December 8, 2008

Here's another set of chemistry reviewer questions.

Stoichiometry Problems

1.Given the equation: 2C2H6 + 7O2 --> 4CO2 + 6H2O, how many g of C2H6 will be needed to produce 3.13 mol of CO2? Answer: 47.06 g of C2H6
2.Based on the following equation: 2ZnS + 3O2 --> 2ZnO + 2SO2, how many mol of ZnS is needed to produce 7.95 g of ZnO? Answer: 0.1 mol of ZnS
3. Given the equation: 2KClO3 + 2KCl --> 3O2 + H2O, how many g of KCl is required so that 3.73 g of H2O is produced? Answer: 30.87 g of KCl
4. Given the equation: 2KClO3 --> 2KCl + 3O2, calculate the weight of KClO3 necessary to produce 1.57 g of KCl. Answer: 2.58 g of KClO3
5.Based on the following equation: 3KClO --> 2KCl + KClO3, calculate the amount of KClO3 that can be produced from the decomposition of 7.62 g of KClO. Answer: 3.44 g of KClO3


Percent Composition Problems

1.Calculate the percentage composition of AlCl3. Solution: Al = 20.24% Cl = 79.76%
2.Calculate the amount of S contained in 2.88 g of FeSO4.H2O. Solution: 0.54 g of S
3.Calculate the percentage composition of BaC2O4.2H2O. Solution: H = 1.54% O = 36.73% Ba = 52.54% C = 9.19%
4.Calculate the amount of Ba contained in 3.76 g of BaI2. Solution: 1.32 g of Ba
5.Determine the weight of KSCN that will contain 7.69 g of C. Solution: 62.22 g of KSCN
6. A laboratory sample was found to contain 92.06 % LiNO3. Compute the amount in g of Li present in 2.72 g of the sample. Solution: 0.25 g
7.A laboratory sample was found to contain 18.83 % PbC2O4. Compute the amount in g of O present in 0.56 g of the sample. Solution: 0.023 g
8.A sample mixture containing Ba(CH3COO)2 has 1.42 % O. Calculate the percentage of Ba(CH3COO)2 in the sample. Solution: 5.67 %
9. A sample mixture containing NH4HCO3 has 3.23 % C. Calculate the percentage of NH4HCO3 in the sample. Solution: 21.26 %
10. Determine the weight of Cd(NO3)2 that will contain 0.84 g of O. Solution: 2.07 g


Limiting Reagent Problems

1. Based on the following equation: NaCl + AgNO3 --> AgCl + NaNO3, calculate the weight of AgCl which can be produced by the reaction of 7.45 g of NaCl with 7.48 g of AgNO3.Answer: AgNO3 is the limiting reagent; 6.31 g of AgCl can be produced. The weight of excess NaCl is 4.88 g.
2.Given the balanced equation: 2SO2 + O2 --> 2SO3, calculate the weight of SO3 which can be produced by the reaction of 7.07 g of SO2 with 7.09 g of O2. Answer: SO2 is the limiting reagent; 8.84 g of SO3 can be produced. The weight of excess O2 is 5.32 g.


Formula Calculation Problems

1. What is the formula weights of the following compounds: (a) KMnO4, (b) KI, (c) CoCl2, (d) Sr(OH)2, (e) (NH4)2S, (f) CdCl2.H2O, (g) B2O3. Answer: (a) 158.0339, (b) 166.0028, (c) 129.8392, (d) 121.6346, (e) 68.1366, (f) 201.3312, (g) 69.6182
2.Calculate the number of moles of AlCl3 that will contain 6.02 x 1023 atoms of Cl. Answer: 0.33 mol
3.Calculate the number of moles of PbC2O4 that will contain 6.02 x 1023 atoms of O. Answer: 0.25 mol
4. How many number of O atoms are contained in 84.94 g of KNO3? Answer: 1.52 x 1024 atoms
5.How many number of Na atoms are contained in 33.99 g of Na3PO4? Answer: 3.74 x 1023 atoms
6.Determine the number of molecules of KBrO3 present in 36.77 g of KBrO3. Answer: 1.33 x 1023 molecules
7.Determine the number of molecules of SbCl3 present in 60.83 g of SbCl3. Answer: 1.61 x 1023 molecules
8.Calculate the weight in grams of 5.12 mol NaCl. Answer: 299.23 g
9. Calculate the weight in grams of 0.85 mol CdCl2.H2O. Answer: 171.13 g
10. Calculate the number of O atoms in 2.44 x 10-4 mol of KCH3COO. Answer: 2.94 x 1020 atoms

