a.
(5/11 + 6/11 ) + ( 1/4 +3/4) + ( 6/25 + 9/25)
= 11/11 + 4/4 + 15/25
= 1 +1 + 3/5
= 2+3/5 = 13/5
b.
( 37/100 + 163/100) + (1/8 + 3/8 ) + 19/4 + 1/2
=  200/100 + 4/8 + ( 19/4 + 2/4)
=    2 + 1/2 + 21/4
=  31/4

b: \(\dfrac{163}{257}< \dfrac{163}{221}\)

mà 149/257<163/257

nên 149/257<163/257<163/221

c: \(\dfrac{15}{18}=\dfrac{5}{6}=\dfrac{100}{120}\)

\(\dfrac{17}{20}=\dfrac{102}{120}\)

\(\dfrac{21}{24}=\dfrac{105}{120}\)

mà 100<102<105

nên 15/18<17/20<21/24

=>-15/17>-17/20>-21/24

a: =(375-175)+(369-169)+...+(207-7)

=200+200+...+200

=200*[(375-207)/2+1]

\(=200\cdot85=17000\)

b: \(=\left(24-11\right)+\left(32-19\right)+\left(40-27\right)+...+\left(336-323\right)\)

\(=13\cdot\left[\left(336-24\right):8+1\right]=13\cdot40=520\)

c: \(=\left(5-2\right)+\left(8-4\right)+\left(11-6\right)+...+\left(140-92\right)\)

=3+4+5+...+48

Số số hạng là (48-3):1+1=45+1=46(số)

Tổng là: (48+3)*46/2=51*23=1173

d: \(=\left(300-285\right)+\left(295-278\right)+\left(290-271\right)+...+\left(100-5\right)+10\)

=15+17+19+...+95+10

Số số lẻ trong khoảng từ 15 đến 95 là:

(95-15):2+1=41(số)

Tổng của dãy số trên là:

10+(95+15)*41/2

=10+55*41

=2265

\(3\cdot2x=15\cdot2^{12}+9\cdot8^4\)

=>\(3\cdot2x=15\cdot2^{12}+9\cdot2^{12}\)

=>\(3\cdot2x=24\cdot2^{12}\)

=>\(2x=8\cdot2^{12}=2^{15}\)

=>\(x=2^{14}\)

a. -37 + 54 + -70+ -163 + 246

= ( 54 + 246) + (-37 - 163 )  - 70

= 300 -200 -  70 = 30

b. -359+ 181+ -123+ 350+ -172

=(-178)+227+(-172)

=49+(-172)

=-123

c.-69+ 53+ 46+ -94+-14+ 78

=(-16)+(-48)+64

=-64+64

=0

d. 13- 12+ 11+10- 9+ 8- 7- 6+ 5- 4+ 3+2- 1

= 13 - (13 - 1) + (13 - 2) + (13 - 3) - (13 - 4) + (13 - 5) - (13 - 6) - (13 - 7) + (13 - 8) - (13 - 9) + (13 - 10) + (13 - 11) - (13 - 12)

= 13 - 13 + 1 + 13 - 2 + 13 - 3 - 13 + 4 + 13 - 5 - 13 + 6 - 13 + 7 + 13 - 8 - 13 + 9 + 13 - 10 + 13 - 11 - 13 + 12

= (13 - 13 + 13 + 13 - 13 + 13 - 13 - 13 + 13 - 13 + 13 + 13 - 13) + (1 - 2 - 3 + 4 - 5 + 6 + 7 - 8 + 9 - 10 - 11 = 12)

= 13 + 0

= 13

a) \(-37+54+\left(-70\right)+\left(-163\right)+246\)

\(=\left(246+54\right)-\left(37+163\right)-70\)

\(=300-200-70\)

\(=100-70=30\)

b) \(-359+181+\left(-123\right)+350+\left(-172\right)\)

\(=-359+181-123+350-172\)

\(=\left(-359+350\right)+\left(181-172\right)-123\)

\(=-9+9-123\)

\(=-123\)

c) \(-69+53+46+\left(-94\right)+\left(-14\right)+78\)

\(=-69+53+46-94-14+78\)

\(=\left(-69+78\right)+\left(53-14\right)+\left(46-94\right)\)

\(=9+39-48\)

\(=48-48=0\)

d) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)

\(=\left(13-12\right)+\left(11+10\right)-\left(9-8\right)-\left(7+6\right)+\left(5-4\right)+\left(3+2-1\right)\)

\(=1+21-1-13+1+5\)

\(=21-13+1+5\)

\(=8+1+5=9+5=14\)

1. 234 + ( 345 - x ) = 500

345 - x = 500 - 234

345 - x = 266

x = 345 - 266

x = 79

2. 456 - ( x + 23 ) = 326

x + 23 = 456 - 326

x + 23 = 130

x = 130 - 23

x = 107

3. ( 567 - x ) . 212 = 605

567 - x = 605 : 212

567 - x = ...

=> Đề sai

4. ( 5 . x - 15 ) : 5 = 0

5 . x - 15 = 0 : 5

5 . x - 15 = 0

5 . x = 0 + 15

5 . x = 15

x = 15 : 5

x = 3

5. 14 x ( x - 7 ) = 210

x - 7 = 210 : 14

x - 7 = 15

x = 15 + 7

x = 22

6. 84 - 4 x ( 2 . x + 1 ) = 48

4 x ( 2 . x + 1 ) = 84 - 48

4 x ( 2 . x + 1 ) = 36

2 . x + 1 = 36 : 4

2 . x + 1 = 9

2 . x = 9 - 1

2 . x = 8

x = 8 : 2

x = 4

1. 345 - x = 500 - 234

345-x=266

x=345-266

x=79

2. x+23 =456-326

x+23=130

x=130-23

x=107

4. 5 x X - 15 =5 x0 

5xX -15=0

5 x X = 0+15

5x X = 15

X = 15:5

X =3

5 . x-7 = 210 :14

x - 7 =15

x=15+7

x=22

a: =17-70-163+246

=-43-163+246

=246-206

=40

2:

a: =4+3/8+5+2/3

=9+3/8+2/3

=216/24+9/24+16/24

=216/24+25/24

=241/24

b; =2+3/8+1+1/4+3+6/7

=6+3/8+1/4+6/7

=6+5/8+6/7

=419/56

c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)

=6+3/8-1/4+1/3

=6+1/8+1/3

=6+11/24

=155/24

d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)

=3+13+5/6

=16+5/6

=101/6

e: =3+1/2+4+5/7-5-5/14

=3+4-5+1/2+5/7-5/14

=2+7/14+10/14-5/14

=2+12/14

=2+6/7=20/7

f: =9/2+1/2:11/2

=9/2+1/11

=99/22+2/22=101/22

2:

a: =4+3/8+5+2/3

=9+3/8+2/3

=216/24+9/24+16/24

=216/24+25/24

=241/24

b; =2+3/8+1+1/4+3+6/7

=6+3/8+1/4+6/7

=6+5/8+6/7

=419/56

c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)

=6+3/8-1/4+1/3

=6+1/8+1/3

=6+11/24

=155/24

d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)

=3+13+5/6

=16+5/6

=101/6

e: =3+1/2+4+5/7-5-5/14

=3+4-5+1/2+5/7-5/14

=2+7/14+10/14-5/14

=2+12/14

=2+6/7=20/7

f: =9/2+1/2:11/2

=9/2+1/11

=99/22+2/22=101/22

(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20)*(21*4+6-84)=330

330 nha