1- 1/3[x- 1/3+x/3]= x/2- 1/2[2x- 10/3+7x/3]
1- 1/3[4x/3- 1/3]= x/2- 1/2[ 13x/3- 10/3]
1-4x/9- 1/9 = x/2- 13x/6+ 10/6
4x/9-x/2+ 13/6 = 10/6-4- 1/9
8x/ 18-9x/ 18+39x/ 18 = 30/ 18- 18/ 18-2/ 18
38x/ 18= 18/ 10
x = 10/ 18÷38/ 18
x = 10/ 18× 18/38
x=5/ 19
(5x2-2x+3)+(3x2+5x+2)
x2y +2xy2
–y3+3xy 2
–4x2y-x3
3ab-4ab+8ab-7ab+ab=______。
7x-(5x-5y)-y=______。
23 a3 BC 2- 15 ab2c+8 ABC-24 a3 BC 2-8 ABC = _ _ _ _ _ _。
-7x 2+6x+ 13 x2-4x-5x 2 = _ _ _ _ _ _。
2y+(-2y+5)-(3y+2)=______。
1.3/7 × 49/9 - 4/3
2.8/9 × 15/36 + 1/27
3. 12× 5/6 – 2/9 ×3
4.8× 5/4 + 1/4
5.6÷ 3/8 – 3/8 ÷6
6.4/7 × 5/9 + 3/7 × 5/9
7.5/2 -( 3/2 + 4/5 )
8.7/8 + ( 1/8 + 1/9 )
9.9 × 5/6 + 5/6
10.3/4 × 8/9 - 1/3
0. 12χ+ 1.8×0.9=7.2 (9-5χ)×0.3= 1.02 6.4χ-χ=28+4.4
1 1.7 × 5/49 + 3/ 14
12.6 ×( 1/2 + 2/3 )
13.8 × 4/5 + 8 × 1 1/5
14.3 1 × 5/6 – 5/6
15.9/7 - ( 2/7 – 10/2 1 )
16.5/9 × 18 – 14 × 2/7
17.4/5 × 25/ 16 + 2/3 × 3/4
18. 14 × 8/7 – 5/6 × 12/ 15
19. 17/32 – 3/4 × 9/24
20.3 × 2/9 + 1/3
2 1.5/7 × 3/25 + 3/7
22.3/ 14 ×× 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24.9/22 + 1/ 1 1 ÷ 1/2
25.5/3 × 1 1/5 + 4/3
26.45 × 2/3 + 1/3 × 15
27.7/ 19 + 12/ 19 × 5/6
28. 1/4 + 3/4 ÷ 2/3
29.8/7 × 2 1/ 16 + 1/2
30. 10 1 × 1/5 – 1/5 × 2 1
3 1.50+ 160÷40 (58+370)÷(64-45)
32. 120- 144÷ 18+35
33.347+45×2-4 160÷52
34(58+37)÷(64-9×5)
35.95÷(64-45)
36. 178- 145÷5×6+42 420+580-64×2 1÷28
37.8 12-700÷(9+3 1× 1 1) ( 136+64)×(65-345÷23)
38.85+ 14×( 14+208÷26)
39.(284+ 16)×(5 12-8208÷ 18)
40. 120-36×4÷ 18+35
4 1.(58+37)÷(64-9×5)
42.(6.8-6.8×0.55)÷8.5
43.0. 12× 4.8÷0. 12×4.8
44.(3.2× 1.5+2.5)÷ 1.6 (2)3.2×( 1.5+2.5)÷ 1.6
45.6- 1.6÷4= 5.38+7.85-5.37=
46.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=
47.6.5×(4.8- 1.2×4)= 0.68× 1.9+0.32× 1.9
48. 10. 15- 10.75×0.4-5.7
49.5.8×(3.87-0. 13)+4.2×3.74
50.32.52-(6+9.728÷3.2)×2.5
5 1.-5+58+ 13+90+78-(-56)+50
52.-7*2-57/(3
53.(-7)*2/( 1/3)+79/(3+6/4)
54. 123+456+789+98/(-4)
55.369/33-(-54-3 1/ 15.5)
56.39+{3x[42/2x(3x8)]}
57.9x8x7/5x(4+6)
58. 1 1x 22/(4+ 12/2)
59.94+(-60)/ 10
( 1)23+(-73)
(2)(-84)+(-49)
(3)7+(-2.04)
(4)4.23+(-7.57)
(5)(-7/3)+(-7/6)
(6)9/4+(-3/2)
(7)3.75+(2.25)+5/4
(8)-3.75+(+5/4)+(- 1.5)
(9)(- 17/4)+(- 10/3)+(+ 13/3)+( 1 1/3)
( 10)(- 1.8)+(+0.2)+(- 1.7)+(0. 1)+(+ 1.8)+(+ 1.4)
