Bài tập: Cộng, trừ số hữu tỉ

2512+−412=25+−412=2112=74

−47−2−3=−47+23=−1221+1421=221

−108+154=−54+154=−5+154=104=52

314−113=134−43=3912−1612=2312

38+−146=924+−5624=9+−5624=−4724

54545757−171717191919=54.10157.101−17.1010119.10101=5457−1719=1819−1719=119

58+−34+156=1524+−1824+6024=15+−18+6024=5724=198

172−−37+53=172−−921+3521=172−2621=35742−5242=30542

12−34+−56−712=12−34+56−712=6−9+10−712=0

−3−23+−109−253−56=−3−23−109−253−56=−54−12−20−150−1518=−25118

    5−7−−5−7+43=−57−57+43=−107+43=−30+2821=−221

   73+−56+−23=73+−56+−23=73+−23+−56=53+−56=10+−56=56

   43−−116−29+53=43+116+29+53=43+116+29+53=24+33+4+3018=9118

8−94+27−−6−37+54−3+24−97=8−94+27+6+37−54−3−24+97=8+6−3+−94−54−24+27+37+97=11−4+2=9

A=13−34−−35+172−29−136+115=13−34+35+172−29−136+115=13+35+115+−34−29−136+172=515+915+115+−2736−836−136+172=1−1+172=172

B=399.96−396.93−393.90−...−37.4−34=399.96−396.93+396.93+...+37.4+34.1=399.96−31.4+34.7+...+390.93+393.96=399.96−1−14+14−17+...+190−193+193−196=196−199−1−196=196−199−1+196=148−1−199=−4748−199=−15671584

x+15=37x=37−15x=15−735x=835

x−34=12x=34+12x=3+24x=54

1112−25+x=2325+x=1112−2325+x=1112−81225+x=14

        x=14−25        x=−320

x+23=35−−16x+23=35+16x+23=2330        x=2330−23        x=23−2030        x=110

x−172−−37+53=−13x−172+37−53=−13x−35742+1842−7042=−13                            x−30542=−13x = -13+30542x=-1442+30542x=29142=9714

92−23−x+74=−54

23−x+74 =92−−54

23−x+74 =92+54

23−x+74 =234

x+74 =23−234

x+74=8−6912

x+74=−6112

x=−6112−74

x=−6112−2112

x=−8212

x=−416.

Vậy x=−416.

x2−1x=112x2−22x=11212x2−2=2x   6x2−2=x6x2−x−12=06x2+8x−9x−12=02x3x+4−33x+4=03x+42x−3=0

TH1: 3x + 4 = 0

3x=−4   x=−43

TH2: 2x - 3 = 0

2x=3   x=32Vậy x∈−43;  32

2x−12.3x−13<0

TH1: 2x−12>03x−13<0⇔2x>123x<13⇔x>14x<19⇒không tìm được x

TH2: 2x−12<03x−13>0⇔2x<123x>13⇔x<14x>19⇔19<x<14

Vậy: 19<x<14

x+32x−23<0 Đk: x≠23

Ta có: x−23<x+32 nên

x−23<0x+32>0⇔x<23x>−32⇔−32<x<23

Vậy: −32<x<23

Ta có: 4<x<215

Vì 215=4,2 nên 4 < x < 4,2 

Vậy không có số nguyên x nào thỏa mãn yêu cầu bài toán.

Ta có: 0 < x < 2

Vì x nguyên nên x = 1

Vậy x = 1.

Vì −92<x≤−4 và x nguyênNên x = -4

Vì −119<x<0Nên  x=-1 (do x nguyên)

1x−y6=136−xy6x=1336−xy=6x6−xy=2xxy+2x=6xy+2=6

Vì x, y là các số nguyên mà 6=6.1=−6.−1=2.3=−2.−3

Ta có:

Vậy  x;  y=−6;−3;  −3;−4;  −2;−5;  −1;−8;  1;4;  2;1;  3;0;  6;−1.

x2+3y=54xy+62y=544xy+6=10y2xy+12=5y2xy−5y=−12y2x−5=−12

Vì x,y nguyên nên 2x-5 nguyên

mà −12=1.−12=12.−1=2.−6=6.−2=3.−4=4.−3

nên

(các ước khác của 12 không thỏa mãn 2x - 5 nguyên)

Vậy x;y=−1;4;  2;12;  3;−12;  4;−4

−121+−114=−242+−342=−542

−19−512=-1936

−1420+0,6=-110

4,5−−75=5910

Ba cách viết như sau:

−415=−115+-15;−415=−130+−730;−415=−215+-215

Ta thực hiện −112+−56−43=−224+−2024+−3224=−5424=−94

Ta thực hiện −2411+211+−1913+−2013=(−2)+(−3)=−5

Ta thực hiện −x=45−310−165=−2710=>x=2710

x−85=120−110=>x−85=−120=>x=−120+85=>x=3120

−1125=−15+−625;−1125=−325+−825;−1125=−225+−925

−1125=425−35;−1125=125−1225;−1125=32−9750

A=13−13+35−35+57−57+79−79+911−911+1113−1113+1315=>A=1315.

Ta có:

 B=19.10−11.2+12.3+...+17.8+18.9= 19.10-1-12+12-13+...+17-18+18-19= 190-1-19=190-89=190-8090=−7990

Vậy B = -7990