November 27, 2008

Wait...there is more! Tutor Partner has more to offer. Starting today, I'm adding problems on Chemistry here on my blog. The answer is provided for every problem. So stop working on those problems like you're doing homeworks all over again. Take a break; and then take your pick. Stoichiometry Problems 1. Based on the following equation: Na2CO3 + Ba(OH)2 --> BaCO3 + 2NaOH, calculate the number of mol of Na2CO3 required to yield 3.95 mol of NaOH. Answer: 1.98 mol of Na2CO3 2. Based on the following equation: 4FeS2 + 11O2 --> 2Fe2O3 + 8SO2, how many mol of O2 will be needed to produce 7.29 mol of SO2? Answer: 10.02 mol of O2 3. According to the equation: 4Fe + 3O2 --> 2Fe2O3, calculate the mass of O2 required so that 7.16 mol of Fe2O3 will be produced. Answer: 343.67 g of O2 4. According to the equation: 4Fe + 3O2 --> 2Fe2O3, how many g of Fe will be needed to produce 1.75 mol of Fe2O3? Answer: 195.46 g of Fe 5. Given the equation: 4Fe + 3O2 --> 2Fe2O3, how many mol of O2 is needed to produce 8.9 g of Fe2O3? Answer: 0.08 mol of O2 6. For the equation: NaHCO3 + HCl --> NaCl + CO2 + H2O, how many g of NaHCO3 is required so that 1.99 g of NaCl is produced? Answer: 2.86 g of NaHCO3 7. Based on the following equation: CaCO3 --> CaO + CO2, calculate the weight of CaCO3 necessary to produce 7.96 g of CO2. Answer:18.1 g of CaCO3 8. Based on the following equation: 4KClO3 --> 3KClO4 + KCl, calculate the amount of KClO4 that can be produced from the decomposition of 1.68 g of KClO3. Answer: 1.42 g of KClO4 9. According to the equation: 2KClO3 --> 2KCl + 3O2, calculate the number of mol of KClO3 required to yield 5.25 mol of O2. Answer: 3.5 mol of KClO3 10. Based on the following equation: Ni + 4CO --> Ni(CO)4, how many g of Ni will be needed to produce 4.34 mol of Ni(CO)4? Answer: 254.76 g of Ni Percent Composition Problems Calculate the percent composition of the following compounds: 1. PbBr2 Solution: Pb = 56.46% Br = 43.54% 2. FeCl2.4H2O Solution: H = 4.06% O = 32.19% Fe = 28.09% Cl = 35.66% 3. CuSO4 Solution: Cu = 39.81% S = 20.09% O = 40.1% 4. PbC2O4 Solution: Pb = 70.19% C = 8.14% O = 21.68% 5. MgCO3 Solution: Mg = 28.83% C = 14.25% O = 56.93% Limiting Reagent Problems 1. Based on the following equation: Ni + 4CO --> Ni(CO)4, calculate the weight of Ni(CO)4 which can be produced by the reaction of 1.81 g of Ni with 5.94 g of CO. Answer: Ni is the limiting reagent; 5.26 g of Ni(CO)4 can be produced. The weight of excess CO is 2.49 g. 2. Based on the following equation: Cu2S + O2 --> 2Cu + SO2, calculate the weight of Cu which can be produced by the reaction of 4.7 g of Cu2S with 1.83 g of O2. Answer: Cu2S is the limiting reagent; 3.75 g of Cu can be produced. The weight of excess O2 is 0.89 g. 3. Given the balanced equation: CaO + 2HCl --> CaCl2 + H2O, calculate the weight of H2O which can be produced by the reaction of 4.26 g of CaO with 4.8 g of HCl. Answer: HCl is the limiting reagent; 1.19 g of H2O can be produced. The weight of excess CaO is 0.57 g. 4. For the reaction: Ca(HCO3)2 + 2HCl --> CaCl2 + 2CO2 + 2H2O, calculate the weight of H2O which can be produced by the reaction of 9.92 g of Ca(HCO3)2 with 8.44 g of HCl. Answer: Ca(HCO3)2 is the limiting reagent; 2.2 g of H2O can be produced. The weight of excess HCl is 3.98 g. 5. According to the equation: CaO + 2HCl --> CaCl2 + H2O, calculate the weight of CaCl2 which can be produced by the reaction of 3 g of CaO with 6.02 g of HCl. Answer: CaO is the limiting reagent; 5.94 g of CaCl2 can be produced. The weight of excess HCl is 2.12 g.

April 7, 2008

Analytic Geometry: Distance Between Two Points

Given two points, their distance and the slope of the line joining them are solved.