( 1 1)(+ 1.3)- (+ 17/7)
( 12)(-2)- (+2/3)
( 13)| (-7.2)-(-6.3)+( 1. 1)|
( 14)|(-5/4)-(-3/4)|-| 1-5/4-|-3/4|)
( 15)(-2/ 199)*(-7/6-3/2+8/3)
( 16)4a)*(-3b)*(5c)* 1/6
1)23+(-73)
(2)(-84)+(-49)
(3)7+(-2.04)
(4)4.23+(-7.57)
(5)(-7/3)+(-7/6)
(6)9/4+(-3/2)
(7)3.75+(2.25)+5/4
(8)-3.75+(+5/4)+(- 1.5)
(9)(- 17/4)+(- 10/3)+(+ 13/3)+( 1 1/3)
( 10)(- 1.8)+(+0.2)+(- 1.7)+(0. 1)+(+ 1.8)+(+ 1.4)
( 1 1)(+ 1.3)-(+ 17/7)
( 12)(-2)-(+2/3)
( 13)|(-7.2)-(-6.3)+( 1. 1)|
( 14)|(-5/4)-(-3/4)|-| 1-5/4-|-3/4|)
( 15)(-2/ 199)*(-7/6-3/2+8/3)
( 16)4a)*(-3b)*(5c)* 1/6
There are still 50 questions, but there are no answers.
1.3/7 × 49/9 - 4/3
2.8/9 × 15/36 + 1/27
3. 12× 5/6 – 2/9 ×3
4.8× 5/4 + 1/4
5.6÷ 3/8 – 3/8 ÷6
6.4/7 × 5/9 + 3/7 × 5/9
7.5/2 -( 3/2 + 4/5 )
8.7/8 + ( 1/8 + 1/9 )
9.9 × 5/6 + 5/6
10.3/4 × 8/9 - 1/3
0. 12χ+ 1.8×0.9=7.2 (9-5χ)×0.3= 1.02 6.4χ-χ=28+4.4
1 1.7 × 5/49 + 3/ 14
12.6 ×( 1/2 + 2/3 )
13.8 × 4/5 + 8 × 1 1/5
14.3 1 × 5/6 – 5/6
15.9/7 - ( 2/7 – 10/2 1 )
16.5/9 × 18 – 14 × 2/7
17.4/5 × 25/ 16 + 2/3 × 3/4
18. 14 × 8/7 – 5/6 × 12/ 15
19. 17/32 – 3/4 × 9/24
20.3 × 2/9 + 1/3
2 1.5/7 × 3/25 + 3/7
22.3/ 14 ×× 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24.9/22 + 1/ 1 1 ÷ 1/2
25.5/3 × 1 1/5 + 4/3
26.45 × 2/3 + 1/3 × 15
27.7/ 19 + 12/ 19 × 5/6
28. 1/4 + 3/4 ÷ 2/3
29.8/7 × 2 1/ 16 + 1/2
30. 10 1 × 1/5 – 1/5 × 2 1
3 1.50+ 160÷40 (58+370)÷(64-45)
32. 120- 144÷ 18+35
33.347+45×2-4 160÷52
34(58+37)÷(64-9×5)
35.95÷(64-45)
36. 178- 145÷5×6+42 420+580-64×2 1÷28
37.8 12-700÷(9+3 1× 1 1) ( 136+64)×(65-345÷23)
38.85+ 14×( 14+208÷26)
39.(284+ 16)×(5 12-8208÷ 18)
40. 120-36×4÷ 18+35
4 1.(58+37)÷(64-9×5)
42.(6.8-6.8×0.55)÷8.5
43.0. 12× 4.8÷0. 12×4.8
44.(3.2× 1.5+2.5)÷ 1.6 (2)3.2×( 1.5+2.5)÷ 1.6
45.6- 1.6÷4= 5.38+7.85-5.37=
46.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=
47.6.5×(4.8- 1.2×4)= 0.68× 1.9+0.32× 1.9
48. 10. 15- 10.75×0.4-5.7
49.5.8×(3.87-0. 13)+4.2×3.74
50.32.52-(6+9.728÷3.2)×2.5
5 1.-5+58+ 13+90+78-(-56)+50
52.-7*2-57/(3
53.(-7)*2/( 1/3)+79/(3+6/4)
54. 123+456+789+98/(-4)
55.369/33-(-54-3 1/ 15.5)
56.39+{3x[42/2x(3x8)]}
57.9x8x7/5x(4+6)
58. 1 1x 22/(4+ 12/2)
59.94+(-60)/ 10
1.
a^3-2b^3+ab(2a-b)
=a^3+2a^2b-2b^3-ab^2
=a^2(a+2b)-b^2(2b+a)
=(a+2b)(a^2-b^2)
=(a+2b)(a+b)(a-b)
2.
