000}+\frac{49}{1000}+\frac{51}{1000}+\frac{63}{1000}+\frac{75}{1000}+\frac{87}{1000}+\frac{99}{1000}

Bài 4. Tìm số x theo cách nhanh nhất:

a)              \displaystyle x : 25 = 100 : 250

b)             \displaystyle x\times \frac{2}{3}-\frac{2}{3}+\frac{3}{4}=\frac{9}{12}

c)              \displaystyle x+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}=2

d)             \displaystyle \frac{3}{4}:x+\frac{1}{2}:\frac{1}{4}=4………………

Bài 5. Sắp xếp các số sau theo thứ tự từ bé đến lớn

a)  (1) \displaystyle \frac{7}{2}       (2) \displaystyle \frac{6}{15}        (3) \displaystyle \frac{3}{5}          (4) \displaystyle \frac{9}{4}       (5) \displaystyle \frac{3}{4}

……………………………………………………………………………………..

b)  (1)\displaystyle \frac{2009}{2010}  (2) \displaystyle \frac{2010}{2011}   (3) \displaystyle \frac{2011}{2012}     (4) \displaystyle \frac{2012}{2013}      (5) \displaystyle \frac{2013}{2014}

………………………………………………………………..

c)  (1) \displaystyle \frac{33}{47}          (2) \displaystyle \frac{40}{54}         (3) \displaystyle \frac{15}{17}             (4)\displaystyle \frac{1}{2}           (5) \displaystyle \frac{13}{18}

………………………………………………………………….

d)  (1) \displaystyle \frac{96}{10}   (2) \displaystyle \frac{9599}{1000}   (3) \displaystyle \frac{9573}{1000}         (4) \displaystyle \frac{965}{100}    (5) \displaystyle \frac{59}{8}

Bài 6.     Thực hiện phép tính:

a) A=\displaystyle \frac{7}{8}:\left( \frac{14}{3}+\frac{7}{2} \right)+\frac{4}{28} = ………………………………………………………………….

b) B = \displaystyle \left( 6-\frac{14}{5} \right)\times \frac{25}{8}+\frac{18}{5}:\frac{1}{20}= ……………………………………………………………….

c)  C = \displaystyle C=\frac{175}{100}+\frac{18}{21}+\frac{13}{32}+1\frac{1}{4}+\frac{1}{7}-\frac{45}{32}=

d) D=\displaystyle \frac{1+3+5+......+19}{21+23+25+....+39}

Bài 7.     Tính giá trị biểu thức:

a)  A=\displaystyle \frac{198:2\times 4444\times 2\times 132:25}{33\times 8888:5\times 66:125\times 5} =

b)  B=\displaystyle \frac{1248:5\times 625\times 4\times 2}{2\times 312\times 125:25\times 10}

c)  C=\displaystyle 1\frac{1}{24}\times 5\frac{2}{5}\times 2\times 3\frac{7}{9}\times 2\frac{2}{17}

d)  D =\displaystyle 1\frac{6}{17}\times 4\frac{3}{9}\times \frac{35}{46}:\frac{49}{14}\times 3\frac{12}{13}:10 =

e)  E =\displaystyle 4\frac{2}{5}\times \frac{6}{121}\times 2\frac{3}{4}\times \frac{3}{5}\times \frac{1}{3}\times 1\frac{1}{4}

Bài 8.  Tính giá trị của biểu thức:

a)  A=\displaystyle 2\frac{3}{13}\times \frac{13}{58}\times 8\times 2\frac{15}{24}\times \frac{8}{21}

b) B=\displaystyle \frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times ..........\times \frac{120}{121}

c)  C=\displaystyle (\frac{1}{2}+1 )\times ( \frac{1}{3}+1 )\times ( \frac{1}{4}+1 )\times .....\times ( \frac{1}{99}+1)

d) D=\displaystyle ( 1-\frac{1}{2} )\times ( 1-\frac{1}{3} )\times ( 1-\frac{1}{4} )\times .....\times ( 1-\frac{1}{100} )