ProblemGiven PointsDistanceSlope
1P1(2,3) P2(-3,8)sqrt of 501/-1
2P1(7,1) P2(-5,-7)sqrt of 208-2/-3
3P1(9,4) P2(2,7)sqrt of 583/-7
4P1(7,-6) P2(-9,-9)sqrt of 265-3/-16
5P1(2,1) P2(9,3)sqrt of 532/7
6P1(-7,1) P2(-4,-9)sqrt of 109-10/3
7P1(-4,5) P2(2,-4)sqrt of 117-3/2
8P1(4,6) P2(5,-9)sqrt of 226-15/1
9P1(9,8) P2(1,5)sqrt of 73-3/-8
10P1(5,7) P2(7,6)sqrt of 5-1/2
11P1(1,6) P2(2,8)sqrt of 52/1
12P1(5,1) P2(7,2)sqrt of 51/2
13P1(-3,2) P2(-6,-8)sqrt of 109-10/-3
14P1(7,9) P2(8,3)sqrt of 37-6/1
15P1(7,8) P2(-9,-4)sqrt of 400-3/-4
16P1(1,8) P2(-7,9)sqrt of 651/-8
17P1(5,9) P2(6,-7)sqrt of 257-16/1
18P1(2,-7) P2(-7,-5)sqrt of 852/-9
19P1(-3,9) P2(6,-4)sqrt of 250-13/9
20P1(4,3) P2(7,1)sqrt of 13-2/3
21P1(-5,6) P2(1,-2)sqrt of 100-4/3
22P1(8,3) P2(-5,8)sqrt of 1945/-13
23P1(5,5) P2(-7,-4)sqrt of 225-3/-4
24P1(2,8) P2(3,-6)sqrt of 197-14/1
25P1(6,3) P2(8,8)sqrt of 295/2
26P1(4,9) P2(7,8)sqrt of 10-1/3
27P1(-7,5) P2(-8,-3)sqrt of 65-8/-1
28P1(6,5) P2(3,8)sqrt of 181/-1
29P1(9,7) P2(3,3)sqrt of 52-2/-3
30P1(8,-4) P2(-3,-9)sqrt of 146-5/-11
31P1(-8,9) P2(6,-6)sqrt of 421-15/14
32P1(5,9) P2(-1,7)sqrt of 40-1/-3
33P1(9,1) P2(-5,-9)sqrt of 296-5/-7
34P1(2,4) P2(7,1)sqrt of 34-3/5
35P1(8,9) P2(2,3)sqrt of 721/1
36P1(2,9) P2(7,-2)sqrt of 146-11/5
37P1(4,7) P2(2,4)sqrt of 13-3/-2
38P1(-4,3) P2(-1,-7)sqrt of 109-10/3
39P1(7,5) P2(1,9)sqrt of 522/-3
40P1(7,-2) P2(-5,-3)sqrt of 145-1/-12
41P1(3,5) P2(2,9)sqrt of 174/-1
42P1(1,6) P2(4,-9)sqrt of 234-5/1
43P1(4,1) P2(5,5)sqrt of 174/1
44P1(8,-7) P2(-7,-9)sqrt of 229-2/-15
45P1(1,9) P2(-3,7)sqrt of 20-1/-2
46P1(2,2) P2(-7,-8)sqrt of 181-10/-9
47P1(9,2) P2(5,6)sqrt of 321/-1
48P1(1,8) P2(7,1)sqrt of 85-7/6
49P1(-9,8) P2(4,-2)sqrt of 269-10/13
50P1(-8,1) P2(-5,-6)sqrt of 58-7/3

Analytic Geometry: Equation of a Line

Given two points, the equation of a line whose points are equidistant from the two given points is determined.

ProblemGiven PointsEquation of the Line
1P1(6,9) P2(3,-8)3x+17y-22=0
2P1(1,-2) P2(-3,-1)8x-2y+5=0
3P1(5,9) P2(-5,-7)5x+8y-8=0
4P1(-3,3) P2(-9,-3)1x+1y+6=0
5P1(6,2) P2(-7,9)13x-7y+45=0
6P1(-6,7) P2(8,-7)1x-1y-1=0
7P1(5,5) P2(6,-5)2x-20y-11=0
8P1(1,9) P2(-3,-5)2x+7y-12=0
9P1(5,-8) P2(-3,-8)1x-0y-1=0
10P1(-2,1) P2(9,-4)11x-5y-46=0
11P1(-6,3) P2(-4,-8)4x-22y-35=0
12P1(8,4) P2(-9,4)34x-0y+17=0
13P1(1,3) P2(4,-1)6x-8y-7=0
14P1(-5,2) P2(7,-3)24x-10y-29=0
15P1(5,1) P2(-8,-8)13x+9y+51=0
16P1(3,-7) P2(-1,-1)2x-3y-14=0
17P1(-3,7) P2(-1,-8)4x-30y-7=0
18P1(4,7) P2(-5,5)18x+4y-15=0
19P1(3,1) P2(-7,-9)1x+1y+6=0
20P1(7,8) P2(-4,9)11x-1y-8=0
21P1(-6,9) P2(-3,-7)6x-32y+59=0
22P1(-7,8) P2(5,-5)24x-26y+63=0
23P1(4,8) P2(1,-2)6x+20y-75=0
24P1(5,-7) P2(-5,-5)5x-1y-6=0
25P1(-8,5) P2(-1,-5)14x-20y+63=0
26P1(6,7) P2(-3,6)9x+1y-20=0
27P1(-5,8) P2(3,-7)16x-30y+31=0
28P1(8,2) P2(-7,-8)6x+4y+9=0
29P1(6,-9) P2(-5,-6)11x-3y-28=0
30P1(3,5) P2(7,-3)1x-2y-3=0

Greatest Common Divisor (GCD)

