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a,(-15)-23+(-85)-77=[(-15)+(-85)]-(23+77)=(-100)-100=-200
b,(-24) + 4 + (-6) + 26 =[(-24)+(-6)]+(4+26)=(-30)+30=0
c, 34 + 35 + 36 + 37 - 14 - 15 - 16 - 17 =(34-14)+(35-15)+(36-16)+(37-17)=20+20+20+20=80
Bài 1:
a) \(24 - (-15) - 2\)
\(=39-2\)
\(=37\)
b) \((-85) + 10 - (-85) - 50\)
\(=[(-85)-(-85)]+10-50\)
\(=0+10-50\)
\(=10-50\)
\(=-40\)
c) \(71 - (-30) - (+18) + (-30)\)
\(=[(-30)-(-30)]+71-(+18)\)
\(=0+71-18\)
\(=71-18\)
\(=53\)
d) \(-(30) - (+37) + (+37) + (-85)\)
\(=[-(+37)+(+37)]-(30)+(-85)\)
\(=0-(30)+(-85)\)
\(=(-30)+(-85)\)
\(=-115\)
e) \((35-815) - (795-65)\)
\(=(-780)-730\)
\(=-1510\)
g) \((2002-79+15) + (-79+15)\)
\(=1938+(-64)\)
\(=1874\)
Bài 2:
a) \(25 - (30+x) = x - (27-8)\)
\(25-30-x=x-27+8\)
\(x+x=25-30+27-8\)
\(2x=14\)
\(x=14\div2\)
\(x=7\)
b) \((x-12) - 15 = (20-17) - (18+x) \)
\(x-12-15=13-18-x\)
\(x-27=-5-x\)
\(x+x=-5+27\)
\(2x=22\)
\(x=22\div2\)
\(x=11\)
c) \(15 - x = 7 - (-2)\)
\(15-x=9\)
\(x=15-9\)
\(x=6\)
d) \(x - 35 = (-12) - 3\)
\(x-35=-15\)
\(x=-15+35\)
\(x=20\)
e) \(\left|5-x\right|-26=-15\)
\(\left|5-x\right|=-15+26\)
\(\left|5-x\right|=11\)
Từ đây ta có:
*Nếu \(5-x=11\)
\(x=5-11\)
\(x=-6\)
*Nếu \(5-x=-11\)
\(x=5-(-11)\)
\(x=16\)
Vậy \(x=-6;x=16\)
Câu a:
Ta thấy 37 - 37 = 0
nên nhóm lại kết quả là 14 + 26 = 40
Câu b:
tương tự, kết quả là 6 + 10 = 16
Các câu còn lại như vậy
( -37)+14 +26 +37
=( -37 )+ 37 + (14 + 26 )
=0 +40 = 40
- 24 + 6 +10 +24
=( -24 ) + 24 +( 6 + 10 )
=0 + 16 = 16
15 + 23 + (-25 ) + ( -23 )
= 15 + ( -25 ) + 23 +( -23 )
= -10 + 0
= - 10
a) (-37)+14+26+37 = ( -37 + 37) + ( 14 + 26) = 40
b) (-24)+6+10+24 = ( - 24 + 24) + ( 6 + 10) = 16
c) 15+23+9-25)+(-33) = (15 - 25) + ( 23 - 33) + 9
= - 10 - 10 + 9
= - 11
d) 60+33+(-50)+(-33) = ( 60 -50) + ( 33 - 33)
= 10
e) (-16)+(-209)+(-14)+209 = ( - 16 - 14) + ( - 209 + 209)
= - 30
g) (-12)+(-13)+36+(-11)= ( - 11 -12 - 13 ) + 36
= - 36 + 36 = 0
h) -16+24+16-34 = ( - 16 + 16)+(24 - 34) = - 10
r) 25+37-48-25-37 = (25 - 25)+(37 - 37) - 48 = - 48
u) 2575+37-2576-29 = ( 2575 - 2576) + ( 37 - 29)
= - 1 + 8 = 7
i) 34+35+36+37-14-15-16-17 = ( 34 - 14 )+(35 - 15)+(36-16)+ (37 - 17)
= 80
2 . Bỏ ngoặc rồi tính
a)-7264+(1543+7264) = - 7264 + 1543 + 7264
= 1543
b) (144-97)-144 = 144 - 97 - 144 = - 97
c) (-145)-(18-145) = - 145 - 18 + 145 = - 18
