October 15, 2007

Arithmetic: Multiplication of Decimal Numbers

ProblemMultiplicandMultiplierProduct
161.24980.03322.03349336
21.1672.39482.7947316
333.0316226.56757483.887033
4921.90360.075869.88029288
572.60519.5657694.51860507
60.861549.348442.5136466
799.978679.237267908.7767816
80.28327.85162.22357312
90.08734.78933.0266691
100.721803.2288579.1279648
11792.95310.088570.17634935
1275.76521.33741616.628111
130.098142.426313.9577774
140.80080.6270.5021016
150.00189.62510.01732518
160.472189.087342.05811433
1766.57860.259217.25717312
180.27820.08650.0240643
1995.15996.438612.6394362
2052.43294.2871224.78508559
214.9050.18140.889767
220.77640.48320.37515648
2390.14198.451761.7891969
24817.191158.666247941.49651082
250.21480.02350.0050478
260.70860.64440.45662184
27129.35884.8263624.32437644
2885.8494618.434753092.24793418
29113.87928.82281004.73340576
300.012619.44730.24503598
311.5701347.4133545.47362233
324.78580.02690.12873802
33755.73350.046535.14160775
341.1054.43734.9032165
350.0229372.4698.5295401
3642.29880.08563.62077728
370.68510.81920.56123392
38860.05583.86993328.32994042
3916.3240.06721.0969728
400.110.08390.009229
410.08845.37490.47514116
42466.482720.5819600.6804487
430.0009994.98150.89548335
440.16410.67130.11016033
453.3912967.02253279.366702
467.789272.7784566.88551328
470.6060.23690.1435614
48881.78668.41537420.49877498
497.3634896.60176602.03695778
5040.4917895.855236274.70000184

Arithmetic: Division of Decimal Numbers

ProblemDividendDivisorQuotient
10.00020.20.001
20.8786490.3272.687
30.013860.0770.18
487915.7398153.444572.95
50.2352660.6940.339
658.69691998.9830.593
7818906.792515883.045927.367
81.4730544.0580.363
962.2846770.67792.001
1037093.80985843.811846.678
110.0201940.8780.023
12638.956773780.1670.819
130.0960240.0128.002
140.0191580.0930.206
154.2103544.4180.953
160.4969450.0955.231
17416.076934842.2610.494
18432.755196319.1411.356
19178877.223162445.059401.918
203.6078186.1990.582
21403.331658493.6740.817
22196.3232314.51143.521
233.31081813.9110.238
240.4069120.5440.748
250.0014060.0370.038
2625859.60022832.948784.861
275.385390.08960.51
281.4134680.06322.436
290.0010140.0130.078
303485.31942600.715.802
311.5819840.2167.324
32442.1418751.125393.015
335319.0783018.399633.299
345.45019363.3460.015
350.674050.7930.85
3624562.9627237.332657.96
370.7010180.001701.018
389.64812810.7680.896
390.9091060.9610.946
400.009550.010.955
4112076.32814241.714289.503
42496.1515440.692716.982
430.1602590.0179.427
44541731.978424570.892948.922
457.18429588.6950.081
463.98576749.2070.081
4720.44532.7120.625
48428.244416863.3960.496
490.090120.00190.12
50176.1738169.35918.824

Arithmetic: Addition of Decimal Numbers

ProblemFirst NumberSecond NumberTotal
10.2062971.9982972.2044
20.00960.01990.0295
30.68320.03660.7198
40.59260.85641.449
50.000962.190362.1912
6183.4243591.3829774.8072
70.48965.94776.4373
8763.19960.0541763.2537
9564.74190.8738565.6157
10719.34259.9659729.3084
117.03885.554312.5931
120.30115.89156.1926
130.358830.392330.7511
14639.45550.0033639.4588
152.29949.326811.6262
16260.23039.5765269.8068
170.06650.17450.241
180.094480.946381.0407
190.07090.01680.0877
200.37688.97729.354
210.06910.50450.5736
22661.57150.283661.8545
230.03732.7852.8223
248.90248.386917.2893
254.774230.748835.523
26627.44080.0142627.455
270.10480.05310.1579
280.08120.20020.2814
290.065118.591318.6564
3052.94750.458553.406
3186.80860.017886.8264
3298.9672.5158771.4158
330.5134523.1954523.7088
34287.06970.57287.6397
3575.301531.3465106.648
364.9884922.2368927.2252
37173.3745932.69141106.0659
384.368949.447453.8163
390.72790.00990.7378
4035.92130.645336.5666
410.90940.22441.1338
420.6970.60721.3042
430.30121.98672.2879
440.02480.02290.0477
450.09715.77925.8763
460.07750.4160.4935
470.16440.01020.1746
480.03846.49446.5328
490.5738105.1179105.6917
50961.39840.0058961.4042

