j) \(\dfrac{-3}{4}\) + \(\dfrac{2}{7}\) + \(\dfrac{-1}{4}\) +\(\dfrac{3}{5}\) +\(\dfrac{5}{7}\)
k) \(\dfrac{-2}{17}\)+ \(\dfrac{15}{23}\) + \(\dfrac{-15}{17}\) + \(\dfrac{4}{19}\) +\(\dfrac{8}{23}\)
`@` `\text {Ans}`
`\downarrow`
`j)`
`-3/4 + 2/7 + (-1)/4 + 3/5 + 5/7`
`= (-3/4 - 1/4) + (2/7 + 5/7) + 3/5`
`= -1 + 1 + 3/5`
`= 3/5`
`k)`
`-2/17 + 15/23 + (-15)/17 + 4/19 + 8/23`
`= (-2/17 - 15/17) + (15/23 + 8/23) + 4/19`
`= -1 + 1 + 4/19`
`= 4/19`
$#KDN040510$
j: =-3/4-1/4+2/7+5/7+3/5
=-1+1+3/5
=3/5
k: =-2/17-15/17+15/23+8/23+4/19
=-1+1+4/19
=4/19
\(j)\dfrac{-3}{4}+\dfrac{2}{7}+\dfrac{-1}{4}+\dfrac{3}{5}+\dfrac{5}{7}\\ =\left(\dfrac{-3}{4}+\dfrac{-1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\dfrac{3}{5}\\ =\dfrac{-4}{4}+\dfrac{7}{7}+\dfrac{3}{5}\\ =-1+1+\dfrac{3}{5}\\ =0+\dfrac{3}{5}\\ =\dfrac{3}{5}\\ k)\dfrac{-2}{17}+\dfrac{15}{23}+\dfrac{-15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\\ =\left(\dfrac{-2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{15}{23}+\dfrac{8}{23}\right)+\dfrac{4}{19}\\ =\dfrac{-17}{17}+\dfrac{23}{23}+\dfrac{4}{19}\\ =-1+1+\dfrac{4}{9}\\ =0+\dfrac{4}{19}\\ =\dfrac{4}{19}\)
Bài 2: Thực hiện phép tính một cách hợp lí
f) \(\dfrac{7}{19}\) . \(\dfrac{8}{11}\) + \(\dfrac{3}{11}\) . \(\dfrac{7}{19}\) +\(\dfrac{-12}{19}\)
i) ( \(\dfrac{3}{8}\) + \(\dfrac{-3}{4}\)+ \(\dfrac{7}{12}\) ) : \(\dfrac{5}{6}\) +\(\dfrac{1}{2}\)
f: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{7}{19}-\dfrac{12}{19}=\dfrac{-5}{19}\)
i: \(=\left(\dfrac{9}{24}-\dfrac{18}{24}+\dfrac{14}{24}\right)\cdot\dfrac{6}{5}+\dfrac{1}{2}=\dfrac{5}{24}\cdot\dfrac{6}{5}+\dfrac{1}{2}\)
=1/4+1/2=3/4
` 7/19 . 8/11 + 3/11 . 7/19 + (-12)/19 `
`= 7/19 . ( 8/11 + 3/11 ) + (-12)/19 `
`= 7/19 . 11/11 + (-12)/19`
`= 7/19 . 1 + (-12)/19 `
`= 7/19 + (-12)/19 `
`= -5/19 `
`( 3/8 + (-3)/4 + 7/12 ) : 5/6 + 1/2`
`= 3/8 + (-3)4 + 7/12 . 6/5 + 1/2`
`= ( 9+(-18) + 14)/24 . 6/5 + 1/2`
`= 5/24 . 6/5 + 1/2`
`= 1/4 + 1/2 `
`= 3/4`
Bài 1: Thực hiện phép tính một cách hợp lí:
f) \(\dfrac{-5}{9}\) + \(\dfrac{8}{15}\) + \(\dfrac{-2}{11}\) + \(\dfrac{4}{-9}\) +\(\dfrac{7}{15}\)