d) 11+(-11+27) = 11 - 11 + 27 = 27
e) (27+514)-(486-73) = 27 + 514 - 486 + 73
= 128
g) (36+79)+(145-79-66) = 36 + 79 + 145 - 79 - 66
= 115
h) 10-[12-(-9-1) = 10 - ( 12 + 9 + 1)
= 10 - 22
= - 12
r) (-28-29+43)-(43+38) = - 28 - 29 + 43 - 43 - 38
= - 95
u ) 271 - [(-43)+271-(-17)] = 271 + 43 - 271 - 17 = 26
i ) -144-[29-(+144)-(+144) = - 144 - 29 - 144 + 144 = -173
e. = 12 - 25 + 38 + 25 - 38 + 88 - 250
= ( -25 + 25) + (38 - 38) + ( 12 + 88) - 250
= -150
f. = (-12).44 + 44.(-88)
= 44 ( -12 -88 )
= 44 . 100
= 4400
g. = -48 + 54 -77 -24 + 48 + 77
= (-48 + 48) + (-77+77) + (54 -24)
= 30
h. = 11.(-42) + 11.(-26) + 42.11 + 42.26 -26.11 - 42.26
= \([11.\left(-42\right)+11.42]+\left[11.\left(-26\right)-26.11\right]+[42.26-42.26]\)
= 11. (-52)
= - 572
\(e.-\left(-12+25-38\right)+\left(25-38+88\right)-250\\ =12-25+38+25-38+88-250\\ =\left(25-25\right)+\left(38-38\right)+\left(12+88\right)-250\\ =0+0+100-250=-150\)
\(f.\left(-12\right)\cdot\left(67-23\right)+44\cdot\left(-88\right)\\ =\left(-12\right)\cdot44+44\cdot\left(-88\right)\\ =44\cdot\left[-12+\left(-88\right)\right]\\ =44\cdot\left(-100\right)=-4400\)
\(g.\left(-48+54-77\right)-\left(24-48-77\right)\\ =-48+54-77-24+48+77\\ =\left(48-48\right)+\left(54-24\right)+\left(77-77\right)\\ =0+30+0=30\)
\(h.11\cdot\left(-42-26\right)+42\cdot\left(11+26\right)-26\cdot11-42\cdot26\\ =11\cdot\left(-68\right)+42\cdot37-26\cdot11-42\cdot26\\ =-748+1554-286-1092=-572\)
( -37 ) + 14 + 26 + 37 = [ ( -37 ) + 37 ] + ( 14 + 26 ) = 0 + 40 = 40
1. ( -24 ) + 6 + 10 + 24 = [ ( -24 ) + 24 ] + ( 6 + 10 ) = 0 + 16 = 16
2. 15 + 23 + ( -25 ) + ( -23 ) = [ 15 + ( -25 ) ] + [ 23 + ( -23 ) = ( -10 ) + 0 = -10
3. 60 + 33 + ( -50 ) + ( -33 ) = [ 60 + ( -50 ) ] + [ 33 + ( -33 ) ] = 10 + 0 = 10
4. ( -16 ) + ( -209 ) + ( -14 ) + 209 = [ ( -16 ) + ( -24 ) ] + [ ( -209 ) + 209 ] - ( -40 ) + 0 = -40
5.( -12 ) + ( -13 ) + 36 + ( -11 ) = [ ( -12 ) + ( -13 ) + ( -11 ) ] + 36 = ( -36 ) + 36 = 0
6. ( -16 ) + 24 + 16 - 34 = [ ( -16 ) + 16 ] + ( 24 - 34 ) = 0 + ( - 10 ) = -10
7. 25 + 37 - 48 - 25 - 37 = ( 25 - 25 ) + ( 37 - 37 ) - 48 = 0 + 0 - 48 = -48
8. 2575 + 37 - 2576 - 29 = ( 2575 - 2576 ) + ( 37 - 29 ) = ( -1 ) + 8 = 7
34 + 35 + 36 - 14 - 15 - 16 - 17 = ( 34 - 14 ) + ( 35 - 15 ) + ( 36 - 16 ) - 17 = 20 + 20 + 20 - 17 = 60 - 17 = 43