Arithmetic: Subtraction of Decimal Numbers

ProblemMinuendSubtrahendDifference
18.46895.00483.4641
289.315157.191932.1232
373.30050.092973.2076
4704.27840.0442704.2342
50.84950.02990.8196
6736.49217.6512718.8408
74.98330.06254.9208
83.09380.57412.5197
942.6980.058642.6394
10439.876623.9916415.885
1132.12740.017732.1097
120.99060.16850.8221
1373.89260.019973.8727
14188.85150.0009188.8506
15699.315524.2184675.0971
16412.28315.3365396.9465
17289.830163.2924226.5377
180.56460.08310.4815
194.68220.61684.0654
2047.238122.525824.7123
21708.9366677.325531.6111
22423.88460.0182423.8664
23260.70315.7613254.9418
240.02890.0010.0279
250.4090.02830.3807
268.5934.21044.3826
27754.062553.6559700.4066
28856.36140.0691856.2923
294.83810.01394.8242
3049.74880.045349.7035
31725.83580.6919725.1439
32357.96517.8646350.1005
3319.60240.066119.5363
3465.53740.063665.4738
35335.34710.0635335.2836
361.2150.05091.1641
370.19140.15230.0391
3879.15840.358778.7997
392.23970.00092.2388
408.91530.07238.843
4123.23250.377722.8548
420.08260.0030.0796
430.90440.0010.9034
44830.647379.9167750.7306
4544.24270.029144.2136
46473.83360.0731473.7605
4745.28320.089445.1938
484.88131.70423.1771
4953.68370.046253.6375
500.68780.06690.6209

Algebra: Least Common Multiple (LCM)

Solution SetGiven NumbersLCM
123,5,131495
215,14,132730
318,22,234554
417,28,14476
523,14,121932
68,24,7168
720,24,6120
83,15,19285
910,12,14420
1013,19,235681
119,24,372
122,10,21210
1324,14,12168
1421,23,167728
1510,17,161360
1613,24,16624
1710,9,22990
185,11,7385
194,13,211092
204,20,17340
2115,8,6120
228,5,15120
2319,6,221254
2422,10,8440
256,12,784
2613,21,51365
273,16,2448
2818,17,81224
292,5,420
303,2,1166
315,18,8360
3213,6,191482
333,2,1030
3423,15,72415
3519,6,12228
3619,13,153705
3720,7,131820
3811,10,6330
3919,12,24456
4024,21,4168
4115,12,9180
424,22,20220
434,9,336
4421,18,10630
4510,17,111870
4617,20,121020
472,8,15120
4815,20,18180
4914,30,7210
5021,10,20420

Algebra: Greatest Common Divisor (GCD)

Solution SetGiven NumbersGCD
144,11,6611
2570,133,32319
363,56,147
448,12,7212
555,33,6611
663,18,459
784,60,1212
845,20,355
921,12,183
1011,33,5511
1112,84,4812
1236,16,284
1363,36,459
1454,30,186
1540,48,728
1660,30,7010
1756,70,4214
1850,30,6010
19207,253,36823
2018,12,102
2135,70,147
2245,36,729
2355,11,3311
2444,55,7711
2548,12,6012
2684,98,5614
2728,7,357
28340,187,52717
2956,14,8414
3060,40,1010
3160,10,5010
3265,39,29913
3345,20,105
3470,98,8414
3577,66,3311
3630,18,66
3766,44,3311
38527,85,22117
3963,28,567
4081,90,639
4139,169,40313
4235,10,255
4363,54,369
4463,28,497
45456,133,36119
4681,27,459
4742,7,287
48551,145,66729
49138,713,29923
5051,34,39117

