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Đặt A = \(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
=> \(\frac{1}{7}A=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
=> \(\frac{1}{7}A=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
=> \(\frac{1}{7}A=\frac{1}{2}-\frac{1}{28}\)
=> \(\frac{1}{7}A=\frac{14}{28}-\frac{1}{28}\)
=>\(\frac{1}{7}A=\frac{13}{28}\)
=> A = \(\frac{13}{28}:\frac{1}{7}\)
=> A =\(\frac{13}{28}.7\)
=> A = \(\frac{13}{4}\)
a) x= \(\frac{-5}{12}\)
b) x = \(\frac{2}{5}\)
c) x =\(\frac{-87}{140}\)
d) x = \(\frac{109}{140}\)
e) x = \(\frac{13}{63}\)
trả lời:
B = 7x( 5/2x7 + 4/7x11 + 3/11x14 + 1/14x15 + 13/15x28 )
B = 7x(1/2 - 1/7 + 1/7 - 1/11 +....+ 1/15 - 1/28)
B = 7x(1/2 - 1/28)
B = 7x13/28
B = 13/4
Bàì làm:
\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(B=7.\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)
\(B=7.\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)
\(B=7.\left(\frac{1}{2}-\frac{1}{28}\right)\)
\(B=7.\frac{13}{28}\)
\(B=\frac{13}{4}\)
\(a,1\dfrac{4}{7}.3\dfrac{4}{11}.3\dfrac{11}{15}.5\dfrac{5}{8}\)
\(=\dfrac{11}{7}.\dfrac{27}{11}.\dfrac{56}{15}.\dfrac{45}{8}\)
\(=\dfrac{11.27.56.45}{7.11.15.8}\)
\(=\dfrac{1.3.7.3}{1.1.1.1}\)
\(=63\)
\(b,\dfrac{3}{4}.1\dfrac{1}{2}+\dfrac{3}{4}.\dfrac{1}{2}\)
\(=\dfrac{3}{4}.\left(1\dfrac{1}{2}+\dfrac{1}{2}\right)\)
\(=\dfrac{3}{4}.2\)
\(=\dfrac{3}{2}\)
\(x-\dfrac{11}{15}=3+\dfrac{x}{5}\\ \Leftrightarrow\dfrac{4}{5}x=\dfrac{56}{15}\\ \Leftrightarrow x=\dfrac{14}{3}\)
\(\dfrac{2}{5}\times\dfrac{1}{x}+\dfrac{1}{x}\times2+\dfrac{2}{5}=\dfrac{1}{2}\\ \Leftrightarrow\dfrac{12}{5}\times\dfrac{1}{x}=\dfrac{1}{10}\\ \Leftrightarrow\dfrac{1}{x}=\dfrac{1}{24}\\ \Leftrightarrow x=24\)
b)0,5x+2/3x+2/3=7/2
1/2x+2/3x+2/3=7/2
x(1/2+2/3)+2/3=7/12
x.7/6+2/3 =7/12
x.7/6 =7/12-2/3
x.7/6 =-1/12
x =-1/12:7/6
x =-1/14
b)3/5-2/15:x=1/2
2/15:x =3/5-1/2
2/15:x =1/10
x =2/15:1/10
x = 4/3
x × 3/5 + x × 1/2 = 11/15
x × (3/5 + 1/2) = 11/15
x × 11/10 = 11/5
x = 11/5 : 11/10
x = 2