Solution SetGiven NumbersGCD
121,18,33
227,18,123
350,10,3010
4527,62,89931
5475,361,43719
630,36,546
7744,961,89931
866,44,5511
940,80,728
1056,80,328
11285,209,51319
12348,725,37729
1345,90,729
14620,217,43431
1530,60,5010
16116,580,66729
1724,8,568
1815,18,273
19266,437,24719
2056,98,7014
21299,26,24713
2249,28,707
2324,6,186
2470,10,5010
2512,20,284
26551,38,58919
2740,16,728
2845,40,255
2956,48,88
3014,4,182
3139,299,37713
3215,6,273
3377,66,1111
3472,56,408
35391,85,11917
36551,209,36119
3781,54,639
3840,80,488
39558,713,58931
4065,143,16913
4112,21,153
4287,203,55129
43589,93,71331
4435,30,205
45221,187,32317
4642,14,7014
47114,437,58919
4863,70,147
4981,36,909
5015,27,93

Least Common Multiple (LCM)

Solution SetGiven NumbersLCM
12,21,9126
218,23,135382
35,14,231610
424,15,3120
519,9,233933
68,24,224
722,21,152310
85,14,13910
919,2,16304
1023,18,212898
1121,19,239177
127,3,5105
138,13,14728
1418,6,1236
1515,7,21105
1615,10,530
1723,22,82024
189,6,590
1911,6,4132
2024,22,133432
2123,22,246072
228,11,12264
2313,11,101430
2423,12,6276
2522,12,131716
2620,16,191520
2713,6,171326
2817,18,223366
2915,7,191995
3024,4,22264
3117,8,91224
322,10,330
3313,24,175304
3421,9,13819
358,3,17408
3623,3,4276
379,16,5720
3813,8,10520
393,5,8120
4013,10,221430
4116,3,21336
4221,16,14336
433,19,17969
4419,15,133705
4524,3,19456
4623,4,9828
4722,23,73542
4811,13,182574
496,19,221254
502,10,990

Algebra: Multiplication of Polynomials



ProblemGiven PolynomialsSolution
18x+6 and 7x+956x2+114x+54
27x+12 and 1x-27x2-2x-24
31x-14 and 2x+32x2-25x-42
48x-8 and 6x-1348x2-152x+104
55x-3 and 7y-1435xy-70x-21y+42
64x4+4 and 4x2+1416x6+56x4+16x2+56
72x+1 and 5x2-1310x3-26x1+5x2-13
86x3-10 and 5y2+1430x3y2+84x3-50y2-140
91x-12 and 7y2-127xy2-12x-84y2+144
108x2-11 and 6y3-1448x2y3-112x2-66y3+154
112x2+7y4 and 3x2+7y36x4+14x2y3+21x2y4+49y7
125x2-5y4 and 4x4+5y220x6+25x2y2-20x4y4-25y6
133x4+4y2 and 7x2-8y421x6-24x4y4+28x2y2-32y6
143x2-7y3 and 7x-1y21x3-3x2y-49xy3+7y4
156x+2y3 and 4x24x2+8xy3
163x3+5y4 and 2x6x4+10xy4
175x4-3y and 4x420x8-12x4y
186x+8 and 2x+312x2+34x+24
191x+1 and 4x-74x2-3x-7
201x-14 and 4x+114x2-45x-154
213x-8 and 7x-821x2-80x+64
223x-11 and 5y-315xy-9x-55y+33
234x4+11 and 4x2+116x6+4x4+44x2+11
246x+4 and 5x2-530x3-30x1+20x2-20
258x3-13 and 4y2+332x3y2+24x3-52y2-39
265x-14 and 1y2-145xy2-70x-14y2+196
271x2-10 and 4y3-84x2y3-8x2-40y3+80
284x4+2y4 and 8x2+8y232x6+32x4y2+16x2y4+16y6
295x2-2y and 7x4+4y35x6+20x2y-14x4y-8y2
306x4+2y2 and 1x-1y6x5-6x4y+2xy2-2y3
311x-8y4 and 3x3-2y23x4-2xy2-24x3y4+16y6
321x+3y2 and 7x37x4+21x3y2
332x2+4y and 5x310x5+20x3y
341x-1y3 and 6x6x2-6xy3
358x+14 and 7x+256x2+114x+28
365x+13 and 3x-1015x2-11x-130
377x-7 and 3x+1121x2+56x-77
386x-12 and 5x-730x2-102x+84
393x-2 and 3y-89xy-24x-6y+16
408x4+4 and 1x2+78x6+56x4+4x2+28
418x+6 and 5x2-140x3-8x1+30x2-6
423x3-1 and 3y2+99x3y2+27x3-3y2-9
437x-2 and 8y2-156xy2-7x-16y2+2
444x2-3 and 6y3-124x2y3-4x2-18y3+3
456x+4y3 and 2x+6y312x2+44x1y3+24y6
466x4-6y4 and 2x4+8y12x8+48x4y-12x4y4-48y5
473x2+2y and 3x2-4y39x4-12x2y3+6x2y-8y4
483x2-1y and 5x3-2y15x5-6x2y-5x3y+2y2
492x2+1y2 and 5x310x5+5x3y2
503x3+2y3 and 4x212x5+8x2y3

Analytic Geometry: Equation and Slope of a Line

Given two points each for line P1P2 and line AB, the equations and slopes of the lines are determined. Through their slopes,

it's determined whether the lines are parallel or perpendicular to each other.