=-5/9-4/9+8/15+7/15-2/11
=-1+1-2/11
=-2/11
` -5/9 + 8/15 + (-2)/11 + 4/(-9) + 7/15 `
`= ( (-5)/9 + (-4)/9 ) + ( 8/15 + 7/15 ) + (-2)/11`
`= -9/9 + 15/15 + (-2)/11`
`= -1 + 1 + (-2)/11`
`= 0 + (-2)/11`
`= -2/11`
Gọi số học sinh giỏi của lớp 6A và 6B lần lượt là a,b
Theo đề, ta có:
a=2/3b và a-3=3/7(b+3)
=>a-2/3b=0 và a-3/7b=9/7+3=30/7
=>a=12 và b=18
tìm n thuộc N biết (1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062
(1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062
= ( \(\dfrac{6}{2.3}\) -\(\dfrac{2}{2.3}\) ). (\(\dfrac{12}{3.4}\) - \(\dfrac{2}{3.4}\) )......( \(\dfrac{9900}{99.100}\) - \(\dfrac{2}{99.100}\) )
= 4/2.3 .10/3.4..... 9898/99.100
= 1.4/2.3 . 2.5/3.4 .... 98.101/99.100
=\(\dfrac{1.2.3.4...98}{2.3...99}\) . \(\dfrac{4.5.6...101}{3.4.5...100}\)
= 1/99.101/3
= 101/297
(1-2/2.3).(1-2/3.4).....(1-2/n.(n-1))=2021/6062
= ( 22.322.3 ). (23.423.4 )......( 299.100299.100 )
= 4/2.3 .10/3.4..... 9898/99.100
= 1.4/2.3 . 2.5/3.4 .... 98.101/99.100
=4.5.6...1013.4.5...1004.5.6...1013.4.5...100
= 1/99.101/3
= 101/297
-5/6-x=7/12+-1/3
\(-\dfrac{5}{6}-x=\dfrac{7}{12}+\left(-\dfrac{1}{3}\right)\)
\(\Leftrightarrow-\dfrac{5}{6}-x=\dfrac{7}{12}-\dfrac{1}{3}\)
\(\Leftrightarrow-\dfrac{5}{6}-x=\dfrac{7}{12}-\dfrac{4}{12}\)
\(\Leftrightarrow-\dfrac{5}{6}-x=\dfrac{3}{12}\)
\(\Leftrightarrow-x=\dfrac{3}{12}+\dfrac{5}{6}\)
\(\Leftrightarrow-x=\dfrac{3}{12}+\dfrac{10}{12}\)
\(\Leftrightarrow-x=\dfrac{13}{12}\)
\(\Leftrightarrow x=-\dfrac{13}{12}\)
Sosssssssssssssssss
C/M : A<1/2
A= 1/2mũ2+1/4mũ2+........+1/100mũ2
A=1/4(1/1+1/2^2+...+1/50^2)
=>A=1/4+1/4*(1/2^2+...+1/50^2)
=>A<1/4+1/4*(1-1/2+1/2-1/3+...+1/49-1/50)
=>A<1/4+1/4*49/50=99/200<1/2
-1,5x(7/3-5/3x4)
`-1,5 \times (7/3-5/3 \times 4)`
`= -1,5 \times (7/3-20/3)`
`= -1,5 \times (-13/3)`
`= 13/2`
1/4 - (2X+1/2)2 = 0
\(\dfrac{1}{4}-\left(2x+\dfrac{1}{2}\right)2=0\)
\(\left(2x+\dfrac{1}{2}\right)2=\dfrac{1}{4}\)
\(2x+\dfrac{1}{2}=\dfrac{1}{8}\)
\(2x=-\dfrac{3}{8}\)
\(x=-\dfrac{3}{16}\)
(2x +1/2 ).2=1/4
2x+1/2 =1/8
2x = -3/8
x =-3/16