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(3,3) P2(9,-1)3x-2y-16=0
2P1(7,6) P2(-4,7)11x-1y-10=0
3P1(-7,8) P2(-1,-3)12x-22y+103=0
4P1(8,-7) P2(-9,-6)17x-1y+2=0
5P1(-9,4) P2(-2,-4)14x-16y+77=0
6P1(9,7) P2(1,-3)4x+5y-30=0
7P1(3,-5) P2(-8,-2)11x-3y+17=0
8P1(-7,2) P2(-3,-4)2x-3y+7=0
9P1(6,9) P2(-1,1)14x+16y-115=0
10P1(4,8) P2(-5,7)9x+1y-3=0
11P1(4,-6) P2(-9,-9)13x+3y+55=0
12P1(1,9) P2(-5,-5)3x+7y-8=0
13P1(6,2) P2(7,-5)1x-7y-17=0
14P1(-7,8) P2(-6,-2)2x-20y+73=0
15P1(7,-3) P2(-8,-9)10x+4y+29=0
16P1(3,9) P2(-7,8)20x+2y+23=0
17P1(5,8) P2(-1,3)12x+10y-79=0
18P1(-2,6) P2(-3,-5)1x+11y-3=0
19P1(8,7) P2(-3,-2)11x+9y-50=0
20P1(-8,8) P2(-5,-5)3x-13y+39=0
21P1(-4,4) P2(5,-1)9x-5y+3=0
22P1(-3,7) P2(7,-1)5x-4y+2=0
23P1(5,8) P2(-9,-8)7x+8y+14=0
24P1(3,7) P2(-9,-8)8x+10y+29=0
25P1(9,7) P2(-9,-1)9x+4y-12=0
26P1(3,7) P2(8,-1)10x-16y-7=0
27P1(1,2) P2(-1,1)4x+2y-3=0
28P1(4,6) P2(-2,-1)12x+14y-47=0
29P1(4,-9) P2(-5,-9)2x-0y+1=0
30P1(-2,1) P2(-5,-8)1x+3y+14=0
31P1(9,9) P2(6,-8)3x+17y-31=0
32P1(2,9) P2(9,-2)7x-11y+0=0
33P1(9,5) P2(-5,-4)28x+18y-65=0
34P1(8,6) P2(-4,8)6x-1y-5=0
35P1(-7,4) P2(6,-6)26x-20y-7=0
36P1(8,9) P2(-9,-2)17x+11y-30=0
37P1(4,8) P2(-7,9)11x-1y+25=0
38P1(-5,8) P2(1,-7)4x-10y+13=0
39P1(-4,8) P2(8,-1)8x-6y+5=0
40P1(-6,3) P2(-7,-6)1x+9y+20=0
41P1(6,6) P2(9,-6)2x-8y-15=0
42P1(1,1) P2(6,-2)5x-3y-19=0
43P1(6,-2) P2(-2,-6)2x+1y-0=0
44P1(-4,1) P2(7,-8)11x-9y-48=0
45P1(-6,9) P2(1,-3)14x-24y+107=0
46P1(4,1) P2(-6,-5)5x+3y+11=0
47P1(3,-1) P2(-8,-5)22x+8y+79=0
48P1(-4,7) P2(1,-4)5x-11y+24=0
49P1(9,-8) P2(-9,-8)1x-0y-0=0
50P1(3,3) P2(-2,3)2x-0y-1=0

