DẠNG 1: TÍNH CÁC GIÁ TRỊ CỦA BIỂU THỨC
1. A = (-123) + 77 + (-257) + 23 – 43
2. B = 48 + |48 – 174| + (-74)
3. C = -2012 + (-596) + (-201) + 496 + 301
4. D = 1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + … – 79 – 80 – 81
5. E = – 418 – {- 218 – [- 118 – (- 318) + 2012]}
6. F = 1 – 2 + 3 – 4 + … + 99 – 100
7. G = 1 – 2 – 3 + 4 + 5 – 6 – 7 + … + 97 – 98 – 99 + 100
8. H = 2100 – 299 – 298 – … – 2 – 1 i. I = 2 – 5 + 8 – 11 + 14 – 17 + … + 98 – 101
Đáp án:
Giải thích các bước giải:
`1) A = (-123) + 77 + (-257) + 23 – 43 `
`=[(-123)+23]+[(-257)+77 ]-43`
`=(-100)+(-180)-43`
`=-323`
`2) B = 48 + |48 – 174| + (-74)`
`=48 + 174 – 48 – 74`
`= (48-48)+(174-74)`
`= 0 + 100 `
`= 100`
`3) C = -2012 + (-596) + (-201) + 496 + 301`
`=-2012+[(-596)+496]+[(-201)+301]`
`=-2012+(-100)+100`
`=-2012`
`4) D = 1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + … – 79 – 80 – 81 `
`= ( 1 + 2 -3 -4 ) + ( 5 + 6 – 7 – 8 ) +…. ( 77 + 78 – 79 – 80 ) – 81`
`=(-4)+(-4)+…+(-4)-81`
`=(-4).20-81`
`=-80-81=161`
`5) E = – 418 – {- 218 – [- 118 – (- 318) + 2012]}`
`=-418-{-218-[-118+318+2012]}`
`=-418-{-218+118-318-2012}`
`=-418-{-418+2012}`
`=-418+418+2012`
`=2012`
`6) F = 1 – 2 + 3 – 4 + … + 99 – 100 `
`=(1-2)+(3-4)+…+(99-100)` ( `50` cặp )
`=(-1)+(-1)+…+(-1)`
`=(-1).50=-50`
`7) G = 1 – 2 – 3 + 4 + 5 – 6 – 7 + … + 97 – 98 – 99 + 100 `
`=(1-2-3+4)+(5-6-7+8)+….+(97-98-99+100)`
`=0+0+…+0`
`=0`
`8) H = 2100 – 299 – 298 – … – 2 – 1`
`= 2100 – ( 299 + 298 + … + 2 + 1 ) `
`= 2100 – [ ( 299 + 1 ) . 299 ): 2] `
`= 2100 – [ 300 . 299 :2] `
`= 2100 – 22425 `
`= -20325`
`i. I = 2 – 5 + 8 – 11 + 14 – 17 + … + 98 – 101`
`=(-3)+(-3)+(-3)+…+(-3)` `( 34` số hạng )
`=(-3).34=-102`
`#Xray`
`a)A=(-123)+77+(-257)+23-43`
`=-46-257+23-43=-323`
`b)B=48+|48-174|+(-74)`
`=48+126-74`
`=100`
`c)C=-2012+(-596)+(-201)+496+301`
`=-1475`
`d)D=1+2-3-4+5-6-7-8+…-79-80-81`
`=(1+2-3-4)+(5+6-7-8)+…+(77+78-79-80)-81`
`=-4.20-81`
`=-161`
`e)E=-418-{-218-[-118-(-318)+2012]}`
`=-418-{-218-2212}`
`=-418+218+2212`
`=-200+2212`
`=2012`
`f)F=1-2+3-4+…+99-100`
`=(1-2)+(3-4)+…+(99-100)`
`=-1.50=-50`
`g)G=1-2-3+4+5-6-7+8…+97-98-99+100`
`=(1-2-3+4)+(5-6-7+8)+…+(97-98-99+100)`
`=0+0+0+…+0=0`
`h)H=2100-299-298-…-2.1`
`=2100-(299+298+…+2+1)`
`=2100-{[(299-1):1+1]:2.(299+1)}`
`=2100-22425`
`=-20325`
`i)2-5+8-11+14-17+…+98-101`
`=(2-5)+(8-11)+(14-17)+…+(98-101)`
`=-3.17`
`=-51`