OK
- (-37)+14+26+37 = (-37+37)+(14+26)
= 0+ ( 14+26)
= 0+ 40 = 40
*1.) (-24)+6+10+24 = (-24+24)+(6+10)
= 0+ 16 = 16
2.) 15+23+(-25)+(-23) = (23+-23)+(15+-25)
= 0 + -10 = -10
3.) 60+33+(-50)+(-33) = (33+-33)+(60+(-50)
= 0+ 10 = 10
4.) (-16)+(-209)+(-14)+209 = (-209+209)+(-16+-14)
= 0+ -30 = -30
5.) (-12) +(-13)+36+(-11) = (-12+-13+-11)+36
= -36 + 36 = 0
6.) -16 +24 +16-34 = (-16+16)+(24-34)
= 0+ -10 = -10
8.) 2575 +37-2575-29 =(2575-2575)+(37 -29)
= 0 + 8 = 8
- 34 +35+36+37 -14-15-16-17
= (34-14)+(35-15)+(36-16)+(37-17)
= 10+10+10+10
= 10 . 4 = 40
\(2575+37-2576-29\)
\(=2612-2576-29\)
\(=36-29=7\)'
\(35+35+36+37-14-15-16-17\)
\(=70+\left(36-16\right)+\left(37-17\right)-14-15\)
\(=70+20+20-14-15\)
\(=90+6-15\)
\(=96-15=81\)
\(13\cdot\left(-12\right)+87.\left(-12\right)\)
\(=\left(-12\right)\cdot\left(13+87\right)\)
\(=\left(-12\right)\cdot100=-1200\)
\(26\cdot17+17\cdot74\)
\(=\left(26+74\right)\cdot17\)
\(=100\cdot17=1700\)
\(25\cdot\left(-18\right)+25\left(-82\right)\)
\(=25\cdot\left[\left(-18\right)+\left(-82\right)\right]\)
\(=25\cdot\left(-100\right)=\left(-2500\right)\)
\(25+37-48-25-37\)
\(=\left(25-25\right)+\left(37-37\right)-48\)
\(=0+0-48\)
\(=0-48=\left(-48\right)\)
\(\left(-16\right)+24+16-34\)
\(=\left[\left(-16\right)+16\right]+\left(24-34\right)\)
\(=0+\left(-10\right)=\left(-10\right)\)
a) \(\dfrac{43}{47}=\dfrac{47-4}{47}=\dfrac{47}{47}-\dfrac{4}{47}=1-\dfrac{4}{47}\)
\(\dfrac{53}{57}=\dfrac{57-4}{57}=\dfrac{57}{57}-\dfrac{4}{57}=1-\dfrac{4}{57}\)
Vì \(\dfrac{4}{47}>\dfrac{4}{57}\)=>\(1-\dfrac{4}{47}< 1-\dfrac{4}{57}\)
=>\(\dfrac{43}{47}< \dfrac{53}{57}\)
b) Ta chọn phân số trung gian là: \(\dfrac{64}{81}\)
Vì \(\dfrac{64}{81}>\dfrac{64}{85}\)
Mà \(\dfrac{64}{81}< \dfrac{73}{81}\)
=> \(\dfrac{64}{85}< \dfrac{64}{81}< \dfrac{73}{81}\)
Vậy \(\dfrac{64}{85}< \dfrac{73}{81}\)
c) Ta chọn phân số trung gian là: \(\dfrac{18}{37}\)
Vì \(\dfrac{18}{37}>\dfrac{15}{37}\)
Mà \(\dfrac{18}{37}< \dfrac{18}{31}\)
=> \(\dfrac{15}{37}< \dfrac{18}{37}< \dfrac{18}{31}\)
Vậy \(\dfrac{18}{31}>\dfrac{15}{37}\)
c; 37.(24 - 77) - 24.(37 - 77)
= 37.24 - 37.77 - 24.37 + 24.77
= (37.24 - 24.37) - (37.77 - 24.77)
= 0 - 77.(37 - 24)
= - 77 . 13
= - 1001
e) 17.15 - 34.42 + 19.17
= 17.(15 + 19) - 34.42
= 17.34 - 34.42
= 34.(17 - 42)
= 34. (-25)
= (-850)