Analytic Geometry: Distance Between Two Points

Given two points, their distance and the slope of the line joining them are solved.
ProblemGiven PointsDistanceSlope
1P1(2,4) P2(-9,1)sqrt of 130-3/-11
2P1(-5,3) P2(7,-6)sqrt of 225-3/4
3P1(4,-7) P2(-5,-2)sqrt of 1065/-9
4P1(2,3) P2(-1,-5)sqrt of 73-8/-3
5P1(3,5) P2(9,4)sqrt of 37-1/6
6P1(4,7) P2(6,2)sqrt of 29-5/2
7P1(3,2) P2(1,9)sqrt of 537/-2
8P1(1,3) P2(4,6)sqrt of 181/1
9P1(4,-2) P2(-7,-5)sqrt of 130-3/-11
10P1(6,1) P2(3,8)sqrt of 587/-3
11P1(7,4) P2(3,3)sqrt of 17-1/-4
12P1(3,1) P2(8,8)sqrt of 747/5
13P1(2,-8) P2(-4,-2)sqrt of 721/-1
14P1(6,7) P2(3,6)sqrt of 10-1/-3
15P1(-7,4) P2(6,-6)sqrt of 269-10/13
16P1(6,4) P2(7,1)sqrt of 10-3/1
17P1(-6,3) P2(-2,-1)sqrt of 32-1/1
18P1(8,4) P2(3,9)sqrt of 501/-1
19P1(9,5) P2(5,4)sqrt of 17-1/-4
20P1(-5,6) P2(-6,-8)sqrt of 197-14/-1
21P1(8,9) P2(-2,7)sqrt of 104-1/-5
22P1(5,6) P2(-4,1)sqrt of 106-5/-9
23P1(5,7) P2(7,8)sqrt of 51/2
24P1(-2,3) P2(-7,-9)sqrt of 169-12/-5
25P1(9,5) P2(-8,-3)sqrt of 353-8/-17
26P1(6,3) P2(9,6)sqrt of 181/1
27P1(7,4) P2(1,-9)sqrt of 205-13/-6
28P1(-3,6) P2(2,-5)sqrt of 146-11/5
29P1(7,6) P2(2,3)sqrt of 34-3/-5
30P1(-7,2) P2(4,-7)sqrt of 202-9/11
31P1(-8,7) P2(-2,-2)sqrt of 117-3/2
32P1(5,-9) P2(-4,-8)sqrt of 821/-9
33P1(8,4) P2(1,8)sqrt of 654/-7
34P1(7,1) P2(-5,-4)sqrt of 169-5/-12
35P1(8,2) P2(4,-7)sqrt of 97-9/-4
36P1(-8,6) P2(3,-1)sqrt of 170-7/11
37P1(8,3) P2(6,9)sqrt of 403/-1
38P1(6,7) P2(8,-2)sqrt of 85-9/2
39P1(8,3) P2(-6,2)sqrt of 197-1/-14
40P1(7,9) P2(5,-6)sqrt of 229-15/-2
41P1(2,6) P2(9,2)sqrt of 65-4/7
42P1(3,8) P2(-1,-6)sqrt of 212-7/-2
43P1(4,7) P2(7,4)sqrt of 18-1/1
44P1(-5,8) P2(-8,-9)sqrt of 298-17/-3
45P1(5,2) P2(-9,-9)sqrt of 317-11/-14
46P1(6,-5) P2(-2,-6)sqrt of 65-1/-8
47P1(9,5) P2(-6,9)sqrt of 2414/-15
48P1(8,1) P2(5,-2)sqrt of 18-1/-1
49P1(9,3) P2(3,9)sqrt of 721/-1
50P1(9,4) P2(8,2)sqrt of 5-2/-1