ProblemGiven PointsEquations of the LineSlopes of the Line
1P1(0,8) P2(2,3); A(11,3) B(9,8)5x+2y-16=0, 5x+2y-61=0parallel lines: m1=-5/2 m2=5/-2
2P1(7,0) P2(0,8); A(1,0) B(9,7)8x+7y-56=0, 7x-8y-7=0perpendicular lines: m1=8/-7 m2=7/8
3P1(5,5) P2(1,0); A(3,8) B(8,4)5x-4y-5=0, 4x+5y-52=0perpendicular lines: m1=-5/-4 m2=-4/5
4P1(-4,7) P2(0,8); A(11,7) B(7,6)x-4y+32=0, x-4y+17=0parallel lines: m1=1/4 m2=-1/-4
5P1(-8,0) P2(2,9); A(4,2) B(14,11)9x-10y+72=0, 9x-10y-16=0parallel lines: m1=9/10 m2=9/10
6P1(9,9) P2(8,2); A(9,6) B(2,7)7x-y-54=0, x+7y-51=0perpendicular lines: m1=-7/-1 m2=1/-7
7P1(9,5) P2(8,1); A(8,7) B(4,8)4x-y-31=0, x+4y-36=0perpendicular lines: m1=-4/-1 m2=1/-4
8P1(-7,0) P2(4,8); A(12,12) B(1,4)8x-11y+56=0, 8x-11y+36=0parallel lines: m1=8/11 m2=-8/-11
9P1(-8,0) P2(4,6); A(4,6) B(14,11)x-2y+8=0, x-2y+8=0parallel lines: m1=1/2 m2=1/2
10P1(-9,5) P2(9,8); A(10,2) B(4,1)x-6y+39=0, x-6y+2=0parallel lines: m1=1/6 m2=-1/-6
11P1(3,1) P2(2,3); A(6,7) B(8,8)2x+y-7=0, x-2y+8=0perpendicular lines: m1=2/-1 m2=1/2
12P1(2,3) P2(1,1); A(2,6) B(4,5)2x-y-1=0, x+2y-14=0perpendicular lines: m1=-2/-1 m2=-1/2
13P1(-2,1) P2(2,7); A(12,13) B(10,10)3x-2y+8=0, 3x-2y-10=0parallel lines: m1=3/2 m2=-3/-2
14P1(9,1) P2(8,3); A(4,7) B(6,8)2x+y-19=0, x-2y+10=0perpendicular lines: m1=2/-1 m2=1/2
15P1(8,3) P2(4,0); A(1,4) B(4,0)3x-4y-12=0, 4x+3y-16=0perpendicular lines: m1=-3/-4 m2=-4/3
16P1(-8,1) P2(2,6); A(8,3) B(2,0)x-2y+10=0, x-2y-2=0parallel lines: m1=1/2 m2=-1/-2
17P1(-4,4) P2(7,8); A(1,7) B(12,11)4x-11y+60=0, 4x-11y+73=0parallel lines: m1=4/11 m2=4/11
18P1(4,6) P2(1,1); A(4,6) B(9,3)5x-3y-2=0, 3x+5y-42=0perpendicular lines: m1=-5/-3 m2=-3/5
19P1(4,1) P2(5,3); A(4,5) B(2,6)2x-y-7=0, x+2y-14=0perpendicular lines: m1=2/1 m2=1/-2
20P1(-5,9) P2(4,4); A(4,13) B(13,8)5x+9y-56=0, 5x+9y-137=0parallel lines: m1=-5/9 m2=-5/9

Algebra: Linear Equations in Two Unknown

Given two linear equations, the two equations are solved simultaneously for x and y.

