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\(3\dfrac{1}{5}\times\dfrac{10}{11}+1\dfrac{2}{11}\\ =\dfrac{16}{5}\times\dfrac{10}{11}+\dfrac{13}{11}\\ =\dfrac{16\times10}{5\times11}+\dfrac{13}{11}\\ =\dfrac{160}{55}+\dfrac{13}{11}\\ =\dfrac{32}{11}+\dfrac{13}{11}\\ =\dfrac{32+13}{11}\\ =\dfrac{45}{11}\)
\(5\dfrac{1}{3}:1\dfrac{2}{3}-1\dfrac{1}{5}\\ =\dfrac{16}{3}:\dfrac{5}{3}-\dfrac{6}{5}\\ =\dfrac{16}{3}\times\dfrac{3}{5}-\dfrac{6}{5}\\ =\dfrac{16\times3}{3\times5}-\dfrac{6}{5}\\ =\dfrac{48}{15}-\dfrac{6}{5}\\ =\dfrac{16}{5}-\dfrac{6}{5}\\ =\dfrac{16-6}{5}\\ =\dfrac{10}{5}\\ =2\)
\(3\dfrac{1}{5}\times\dfrac{10}{11}+1\dfrac{2}{11}\\ =\dfrac{3\times5+1}{5}\times\dfrac{10}{11}+\dfrac{1\times11+2}{11}\\ =\dfrac{16}{5}\times\dfrac{10}{11}+\dfrac{13}{11}\\ =\dfrac{160}{55}+\dfrac{13}{11}\\ =\dfrac{32}{11}+\dfrac{13}{11}\\ =\dfrac{45}{11}\)
\(5\dfrac{1}{3}:1\dfrac{2}{3}-1\dfrac{1}{5}\\ =\dfrac{5\times3+1}{3}:\dfrac{1\times3+2}{3}-\dfrac{1\times5+1}{5}\\ =\dfrac{16}{3}:\dfrac{5}{3}-\dfrac{6}{5}\\ =\dfrac{16}{3}\times\dfrac{3}{5}-\dfrac{6}{5}\\ =\dfrac{16}{5}-\dfrac{6}{5}\\ =\dfrac{10}{5}=2\)
a) 1/11 + 2/11 + 3/11 + ... + 10/11
= 1 + 2 + 3 + ... + 10 / 11
= (1 + 10).10:2 / 11
= 11.5/11
= 5
b) 1/10×20 + 1/20×30 + 1/30×40 + ... + 1/90×100
= 1/10×10 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10)
= 1/100 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)
= 1/100 × (1 - 1/10)
= 1/100 × 9/10
= 9/1000
\(\left(6\div\dfrac{3}{5}-1\dfrac{1}{6}\times\dfrac{6}{7}\right)\div\left(4\dfrac{1}{5}\times\dfrac{10}{11}+5\dfrac{2}{11}\right)\)
\(=\left(6\times\dfrac{5}{3}-\dfrac{7}{6}\times\dfrac{6}{7}\right)\div\left(\dfrac{21}{5}\times\dfrac{10}{11}+\dfrac{57}{11}\right)\)
\(=\left(10-1\right)\div\left(\dfrac{210}{55}+\dfrac{57}{11}\right)\)
\(=9\div9\)
\(=1\)
A = ( 6 : 3/5 - 7/6 * 6/7 ) : ( 21/5 * 10/11 + 57/11 )
A = ( 10 - 1 ) : ( 42/11 + 57/11)
A = 9 : 9
A = 1
B = 59 /10 : 3/2 - ( 7/3 * 9/2 - 2 * 7/3 ) : 7/4
B = 59/15 - ( 21/2 - 14/3 ) : 7/4
B = 59/15 - 35/6 : 7/4
B = 59/15 - 10/3
B = 3/5
14/15+3/11+1/15+3/11=10/22
=[14/15+1/15]+[3/11+3/11]
=[14/15+1/15]+[3/11*2]
= 1+6/11
=17/11
\(\frac{7}{10}-\frac{3}{10}x\frac{1}{10}+\frac{4}{25}\)
\(=\frac{7}{10}-\frac{3}{100}+\frac{4}{25}\)
\(=\frac{70}{100}-\frac{3}{100}+\frac{4}{25}\)
\(=\frac{67}{100}+\frac{4}{25}\)
\(=\frac{67}{100}+\frac{16}{100}\)
\(=\frac{83}{100}=0,83\)
\(\frac{6}{11}x\frac{3}{7}+\frac{3}{7}x\frac{5}{11}\)
\(=\frac{18}{77}+\frac{15}{77}\)
\(=\frac{33}{77}=\frac{3}{7}\)
\(49x\left(311-4807:23\right)+98210\)
\(=49x\left(311-209\right)+98210\)
\(=49x102+98210\)
\(=4998+98210\)
\(=103208\)
a) \(\frac{7}{10}-\frac{3}{10}\times\frac{1}{10}+\frac{4}{25}\)
\(=\frac{2}{5}\times\frac{1}{10}+\frac{4}{25}\)
\(=\frac{1}{25}+\frac{4}{25}\)
\(=\frac{5}{25}=\frac{1}{5}\)
b)\(\frac{6}{11}\times\frac{3}{7}+\frac{3}{7}\times\frac{5}{11}\)
\(=\frac{3}{7}\times\left(\frac{6}{11}+\frac{5}{11}\right)\)
\(=\frac{3}{7}\times1\)
\(=\frac{3}{7}\)
c)\(49\times\left(311-4807:23\right)+98210\)
\(=49\times\left(311-209\right)+98210\)
\(=49\times102+98210\)
\(=4998+98210\)
\(=103208\)
=(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
1) 9 x 10 + 10 x 11 + 11 x 12 + ....+ 2015 x 2016
=9x10x11-8x9x10+10x11x12-9x10x11+...+2015x2016x2017-2014x2015x2013
=2015x2016x2017-8x9x10
=8193537360
10 11 : 1 1 3 = 10 11 : 4 3 = 15 22