October 3, 2007

Algebra: Linear Equations in Two Unknown

Given two linear equations, the two equations are solved simultaneously for x and y.
ProblemGiven EquationsSolution
1x+5y = 56; 4x+7y = 94x = 6; y = 10
25x+3y = 25; 6x+8y = 52x = 2; y = 5
36x+4y = 84; 6x+7y = 102x = 10; y = 6
47x-8y = -14; 5x+6y = 154x = 14; y = 14
54x+5y = 108; x+5y = 72x = 12; y = 12
64x+y = 53; 2x+2y = 46x = 10; y = 13
7x+4y = 54; 4x+3y = 60x = 6; y = 12
83x+y = 29; 2x+3y = 38x = 7; y = 8
93x+2y = 29; 7x+3y = 76x = 13; y = -5
104x+6y = 140; 9x+8y = 238x = 14; y = 14
119x+4y = 62; x+6y = 68x = 2; y = 11
128x+8y = 144; 3x+7y = 74x = 13; y = 5
138x+8y = -56; 7x+4y = -16x = 4; y = -11
147x+6y = 176; 6x+7y = 175x = 14; y = 13
159x+8y = -59; 4x+6y = -14x = -11; y = 5
162x+8y = 100; 7x+2y = 38x = 2; y = 12
179x-3y = 96; 7x+4y = 100x = 12; y = 4
188x+4y = 52; x+4y = 10x = 6; y = 1
192x+3y = 48; 9x+8y = 161x = 9; y = 10
202x+5y = 57; 3x+6y = 69x = 1; y = 11
216x+3y = 90; 2x+5y = 62x = 11; y = 8
223x+2y = 45; x+4y = 35x = 11; y = 6
236x+9y = 180; 5x+3y = 87x = 9; y = 14
249x+9y = 144; 3x+9y = 60x = 14; y = 2
254x+7y = 87; 8x+7y = 111x = 6; y = 9
265x+y = 34; 2x+3y = 37x = 5; y = 9
276x+3y = -42; 9x+7y = -58x = -8; y = 2
289x+4y = 121; x+y = 14x = 13; y = 1
29x+2y = 24; 7x+5y = 96x = 8; y = 8
304x+2y = 38; 8x+6y = 74x = 10; y = -1
312x+3y = 24; 5x+4y = 39x = 3; y = 6
328x+7y = 122; 8x+3y = 98x = 10; y = 6
332x+4y = 44; 6x+y = 55x = 8; y = 7
34x+9y = 119; 2x+8y = 118x = 11; y = 12
359x-6y = 12; x+7y = 55x = 6; y = 7
364x+5y = 30; 6x+5y = 40x = 5; y = 2
37x+2y = 31; x+8y = 115x = 3; y = 14
387x+8y = 52; 6x+8y = 48x = 4; y = 3
394x+2y = 36; 7x+3y = 60x = 6; y = 6
403x+9y = 75; 2x+2y = 22x = 4; y = 7
417x+4y = 11; 7x+4y = 11x = 1; y = 1
422x+9y = 110; 3x+6y = 75x = 1; y = 12
437x+2y = 37; 7x+9y = 93x = 3; y = 8
442x+4y = -44; 5x+5y = -40x = 6; y = -14
458x+y = 54; x+y = 12x = 6; y = 6
463x+9y = 54; 9x+6y = 78x = 6; y = 4
472x+6y = -64; 6x+3y = 18x = 10; y = -14
486x+9y = 90; 3x+y = 24x = 6; y = 6
493x+7y = 101; 6x+8y = 118x = 1; y = 14
504x-7y = 1; 5x+3y = 13x = 2; y = 1