ProblemGiven EquationsSolution
16x+3y = 45; 8x+4y = 60x = 14; y = -13
23x-9y = -114; 7x+4y = 84x = 4; y = 14
34x+8y = 104; 5x+y = 76x = 14; y = 6
44x+3y = 59; 2x+9y = 97x = 8; y = 9
56x+y = 21; 2x+5y = 49x = 2; y = 9
63x+3y = 30; x+3y = 14x = 8; y = 2
75x+7y = 139; 4x+5y = 104x = 11; y = 12
86x+7y = 125; 7x+4y = 100x = 8; y = 11
95x+2y = 60; x+8y = 50x = 10; y = 5
109x+y = 16; 4x+9y = -10x = 2; y = -2
11x+8y = 63; 6x+4y = 70x = 7; y = 7
128x+4y = 44; 6x+y = 31x = 5; y = 1
132x+6y = 96; 3x+6y = 102x = 6; y = 14
147x+4y = 63; 5x+8y = 117x = 1; y = 14
158x+5y = 102; 6x+8y = 102x = 9; y = 6
166x+y = 11; 5x+7y = 40x = 1; y = 5
17x+8y = 41; 8x+6y = 38x = 1; y = 5
18x+2y = 0; 5x+7y = -12x = -8; y = 4
196x+4y = 20; 6x+4y = 20x = 2; y = 2
20x+3y = 22; 6x+3y = 42x = 4; y = 6
215x+5y = 95; x+2y = 29x = 9; y = 10
225x-8y = 52; 8x+y = 97x = 12; y = 1
239x+9y = 234; 8x+y = 124x = 14; y = 12
249x+6y = 93; 8x+6y = 88x = 5; y = 8
257x+4y = 41; 5x+7y = -8x = 11; y = -9
262x+6y = -48; 7x+9y = -24x = 12; y = -12
273x+3y = 33; 7x+9y = 89x = 5; y = 6
283x+9y = 96; 3x+9y = 96x = 5; y = 9
299x+2y = 62; 5x+3y = 59x = 4; y = 13
30x+6y = 72; 7x+8y = 164x = 12; y = 10
317x+4y = 43; 8x+4y = 44x = 1; y = 9
324x+6y = 88; 3x-5y = -29x = 7; y = 10
337x+4y = 18; 6x+3y = 15x = 2; y = 1
347x+2y = 32; 8x+8y = 88x = 2; y = 9
35x+3y = 53; 4x+3y = 95x = 14; y = 13
366x+9y = 87; 2x+6y = 38x = 10; y = 3
373x+9y = 36; 4x+2y = 18x = 3; y = 3
384x+5y = 93; 6x+6y = 120x = 7; y = 13
392x+5y = 51; 8x+5y = 69x = 3; y = 9
403x+9y = 126; 5x+9y = 138x = 6; y = 12
418x+7y = 124; 2x+7y = 94x = 5; y = 12
423x+2y = 2; 7x+6y = -10x = 8; y = -11
439x+6y = 135; 8x+7y = 140x = 7; y = 12
447x+y = 34; 4x+2y = 28x = 4; y = 6
459x+6y = 33; 8x+7y = 46x = -3; y = 10
468x+y = 54; 3x+5y = -26x = 8; y = -10
474x+7y = 116; 5x+7y = 124x = 8; y = 12
482x+4y = 38; 2x+5y = 42x = 11; y = 4
495x+5y = 75; 6x-8y = -64x = 4; y = 11
509x+8y = 126; 6x+2y = 54x = 6; y = 9

Addition of Fractions

ProblemFirst NumberSecond NumberTotal
17/247/1849/72
21/205/1859/180
37/81/2411/12
47/247/22161/264
56/75/81 27/56
67/202/1529/60
73/58/91 22/45
83/141/2037/140
91/204/1519/60
101/911/2441/72
111/245/2147/168
123/57/101 3/10
134/215/16169/336
147/185/182/3
155/227/1051/55
166/74/71 3/7
174/213/10103/210
181/151/152/15
197/187/16119/144
205/147/1279/84
215/121/1031/60
227/248/21113/168
235/187/16103/144
248/94/91 1/3
255/241/2031/120
263/165/1229/48
271/145/1822/63
281/147/2059/140
298/218/2116/21
307/153/14143/210
317/127/1835/36
327/127/247/8
331/101/146/35
347/183/2252/99
355/161/2029/80
368/215/2433/56
377/187/20133/180
381/143/142/7
396/71/71
408/157/1883/90
415/245/1835/72
423/414/151 41/60
434/57/81 27/40
441/164/2185/336
451/212/211/7
465/165/1475/112
475/247/2067/120
483/107/1831/45
498/94/91 1/3
501/167/2417/48

Subtraction of Fractions

ProblemMinuendSubtrahendDifference
17/153/101/6
21/181/16-1/144
35/217/15-8/35
41/181/10-2/45
55/141/142/7
66/71/75/7
71/167/15-97/240
87/105/1631/80
97/101/2479/120
106/78/9-2/63
111/145/24-23/168
126/72/74/7
137/121/121/2
147/207/12-7/30
153/168/21-65/336
167/86/71/56
171/211/14-1/42
181/127/12-1/2
192/73/1611/112
201/311/12-7/12
212/158/15-2/5
221/241/10-7/120
233/205/14-29/140
243/145/18-4/63
255/127/10-17/60
267/242/2111/56
276/71/1583/105
283/107/16-11/80
297/247/240
307/105/1217/60
317/225/2137/462
324/217/18-25/126
333/45/4-1/2
347/241/1023/120
357/97/187/18
367/243/2241/264
375/187/24-1/72
386/711/1513/105
397/165/1823/144
407/165/149/112
415/184/151/90
427/244/2117/168
433/147/22-8/77
441/151/14-1/210
457/161/163/8
463/167/18-29/144
477/247/18-7/72
487/245/241/12
497/183/1411/63
508/97/2443/72

