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Trần Khánh Ngọc

Bài 3 Tính nhanh 

a, 4/7 + 3/4 + 2/7+5/4 +1/7

b, 5/2 +6/11 + 3/8 + 7/2 + 6/8 + 5/11

c, 4/3 - 3/5 + -20/3 - 2/5 + 2/3

d, 5/12 + 5/3 - 2/12 - 2/3

e, 1/28 + -1/14 + 3/28 + 1/7 + -5/28 + 3/14 + -1/4

 



Võ Ngọc Phương
14 tháng 2 lúc 20:59

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

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

\(=1+2=3\)

b, \(\dfrac{5}{2}+\dfrac{6}{11}+\dfrac{3}{8}+\dfrac{7}{2}+\dfrac{6}{8}+\dfrac{5}{11}\)

\(=\left(\dfrac{5}{2}+\dfrac{7}{2}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)+\left(\dfrac{3}{8}+\dfrac{6}{8}\right)\)

\(=6+1+\dfrac{9}{8}\)

\(=7+\dfrac{9}{8}=\dfrac{65}{8}\)

c, \(\dfrac{4}{3}-\dfrac{3}{5}+\dfrac{-20}{3}-\dfrac{2}{5}+\dfrac{2}{3}\)

\(=\left(\dfrac{4}{3}+\dfrac{-20}{3}+\dfrac{2}{3}\right)+\left(\dfrac{-3}{5}-\dfrac{2}{5}\right)\)

\(=\dfrac{-14}{3}+\left(-1\right)=\dfrac{-17}{3}\)

d, \(\dfrac{5}{12}+\dfrac{5}{3}-\dfrac{2}{12}-\dfrac{2}{3}\)

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

\(=\dfrac{1}{4}+1=\dfrac{5}{4}\)

e, \(\dfrac{1}{28}+\dfrac{-1}{14}+\dfrac{3}{28}+\dfrac{1}{7}+\dfrac{-5}{28}+\dfrac{3}{14}+\dfrac{-1}{4}\)

\(=\left(\dfrac{1}{28}+\dfrac{3}{28}+\dfrac{-5}{28}\right)+\left(\dfrac{-1}{14}+\dfrac{3}{14}\right)+\dfrac{1}{7}+\dfrac{-1}{4}\)

\(=-\dfrac{1}{28}+\dfrac{1}{7}+\dfrac{1}{7}+-\dfrac{1}{4}\)

\(=\dfrac{-1}{28}+\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{-1}{4}\right)\)

\(=\dfrac{-1}{28}+\dfrac{1}{28}=0\)

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

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

\(=1+2=3\)

b: \(\dfrac{5}{2}+\dfrac{6}{11}+\dfrac{3}{8}+\dfrac{7}{2}+\dfrac{6}{8}+\dfrac{5}{11}\)

\(=\left(\dfrac{5}{2}+\dfrac{7}{2}\right)+\left(\dfrac{3}{8}+\dfrac{6}{8}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\)

\(=\dfrac{12}{2}+\dfrac{9}{8}+\dfrac{11}{11}\)

\(=6+1+\dfrac{9}{8}=7+\dfrac{9}{8}=\dfrac{7\cdot8+9}{8}=\dfrac{65}{8}\)

c: \(\dfrac{4}{3}-\dfrac{3}{5}+\dfrac{-20}{3}-\dfrac{2}{5}+\dfrac{2}{3}\)

\(=\left(\dfrac{4}{3}-\dfrac{20}{3}+\dfrac{2}{3}\right)+\left(-\dfrac{3}{5}-\dfrac{2}{5}\right)\)

\(=\dfrac{-14}{3}+\dfrac{-5}{5}=\dfrac{-14}{3}-1=-\dfrac{17}{3}\)

d: \(\dfrac{5}{12}+\dfrac{5}{3}-\dfrac{2}{12}-\dfrac{2}{3}\)

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

\(=\dfrac{3}{3}+\dfrac{3}{12}=1+\dfrac{3}{12}=\dfrac{15}{12}=\dfrac{5}{4}\)

e: \(\dfrac{1}{28}+\dfrac{-1}{14}+\dfrac{3}{28}+\dfrac{1}{7}+\dfrac{-5}{28}+\dfrac{3}{14}+\dfrac{-1}{4}\)

\(=\left(\dfrac{1}{28}+\dfrac{3}{28}-\dfrac{5}{28}\right)+\left(-\dfrac{1}{14}+\dfrac{3}{14}\right)+\left(\dfrac{1}{7}-\dfrac{1}{4}\right)\)

\(=\dfrac{-1}{28}+\dfrac{2}{14}+\dfrac{1}{7}-\dfrac{1}{4}\)

\(=\dfrac{-1+4+4-7}{28}=0\)


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