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(7,9) P2(6,3); A(8,5) B(2,6)6x-y-33=0, x+6y-38=0perpendicular lines: m1=-6/-1 m2=1/-6
2P1(4,5) P2(9,8); A(3,2) B(0,7)3x-5y+13=0, 5x+3y-21=0perpendicular lines: m1=3/5 m2=5/-3
3P1(2,6) P2(7,0); A(2,2) B(8,7)6x+5y-42=0, 5x-6y+2=0perpendicular lines: m1=-6/5 m2=5/6
4P1(6,1) P2(2,5); A(5,0) B(9,4)x+y-7=0, x-y-5=0perpendicular lines: m1=1/-1 m2=1/1
5P1(-9,4) P2(9,6); A(12,13) B(3,12)x-9y+45=0, x-9y+105=0parallel lines: m1=1/9 m2=-1/-9
6P1(9,2) P2(5,8); A(3,0) B(9,4)3x+2y-31=0, 2x-3y-6=0perpendicular lines: m1=3/-2 m2=2/3
7P1(1,5) P2(0,2); A(9,1) B(6,2)3x-y+2=0, x+3y-12=0perpendicular lines: m1=-3/-1 m2=1/-3
8P1(2,8) P2(7,5); A(5,4) B(8,9)3x+5y-46=0, 5x-3y-13=0perpendicular lines: m1=-3/5 m2=5/3
9P1(-2,0) P2(4,9); A(6,7) B(10,13)3x-2y+6=0, 3x-2y-4=0parallel lines: m1=3/2 m2=3/2
10P1(5,7) P2(1,1); A(6,5) B(0,9)3x-2y-1=0, 2x+3y-27=0perpendicular lines: m1=-3/-2 m2=2/-3
11P1(-4,9) P2(9,6); A(1,11) B(14,8)3x+13y-105=0, 3x+13y-146=0parallel lines: m1=-3/13 m2=-3/13
12P1(-1,6) P2(9,0); A(10,3) B(0,9)3x+5y-27=0, 3x+5y-45=0parallel lines: m1=-3/5 m2=3/-5
13P1(-6,1) P2(2,9); A(7,12) B(1,6)x-y+7=0, x-y+5=0parallel lines: m1=1/1 m2=-1/-1
14P1(9,7) P2(0,9); A(6,0) B(8,9)2x+9y-81=0, 9x-2y-54=0perpendicular lines: m1=2/-9 m2=9/2
15P1(-2,0) P2(3,7); A(4,7) B(9,14)7x-5y+14=0, 7x-5y+7=0parallel lines: m1=7/5 m2=7/5
16P1(7,1) P2(8,4); A(7,0) B(4,1)3x-y-20=0, x+3y-7=0perpendicular lines: m1=3/1 m2=1/-3
17P1(-3,4) P2(2,0); A(6,0) B(1,4)4x+5y-8=0, 4x+5y-24=0parallel lines: m1=-4/5 m2=4/-5
18P1(-8,3) P2(2,8); A(1,6) B(7,9)x-2y+14=0, x-2y+11=0parallel lines: m1=1/2 m2=1/2
19P1(6,2) P2(7,0); A(6,7) B(8,8)2x+y-14=0, x-2y+8=0perpendicular lines: m1=-2/1 m2=1/2
20P1(-6,6) P2(5,3); A(12,6) B(1,9)3x+11y-48=0, 3x+11y-102=0parallel lines: m1=-3/11 m2=3/-11
21P1(-5,6) P2(1,3); A(6,4) B(12,1)x+2y-7=0, x+2y-14=0parallel lines: m1=-1/2 m2=-1/2
22P1(5,3) P2(9,5); A(3,7) B(5,3)x-2y+1=0, 2x+y-13=0perpendicular lines: m1=1/2 m2=-2/1
23P1(-6,2) P2(4,1); A(14,2) B(4,3)x+10y-14=0, x+10y-34=0parallel lines: m1=-1/10 m2=1/-10
24P1(0,5) P2(3,8); A(6,4) B(7,5)x-y+5=0, x-y-2=0parallel lines: m1=1/1 m2=1/1
25P1(4,3) P2(2,8); A(1,3) B(6,5)5x+2y-26=0, 2x-5y+13=0perpendicular lines: m1=5/-2 m2=2/5