Multiplication of Fractions

ProblemMultiplicandMultiplierProduct
13/72/76/49
21/207/107/200
32/51/201/50
47/223/1021/220
51/122/151/90
67/181/107/180
78/91/78/63
87/247/1849/432
93/107/1021/100
101/163/203/320
111/76/76/49
123/227/1621/352
137/153/141/10
147/227/1549/330
157/221/247/528
161/31/121/36
173/205/223/88
185/247/207/96
191/157/207/300
207/227/1249/264
215/125/1625/192
223/49/1427/56
232/157/127/90
243/141/223/308
257/207/1049/200
263/107/1621/160
273/223/229/484
288/97/87/9
295/127/207/48
305/123/145/56
311/165/125/192
327/95/935/81
332/213/141/49
347/181/141/36
358/97/1828/81
361/207/227/440
375/181/151/54
381/187/107/180
391/183/101/60
408/910/2180/189
418/94/932/81
424/151/161/60
433/227/2021/440
447/167/2249/352
451/105/121/24
461/152/152/225
475/99/225/22
485/245/1425/336
491/221/121/264
505/75/825/56

Division of Fractions

ProblemDividendDivisorQuotient
13/46/77/8
25/181/215 5/6
37/91/97
41/207/101/14
51/203/147/30
65/75/223 1/7
73/203/221 1/10
81/215/124/35
95/121/125
102/217/1632/147
111/217/2020/147
121/225/2412/55
135/147/1575/98
141/141/241 5/7
157/167/221 3/8
161/225/126/55
173/105/221 8/25
185/224/1575/88
196/74/71 1/2
203/227/1624/77
215/227/1575/154
221/225/168/55
237/205/1449/50
248/91/2017 7/9
257/247/241
265/187/2050/63
273/143/161 1/7
281/163/105/24
294/711/241 19/77
305/81/74 3/8
312/157/128/35
322/211/121 1/7
332/211/242 2/7
345/88/945/64
351/123/164/9
363/58/927/40
378/211/155 5/7
381/41/41
397/911/241 23/33
401/167/189/56
415/245/147/12
423/201/152 1/4
437/811/1035/44
443/161/203 3/4
457/151/157
461/188/217/48
477/243/1035/36
487/121/1810 1/2
496/74/71 1/2
505/121/145 5/6

Addition of Decimal Numbers

ProblemFirst NumberSecond NumberTotal
10.05061.5871.6376
2390.43835.9718396.4101
30.06020.140.2002
40.0081942.8246942.8327
529.71780.007329.7251
66.8056353.6796360.4852
70.90540.04130.9467
8931.18297.5214938.7043
9584.983264.8744849.8574
1081.7623403.2804485.0427
1121.41130.020121.4314
1294.0603941.26491035.3252
130.0230.78560.8086
140.0570.17990.2369
15901.657882.5607984.2185
16601.3541823.94871425.3028
174.48580.02064.5064
188.71027.59616.3062
196.41310.72637.1394
202.75743.93886.6962
2185.41560.294585.7101
22942.22898.7778951.0067
230.2051448.9193449.1244
248.36610.05118.4172
256.5286906.484913.0126
2614.4538650.3442664.798
273.93250.01363.9461
280.04791.59941.6473
290.01712.42682.4439
300.47510.24580.7209
31256.832397.9562354.7885
32423.17920.0025423.1817
330.4330.01380.4468
3426.86610.841927.708
352.744218.936321.6805
360.1747738.0352738.2099
378.335238.570346.9055
380.6048473.8623474.4671
399.0320.03719.0691
400.48050.26490.7454
410.573694.259294.8328
4220.80313.851224.6543
430.4118479.4381479.8499
445.51130.13875.65
459.61220.01569.6278
460.08130.10250.1838
4738.15580.509538.6653
480.07320.00090.0741
498.46237.837716.3
500.089370.4226370.5116

Subtraction of Decimal Numbers

ProblemMinuendSubtrahendDifference
1418.61410.0311418.583
25.82634.19951.6268
358.30980.692957.6169
415.92320.625615.2976
573.180661.563811.6168
615.15790.000915.157
756.405530.012326.3932
80.03340.0010.0324
95.58640.4635.1234
10901.28091.6911899.5898
117.8246.09961.7244
128.64790.67117.9768
136.9110.07156.8395
149.61177.99171.62
150.01170.00860.0031
1676.590.0876.51
179.50270.78278.72
180.95690.74770.2092
194.12030.98583.1345
2067.10540.092767.0127
2161.4327.361954.0701
220.68390.26680.4171
23376.72480.646376.0788
2463.128862.15170.9771
250.4790.06520.4138
265.42960.52464.905
2777.68168.282169.3995
280.08740.03590.0515
290.09760.00950.0881
300.52730.07450.4528
310.83620.00420.832
3239.61080.893938.7169
338.92350.00988.9137
344.10350.56213.5414
35736.31374.5167731.797
36156.98210.081156.9011
373.85370.01193.8418
389.98340.41729.5662
398.97580.07838.8975
4024.88484.828620.0562
4145.40848.701936.7065
4229.97910.039729.9394
43591.432741.2007550.232
440.09390.00970.0842
454.61831.47543.1429
460.85130.0220.8293
4724.46720.009424.4578
4874.409231.762442.6468
4949.087813.567935.5199
50151.01220.0078151.0044