Bài 9.     Tìm số x, biết:

a)  \displaystyle x:3\frac{1}{15}-\frac{3}{4}=2\frac{1}{4}

b) (\displaystyle 7\frac{1}{2}\times 8\frac{3}{70}+8\frac{3}{70}\times 2\frac{1}{4}+4\frac{3}{4}\times 8\frac{3}{70}+5\frac{1}{2}\times 8\frac{3}{70}) : x =1126

c)  \displaystyle \frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{(x-1)\times x}=\frac{15}{16}

d) x \times 3\displaystyle \frac{2}{3} – 1\displaystyle \frac{2}{3} = 2\displaystyle \frac{1}{3}

e)  \displaystyle \frac{3}{2}x-70\frac{10}{11}:\left( \frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999} \right)=5

f)   \left( \frac{242}{363}+\frac{1616}{2121} \right)=\frac{2}{7}\times x

Bài 10.           So sánh A và B, biết:

a)  A=\displaystyle \frac{1+3+5+7+...+99}{50}B =\displaystyle \frac{2+4+...+98}{49}

b)  A=\displaystyle \frac{3192}{3178}B =\displaystyle \frac{2497}{2486}

c)  A =\displaystyle \frac{1999\times 2000-2}{1998\times 1999+3997} và B =1

d) A = \displaystyle \frac{54.107-53}{53.107+54} và  B =\displaystyle \frac{135.269-133}{134.269+135}

e)  A =\displaystyle \frac{2003.2004-1}{2003.2004} và  B =\displaystyle \frac{2004.2005-1}{2004.2005}

Bài 11.        Tính giá trị của các biểu thức sau:

a)   A =\displaystyle \frac{1\times 3\times 5\,\,\,+\,\,\,2\times 6\times 10\,\,\,+\,\,\,3\times 9\times 15}{3\times 5\times 12\,\,+\,\,\,6\times 10\times 24\,\,\,+\,\,\,9\times 15\times 36}

b)  B =<b> </b>1 +\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}

c)  C =\displaystyle \frac{2001\times 2002-1}{4000\times 2002+4002}

Bài 12.       Tính giá trị của biểu thức:

a)  A =\displaystyle \frac{13}{14}\times 4\frac{1}{4}\times 3\frac{11}{15}\times 1\frac{31}{39}\times \frac{21}{34}\times \frac{25}{49}

b)  B =\displaystyle \frac{45}{62}\times 2\frac{11}{14}\times \frac{49}{90}\times 6\frac{1}{4}\times 4\frac{12}{15}\times \frac{31}{91}

c)  C =\displaystyle 2\frac{7}{15}\times 7\frac{2}{9}\times \frac{35}{111}\times \frac{1}{39}\times \frac{27}{91}\times 5\frac{1}{5}

d)  D =\displaystyle \frac{120}{141}\times 3\frac{47}{201}\times \frac{67}{180}\times 16\frac{23}{25}\times \frac{80}{975}\times \frac{5}{16}

Bài 13.        Tìm số x, biết:

a)   \displaystyle \frac{4}{3}+(x+3)\times 2-\frac{1}{2}=9\frac{1}{2}+4

b) \displaystyle \left( \frac{2}{11\times 13}+\frac{2}{13\times 15}+\frac{2}{15\times 17}+\frac{2}{17\times 19}+\frac{2}{19\times 21} \right)\times 462-x=19

c) \displaystyle \frac{1+3+5+...+99}{2+4+...+98+x}=1

Bài 14.       So sánh A và B, biết:

a)  \displaystyle A=\frac{864\times 48-432\times 96}{48+96+192+...+3072}B =\displaystyle \frac{1}{1000}

b) \displaystyle A=\frac{1978\times 1979+1980\times 21+1958}{1980\times 1979-1978\times 1979}B = 1000

Bài 15.    Tìm số x, biết:

a)    \displaystyle \left( \frac{1}{2}+\frac{1}{3}+\frac{1}{4} \right)\times x=1+\frac{2}{3}+\frac{1}{2}

b)   \displaystyle \left( \frac{1}{2}+\frac{1}{3}-\frac{1}{4} \right):x=\left( \frac{1}{6}+\frac{1}{9}-\frac{1}{12} \right)

c)    \displaystyle \left( \frac{4}{7}+\frac{2}{3} \right):\left( x+\frac{1}{2} \right)=1\frac{1}{7}+1\frac{1}{3}

d)   \displaystyle \frac{3}{5}+\frac{2}{7}:x=1

e)    \displaystyle \frac{6}{5}-x:\frac{1}{2}=\frac{1}{2}

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