26P1(-6,6) P2(2,1); A(0,5) B(8,0)5x+8y-18=0, 5x+8y-40=0parallel lines: m1=-5/8 m2=-5/8
27P1(-6,1) P2(3,2); A(14,13) B(5,12)x-9y+15=0, x-9y+103=0parallel lines: m1=1/9 m2=-1/-9
28P1(-8,4) P2(4,0); A(6,4) B(3,5)x+3y-4=0, x+3y-18=0parallel lines: m1=-1/3 m2=1/-3
29P1(-4,7) P2(0,4); A(5,11) B(9,8)3x+4y-16=0, 3x+4y-59=0parallel lines: m1=-3/4 m2=-3/4
30P1(7,5) P2(6,2); A(5,8) B(8,7)3x-y-16=0, x+3y-29=0perpendicular lines: m1=-3/-1 m2=-1/3
31P1(-1,3) P2(4,2); A(8,10) B(3,11)x+5y-14=0, x+5y-58=0parallel lines: m1=-1/5 m2=1/-5
32P1(7,2) P2(9,5); A(1,7) B(4,5)3x-2y-17=0, 2x+3y-23=0perpendicular lines: m1=3/2 m2=-2/3
33P1(-2,6) P2(4,1); A(1,7) B(7,2)5x+6y-26=0, 5x+6y-47=0parallel lines: m1=-5/6 m2=-5/6
34P1(-3,9) P2(7,7); A(0,12) B(10,10)x+5y-42=0, x+5y-60=0parallel lines: m1=-1/5 m2=-1/5
35P1(-2,2) P2(3,5); A(6,9) B(1,6)3x-5y+16=0, 3x-5y+27=0parallel lines: m1=3/5 m2=-3/-5
36P1(2,8) P2(4,0); A(1,7) B(9,9)4x+y-16=0, x-4y+27=0perpendicular lines: m1=-4/1 m2=1/4
37P1(2,7) P2(8,3); A(1,1) B(5,7)2x+3y-25=0, 3x-2y-1=0perpendicular lines: m1=-2/3 m2=3/2
38P1(-4,1) P2(1,5); A(10,14) B(5,10)4x-5y+21=0, 4x-5y+30=0parallel lines: m1=4/5 m2=-4/-5
39P1(-4,1) P2(1,4); A(9,7) B(14,10)3x-5y+17=0, 3x-5y+8=0parallel lines: m1=3/5 m2=3/5
40P1(7,6) P2(6,4); A(4,6) B(2,7)2x-y-8=0, x+2y-16=0perpendicular lines: m1=-2/-1 m2=1/-2
41P1(0,4) P2(1,2); A(6,7) B(8,8)2x+y-4=0, x-2y+8=0perpendicular lines: m1=-2/1 m2=1/2
42P1(-9,5) P2(1,0); A(10,8) B(6,10)x+2y-1=0, x+2y-26=0parallel lines: m1=-1/2 m2=1/-2
43P1(9,1) P2(0,9); A(0,0) B(8,9)8x+9y-81=0, 9x-8y-0=0perpendicular lines: m1=8/-9 m2=9/8
44P1(-2,4) P2(8,0); A(9,8) B(14,6)2x+5y-16=0, 2x+5y-58=0parallel lines: m1=-2/5 m2=-2/5
45P1(1,2) P2(2,4); A(4,2) B(6,1)2x-y-0=0, x+2y-8=0perpendicular lines: m1=2/1 m2=-1/2
46P1(0,5) P2(9,3); A(9,11) B(0,13)2x+9y-45=0, 2x+9y-117=0parallel lines: m1=-2/9 m2=2/-9
47P1(3,8) P2(8,2); A(2,2) B(8,7)6x+5y-58=0, 5x-6y+2=0perpendicular lines: m1=-6/5 m2=5/6
48P1(2,2) P2(1,4); A(3,0) B(5,1)2x+y-6=0, x-2y-3=0perpendicular lines: m1=2/-1 m2=1/2
49P1(7,8) P2(0,3); A(8,2) B(3,9)5x-7y+21=0, 7x+5y-66=0perpendicular lines: m1=-5/-7 m2=7/-5
50P1(0,7) P2(4,0); A(2,2) B(9,6)7x+4y-28=0, 4x-7y+6=0perpendicular lines: m1=-7/4 m2=4/7