(x^2+y^2)^2-4y(x^2+y^2)+4y^2
=(x^2+y^2-2y)^2
3.
(x^2+2x)^2+3(x^2+2x)+x^2+2x+3
=(x^2+2x)^2+4(x^2+2x)+3
=(x^2+2x+3)(x^2+2x+ 1)
=(x^2+2x+3)(x+ 1)^2
4.
(a+ 1)(a+2)+(2a+ 1)(a-2)- 12
=a^2+3a+2+2a^2-3a-2- 12
=3a^2- 12
=3(a+2)(a-2)
5.
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2
=[x(y+z)-y(x-z)]^2
=(xz+yz)^2
=z^2(x+y)^2
6.
3(a+2)^2+28(a+2)-20
=[3(a+2)-2][(a+2)+ 10]
=(3a+4)(a+ 12)
7.
(a+b)^2-(b-c)^2+a^2-c^2
=(a+b)^2-c^2+a^2-(b-c)^2
=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)
=(a+b-c)(a+b+c+a-b+c)
=2(a+b-c)(a+c)
8.
x(x+ 1)(x^2+x- 1)-2
=(x^2+x)(x^2+x- 1)-2
=(x^2+x)^2-(x^2+x)-2
=(x^2+x-2)(x^2+x+ 1)
=(x+2)(x- 1)(x^2+x+ 1)
9x^2(x- 1)^2-3(x^2-x)-56
=9x^2(x- 1)^2-3x(x- 1)-56
=[3x(x- 1)-8][3x(x- 1)+7]
=(3x^2-3x-8)(3x^2-3x+7)
32.52-(6+9.728÷3.2)×2.5
5.
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2
=[x(y+z)-y(x-z)]^2
=(xz+yz)^2
=z^2(x+y)^2
6.
3(a+2)^2+28(a+2)-20
=[3(a+2)-2][(a+2)+ 10]
=(3a+4)(a+ 12)
7.
(a+b)^2-(b-c)^2+a^2-c^2
=(a+b)^2-c^2+a^2-(b-c)^2
=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)
=(a+b-c)(a+b+c+a-b+c)
=2(a+b-c)(a+c)
8.
x(x+ 1)(x^2+x- 1)-2
=(x^2+x)(x^2+x- 1)-2
=(x^2+x)^2-(x^2+x)-2
=(x^2+x-2)(x^2+x+ 1)
=(x+2)(x- 1)(x^2+x+ 1)
9.
9x^2(x- 1)^2-3(x^2-x)-56
=9x^2(x- 1)^2-3x(x- 1)-56
=[3x(x- 1)-8][3x(x- 1)+7]
=(3x^2-3x-8)(3x^2-3x+7)
Rational number exercise
Exercise1(level b)
(1) Calculation problem:
( 1)23+(-73) (2)(-84)+(-49) (3)7+(-2.04) (4)4.23+(-7.57) (5)(-7/3)+(-7/6) (6)9/4+(-3/2) (7)3.75+(2.25)+5/4 (8)-3.75+(+5/4)+(- 1.5)
5.
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2
=[x(y+z)-y(x-z)]^2
=(xz+yz)^2
=z^2(x+y)^2
6.
3(a+2)^2+28(a+2)-20
=[3(a+2)-2][(a+2)+ 10]
=(3a+4)(a+ 12)
7.
(a+b)^2-(b-c)^2+a^2-c^2
=(a+b)^2-c^2+a^2-(b-c)^2
=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)
=(a+b-c)(a+b+c+a-b+c)
=2(a+b-c)(a+c)
8.
x(x+ 1)(x^2+x- 1)-2
=(x^2+x)(x^2+x- 1)-2
=(x^2+x)^2-(x^2+x)-2
=(x^2+x-2)(x^2+x+ 1)
=(x+2)(x- 1)(x^2+x+ 1)
9.
9x^2(x- 1)^2-3(x^2-x)-56
=9x^2(x- 1)^2-3x(x- 1)-56
=[3x(x- 1)-8][3x(x- 1)+7]
=(3x^2-3x-8)(3x^2-3x+7)
(2) Calculate by a simple method:
( 1)(- 17/4)+(- 10/3)+(+ 13/3)+( 1 1/3) (2)(- 1.8)+(+0.2)+(- 1.7)+(0. 1)+(+ 1.8)+(+ 1.4)
(3) It is known that X =+ 17 (3/4), Y =-9 (5/ 1 1) and Z =-2.25.
Find the value of: (-x)+(-y)+z.
(4) if ">" and "0" are used, then a-ba (c) if ba (d) if a.