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a,(11/15+4/15)+(5/7+2/7)
=1+1
=2
b,5/9x(1/2+6/4)
=5/9x2
=10/9
c,1/2:(7/8+9/8)
=1/2:2
=1
d,(17/10-7/10)+1/2
=1+1/2
=3/2
a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)
\(=2\)
b) \(\frac{5}{9}\times\frac{1}{2}\times\frac{5}{9}\times\frac{6}{4}=\frac{25}{81}\times\frac{3}{4}=\frac{25}{108}\)
c) \(\frac{7}{8}\div\frac{1}{2}+\frac{9}{8}\div\frac{1}{2}=\left(\frac{7}{8}+\frac{9}{8}\right)\div\frac{1}{2}\)
\(=2\div\frac{1}{2}=4\)
d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)
\(=1+\frac{1}{2}=\frac{3}{2}\)
a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}\)
\(=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)
\(=1+1\)
\(=2\)
b) \(\frac{5}{9}.\frac{1}{2}.\frac{5}{9}.\frac{6}{4}\)
\(=\left(\frac{5}{9}\right)^2\left(\frac{1}{2}.\frac{6}{4}\right)\)
\(=\frac{25}{81}.\frac{3}{4}\)
\(=\frac{25}{108}\)
c) \(\frac{7}{8}:\frac{1}{2}+\frac{9}{8}:\frac{1}{2}\)
\(=\frac{7}{8}.2+\frac{9}{8}.2\)
\(=2\left(\frac{7}{8}+\frac{9}{8}\right)\)
\(=2.\frac{16}{8}\)
\(=2.2\)
\(=4\)
d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}\)
\(=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)
\(=1+\frac{1}{2}\)
\(=\frac{2}{2}+\frac{1}{2}\)
\(=\frac{3}{2}\)
a)Ta có:
A= 1/15+1/35+1/63+1/99+1/143
A= 1/3.5+1/5.7+1/7.9+1/9.11+1/11.13
2A= 2/3.5+2/5.7+2/7.9+2/9.11+2/11.13
2A= 1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13
Đơn giản đi ta được:
2A= 1/3-1/13
2A= 10/39
A= 5/39
Vậy A= 5/39
b) Để A và B có giá trị bằng nhau thì:
\(\frac{3}{4}\cdot x+7=\frac{4}{3}\cdot x-35\)
\(7+35=\frac{4}{3}\cdot x-\frac{3}{4}\cdot x\)
\(42=\frac{7}{12}\cdot x\)
\(x=42:\frac{7}{12}\)
\(x=72\)
A= 7/5*7 + 7/7*9 + ... + 7/53*55
A= 7/2*( 2/5*7 + 2/7*9 + ... + 2/53*55 )
A= 7/2*( 7-5/5*7 + 9-7/7*9 + ... + 55-53/53*55 )
A= 7/2*( 1/5-1/7 + 1/7-1/9 + ... + 1/53-1/55 )
A= 7/2*( 1/5-1/55 )
A= 7/2*2/11
A= 7/11
A= 7/11 > 1/2
Nên: A > 1/2
B= 1/3 + 1/15 + 1/35 + ... + 1/99
B= 1/1*3 + 1/3*5 + 1/5*7 + ... + 1/9*11
B= 2*( 2/1*3 + 2/3*5 + 1/5*7 + ... + 2/9*11 )
B= 2*( 3-1/1*3 + 5-3/3*5 + 7-5/5*7 + ... + 11-9/9*11 )
B= 2*( 1/1-1/3 + 1/3-1/5 + 1/5-1/7 + ... + 1/9-1/11 )
B= 2*( 1/1-1/11 )
B= 2*10/11
B= 20/11
B= 20/11 < 1/2
Nên: B < 1/2
A= 7/5*7 + 7/7*9 + ... + 7/53*55
A= 7/2*( 2/5*7 + 2/7*9 + ... + 2/53*55 )
A= 7/2*( 7-5/5*7 + 9-7/7*9 + ... + 55-53/53*55 )
A= 7/2*( 1/5-1/7 + 1/7-1/9 + ... + 1/53-1/55 )
A= 7/2*( 1/5-1/55 )
A= 7/2*2/11
A= 7/11
A= 7/11 > 1/2
Nên: A > 1/2
B= 1/3 + 1/15 + 1/35 + ... + 1/99
B= 1/1*3 + 1/3*5 + 1/5*7 + ... + 1/9*11
B= 2*( 2/1*3 + 2/3*5 + 1/5*7 + ... + 2/9*11 )
B= 2*( 3-1/1*3 + 5-3/3*5 + 7-5/5*7 + ... + 11-9/9*11 )
B= 2*( 1/1-1/3 + 1/3-1/5 + 1/5-1/7 + ... + 1/9-1/11 )
B= 2*( 1/1-1/11 )
B= 2*10/11
B= 20/11
B= 20/11 < 1/2
Nên: B < 1/2
A=1.078688093