Multiplication of Decimal Numbers

ProblemMultiplicandMultiplierProduct
145.8880.85939.417792
20.07064.95560.34986536
30.058520.59391.20474315
45.76950.78844.5486738
50.0096772.537.416288
60.14870.04970.00739039
7573.5382915.5287525090.68264634
80.12968.88781.15185888
9459.4131553.384254231.8589304
100.0767781.92959.9739543
110.03010.02810.00084581
1213.68110.00980.13407478
138.28840.0010.0082884
140.08877.1710.6360677
150.0753336.207725.31643981
16491.774527.6509259484.9936966
170.00090.03230.00002907
182.56480.82282.11031744
190.30030.9060.2720718
20618.00015.63353481.50356335
21261.242157.036814900.41340928
2255.1606539.761729773.57922902
2358.87910.00090.05299119
2422.11715.5005121.65510855
250.39520.18910.07473232
2611.09990.32513.60857749
27869.00355.15974483.79735895
28627.11985.44973417.61477406
2993.160742.71633979.48040941
3032.97920.718923.70874688
310.0111497.10665.51788326
32670.29271.1393763.66447311
3355.339228.51821578.17437344
345.86650.03790.22234035
350.00920.09940.00091448
360.30257.08042.141821
37282.09219.18242590.28249904
3872.58640.02171.57512488
3939.82670.01960.78060332
40498.49970.065132.45233047
410.087158.02195.05370749
421.00174.54294.55062293
430.01571.28990.02025143
440.278854.161615.10025408
455.5809190.91681065.48756912
460.01140.5380.0061332
470.02511.37520.03451752
480.98010.24340.23855634
49212.296549.401110487.68062615
5095.618932.27523086.11912128

Division of Decimal Numbers

ProblemDividendDivisorQuotient
10.0504392.75410.0001
2700.55570.050413899.9147
30.01110.60540.0183
40.514996.41960.0053
50.538596.76120.0056
61.742871.94760.0242
70.05360.05131.0448
899.9610.06591516.8589
9863.95510.68691257.7596
100.57893.79270.1526
110.4591619.07380.0007
128.9347281.0770.0318
130.73250.37451.9559
140.7847.41980.1057
159.92430.0732135.5779
16829.7192816.92511.0157
170.05480.44420.1234
18363.73410.4215862.9516
198.42550.0173487.0231
200.09230.86870.1063
219.978942.39550.2354
229.4893253.44450.0374
23691.5085240.43052.8761
240.85950.055715.4309
25820.19399.208689.0683
26198.00090.009620625.0938
276.15860.0126488.7778
280.83947.45350.1126
290.444451.20010.0087
3080.969532.56652.4863
310.134356.03090.0024
32146.29760.02915027.4089
330.34056.64480.0512
340.340188.21210.0039
35628.7561427.92341.4693
366.52950.000232647.5
37211.55470.07252917.9959
3867.175439.2521.7114
3920.6832845.83080.0245
407.34490.192938.0762
410.40010.89630.4464
420.41710.0765.4882
4316.89620.225574.9277
4423.87580.40658.8074
450.00543.54670.0015
4686.45890.00919500.978
470.23450.13281.7658
4868.99966.434610.7232
490.73465.00040.1469
500.327552.36610.0063

Division of Integers

ProblemDividendDivisorQuotient
17994717
26962924
38586613
47207210
57363223
66275711
77926612
86242624
95611151
103301033
118401084
122301023
138555715
148102730
156483618
16264024110
17667023290
18911234268
196209286722
20955025382
214646397479
224315050863
23523212436
24741411674
25570030190
264521494481
271329861218
282428426934
294756848991
30744849152
318066213
325041828
337003520
348204120
356106110
368255515
377824617
387261166
397806512
405042421
414701047
427675913
434504510
445292323
453501035
462223963353
473923787451
481579622718
491831555333
50326727121

Multiplication of Integers

ProblemMultiplicandMultiplierProduct
14344318662
29099889082
38227360006
41807513500
5430125160
62995616744
79339487702
81899517955
98193831122
103427525650
117765542680
123347826052
133663111346
149346056040
15199448756
16617216133272
17520954496080
18444675299700
19733518379694
20514331170134
21904346312784
22988403398164
23299618184782
24902951857802
25772339261708
2618829956212
27711835593685
28359405145395
29486511248346
3028235299264
318121512180
32303123636
333805119380
347263424684
35317216657
36199316169
378119577045
38125516375
394802311040
407351410290
413787427972
427613828918
433706524050
448213327093
456791510185
46892394351448
4737718670122
48327933305091
49885387342495
50656306200736