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\(\dfrac{3}{5}+\dfrac{6}{11}+\dfrac{7}{13}+\dfrac{2}{5}+\dfrac{16}{11}+\dfrac{19}{13}\\ =\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{6}{11}+\dfrac{16}{11}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)\\ =\dfrac{5}{5}+\dfrac{22}{11}+\dfrac{26}{13}\\ =1+2+2\\ =5\)
\(11-12+13-14+15-16+17-18+19-20+21+22\)
\(=\left(11+13+15+17+19+21+22\right)-\left(12+14+16+18+20\right)\)
\(=\left(A+22\right)-B\)
số số hạng của tổng A là :
( 21 - 11 ) :2 + 1 = 6 ( số )
vậy tổng A là :
( 21 + 11 ) * 6 :2 = 96
số số hạng của tổng B là :
(20-12 ) :2 +1 = 5 ( số )
tổng B là :
( 20 + 12 ) * 5 :2 = 80
vậy \(\left(A+22\right)-B\)
\(=\left(96+22\right)-80\)
\(=118-80\)
\(=38\)
\(11-12+13-14+15-16+17-18+19-20+21+22\)
\(=\left(11-12\right)+\left(13-14\right)+\left(15-16\right)+\left(17-18\right)+\left(19-20\right)+21+22\)
\(=-1+-1+-1+-1+-1+21+22\)
\(=-5+21+22\)
\(=38.\)
\(a,\dfrac{13}{19}+\dfrac{18}{19}+\dfrac{17}{19}=\dfrac{13+18+17}{19}=\dfrac{48}{19}\\ b,\dfrac{3}{5}+\dfrac{3}{16}+\dfrac{13}{16}=\dfrac{3}{5}+\left(\dfrac{3}{16}+\dfrac{13}{16}\right)=\dfrac{3}{5}+\dfrac{16}{16}=\dfrac{3}{5}+1=\dfrac{3}{5}+\dfrac{5}{5}=\dfrac{8}{5}\)
\(a\dfrac{13+18+17}{19}=\dfrac{48}{19}\)
\(b\dfrac{3}{5}+\dfrac{3+13}{16}=\dfrac{3}{5}+1=\dfrac{3}{5}+\dfrac{5}{5}=\dfrac{8}{5}\)
[1+3+...+13+15] x[16 x2+4x16-32x3] =[1+3+...+13+15] x 0 =0
( 1 + 3 + .... + 13 + 15 ) x ( 16 * 2 + 4 * 16 - 32 * 3 )
= ( 1+ 3 + ... + 13 + 15) x ( 16 * 2 + 4 * 16 - 16 * 2 * 3)
= ( 1 + 3 + ...+ 13 + 15) x { [ 16 * ( 2 + 4 - 2 * 3 ) ] }
= ( 1 + 3 + ... + 13 + 15 ) x 16 * 0
= ( 1 + 3 + .... +13 +15 ) x 0
=0
Lời giải:
$1+2+3+....+25$
$=(1+25)+(2+24)+(3+23)+(4+22)+(5+21)+(6+20)+(7+19)+(8+18)+(9+17)+(10+16)+(11+15)+(12+14)+13$
$=\underbrace{26+26+26+...+26}_{12}+13$
$=26\times 12+13=325$
Bài 1 :
a) Hai phân số có chung tử số thì ta so sánh mẫu nếu mẫu lớn hơn thì phân số đó bé hơn
Áp dụng vào đó ta có : 71 < 72 => 15/71 > 15/72
b) Ta có : 21/42 = 1/2 = 23/46
Áp dụng câu a ta có : 46 > 45 => 21/42 < 23/45
c) Ta có : 47/45 = 1 + 2/45 ; 48/46 = 1 + 2/46
Vì 2/45 > 2/46 => 47/45 > 48/46
d) Ta có : 1 - 13/25 = 12/25
1/3 = 12/36
Vì 12/25 > 12/36 => 13/25 > 3/7
Bài 2 :
D = 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/110
D = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + .... + 1/10.11
D = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + .... + 1/10 - 1/11
D = 1 - 1/11
D = 10/11
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20
=(1+19)+(2+18)+(3+17)+(4+16)+(5+15)+(6+14)+(7+13)+(8+12)+(9+11)+20+10
=20+20+20+20+20+20+20+20+20+20+10
=20×10+10
=200+10
=210
= ( 1 + 19 ) + ( 2 + 18 ) + ( 3 + 17 ) + (4 + 16 ) + ( 5 + 15 ) + ( 6 + 14 ) + ( 7 + 13 ) + ( 8 + 12) + ( 9+ 11 ) + 20
= 20 + 20 + 20 +20 + 20 +20 + 20 + 20 + 20 +20
= 20 x 10
= 200
tui đầu tiên đó
`3+1/9+3/9+2+5/9+3+2`
`= ( 3 +2+3+2) +(1/9+ 3/9 + 5/9)`
`= 10 + 9/9`
`=10 + 1`
`=11`
\(3+\dfrac{1}{9}+\dfrac{3}{9}+2+\dfrac{5}{9}+3+2\)
\(=3+\left(\dfrac{1}{9}+\dfrac{3}{9}+\dfrac{5}{9}\right)+2+3+2\)
\(=\left(3+2+3+2\right)+\dfrac{9}{9}\)
\(=10+1=11\)
(20+10)-(11+19)+(12+18)-(13+17)+(14+16)-15
=30-30+30-30-15+30
=15
10-11+12-13+14-15+16-17+18-19+20
= (10+20)+(-11-19)+(12+18)+(-13-17)+(14+16)-15
= 30-30+30-30+30-15
= 15
Bài 1:
\(\dfrac{36}{21}-\dfrac{15}{20}\)
\(=\dfrac{12}{7}-\dfrac{3}{4}\)
\(=\dfrac{48}{28}-\dfrac{21}{28}\)
\(=\dfrac{27}{28}\)
\(----\)
\(\dfrac{63}{45}-\dfrac{20}{25}\)
\(=\dfrac{63}{45}-\dfrac{4}{5}\)
\(=\dfrac{63}{45}-\dfrac{36}{45}\)
\(=\dfrac{27}{45}=\dfrac{3}{5}\)
Bài 2:
\(\dfrac{3}{5}+\dfrac{3}{16}+\dfrac{13}{16}\)
\(=\dfrac{3}{5}+\left(\dfrac{3}{16}+\dfrac{13}{16}\right)\)
\(=\dfrac{3}{5}+1\)
\(=\dfrac{3}{5}+\dfrac{5}{5}\)
\(=\dfrac{8}{5}\)
`36/21-15/20`
`=12/7-3/4`
`=48/28-21/28`
`=27/28`
__
`63/45-20/25`
`=7/5-4/5`
`=3/5`
__
`2)`
`3/5+3/16+13/16`
`=3/5+(3/16+13/16)`
`=3/5+16/16`
`=3/5+1`
`=3/5+5/5`
`=8/5`
`#QiN`