tính bằng cách thuận tiện nhất:
7/11 : 3/5 + 4/11 : 3/5
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`a) 5 / 13 xx 4 / 15 xx 13 = [ 5 xx 4 xx 13 ] / [ 13 xx 5 xx 3 ] = 4 / 3`
`b) ( 3 / 7 + 5 / 2 ) xx 7 / 5 = 3 / 7 xx 7 / 5 + 5 / 2 xx 7 / 5 = 3 / 5 + 7 / 2 = 6 / 10 + 35 / 10 = 41 / 10`
`c) 1 / 5 xx 11 / 18 + 11 / 18 xx 3 / 5 = 11 / 18 xx ( 1 / 5 + 3 / 5 ) = 11 / 18 xx 4 / 5 = [ 11 xx 2 xx 2 ] / [ 2 xx 9 xx 5 ] = 22 / 45`
\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{4}{3}\)
\(b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\left(\dfrac{6}{14}+\dfrac{35}{14}\right)\times\dfrac{7}{5}=\dfrac{41}{14}\times\dfrac{7}{15}=\dfrac{41}{30}\)
\(c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)
=(1/11+10/11)+(2/11+9/11)+(3/11+8/11)+(4/11+7/11)+(5/11+6/11)
=11/11+11/11+11/11+11/11+11/11
=1+1+1+1+1
=5
\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)
(2/7+5/7)+4/9=1+4/9=13/9
17/11+(7/15+5/11)=17/11+7/15+5/11=(17/11+5/11)+7/15=2+5/11=27/11
a) \(1678\cdot24+77\cdot1678-1678=1678\left(24+77-1\right)=167800\)
b) Ta có: \(\dfrac{2}{5}+\dfrac{4}{11}+\dfrac{3}{5}+\dfrac{18}{11}+\dfrac{1}{4}+\dfrac{1}{6}\)
\(=\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\left(\dfrac{4}{11}+\dfrac{18}{11}\right)+\dfrac{1}{4}+\dfrac{1}{6}\)
\(=3+\dfrac{1}{4}+\dfrac{1}{6}\)
\(=\dfrac{36}{12}+\dfrac{3}{12}+\dfrac{2}{12}=\dfrac{41}{12}\)
7/11 : 3/5 + 4/11 : 3/5
= (7/11 + 4/11) : 3/5
=1:3/5=5/3
\(\left(\dfrac{7}{11}+\dfrac{4}{11}\right):\dfrac{3}{5}=\dfrac{11}{11}:\dfrac{3}{5}=\dfrac{1}{1}:\dfrac{3}{5}=\dfrac{1}{1}\times\dfrac{5}{3}=\dfrac{5}{3}\)