Algebra: Multiplication of Polynomials

ProblemGiven PolynomialsSolution
16x+7y and 7x3+2y42x4+12xy+49x3y+14y2
24x4-8y and 4x3-7y316x7-28x4y3-32x3y+56y4
37x4+4y and 2x3-8y214x7-56x4y2+8x3y-32y3
45x2-3 and 7y3-1035x2y3-50x2-21y3+30
52x-5 and 1x+132x2+21x-65
68x4-3y and 7x-5y456x5-40x4y4-21xy+15y5
78x2-13 and 3y3-324x2y3-24x2-39y3+39
82x3+6y4 and 5x410x7+30x4y4
92x+6 and 3x2-26x3-4x1+18x2-12
104x-12 and 5y2-120xy2-4x-60y2+12
112x-12 and 3x+136x2-10x-156
124x+7 and 1x2-104x3-40x1+7x2-70
133x-8 and 1y-63xy-18x-8y+48
148x4+6y4 and 8x364x7+48x3y4
158x+11 and 7x-1456x2-35x-154
163x4+12 and 1x2+53x6+15x4+12x2+60
178x3-6 and 1y2+58x3y2+40x3-6y2-30
187x3-1 and 3y2+521x3y2+35x3-3y2-5
191x3+4y and 7x4+5y27x7+5x3y2+28x4y+20y3
204x4+1y and 8x2+3y432x6+12x4y4+8x2y+3y5
216x-8y and 5x+5y330x2+30xy3-40xy-40y4
226x-10 and 7y2-1142xy2-66x-70y2+110
237x+11 and 6x-1242x2-18x-132
241x-5 and 7x-87x2-43x+40
257x4+2y and 3x221x6+6x2y
262x3-9 and 5y2+1410x3y2+28x3-45y2-126
277x4-4y2 and 3x21x5-12xy2
282x2+1y4 and 7x214x4+7x2y4
298x4-8y4 and 8x3+1y64x7+8x4y-64x3y4-8y5
306x+7 and 5x2-1230x3-72x1+35x2-84
312x+4 and 7x+214x2+32x+8
328x4+10 and 1x2+18x6+8x4+10x2+10
333x+6 and 8x+324x2+57x+18
345x+4 and 3x-615x2-18x-24
354x3-7y and 4x+3y216x4+12x3y2-28xy-21y3
367x-2 and 5y-735xy-49x-10y+14
375x+6y3 and 2x2-6y10x3-30xy+12x2y3-36y4
388x3-2y3 and 6x2-4y248x5-32x3y2-12x2y3+8y5
396x4+13 and 4x2+1124x6+66x4+52x2+143
403x+7y4 and 7x-3y21x2-9xy+49xy4-21y5
415x2-3 and 3y3-615x2y3-30x2-9y3+18
423x+7 and 7x+621x2+67x+42
435x2-7y and 2x310x5-14x3y
443x3+4y4 and 6x218x5+24x2y4
457x+7y3 and 4x28x2+28xy3
465x2-2y3 and 1x5x3-2xy3
473x-2 and 3x-39x2-15x+6
487x-2 and 4y2-528xy2-35x-8y2+10
492x-11 and 2x-14x2-24x+11
506x-2 and 1x+136x2+76x-26

Arithmetic: Multiplication of Fractions

ProblemMultiplicandMultiplierProduct
13/145/1415/196
23/101/143/140
33/141/181/84
45/187/1835/324
57/225/215/66
65/187/2235/396
72/211/201/210
84/157/127/45
97/225/2435/528
101/81/81/64
111/143/103/140
122/217/221/33
137/104/212/15
141/147/201/40
157/125/2435/288
165/187/157/54
171/711/1511/105
183/41/203/80
194/217/154/45
201/51/31/15
211/142/151/105
223/72/32/7
235/87/1835/144
247/201/207/400
258/91/98/81
265/241/145/336
273/165/185/96
281/205/211/84
291/185/125/216
307/101/187/180
3134/1010/15/
323/225/1415/308
334/157/1014/75
345/241/165/384
353/105/241/16
367/107/1649/160
371/77/91/9
387/125/1235/144
397/167/1649/256
404/157/127/45
417/155/187/54
425/211/201/84
437/225/2435/528
447/168/157/30
453/205/163/64
467/185/1235/216
477/183/141/12
481/157/167/240
492/211/141/147
508/92/916/81

Arithmetic: Division of Fractions

ProblemDividendDivisorQuotient
17/203/202 1/3
28/91/1412 4/9
31/102/153/4
45/145/161 1/7
57/223/141 16/33
61/97/1010/63
75/245/121/2
85/228/21105/176
97/81/87
108/211/145 1/3
117/101/149 4/5
121/241/105/12
138/92/94
145/187/2255/63
158/215/181 13/35
167/128/211 17/32
177/207/201
186/77/121 23/49
197/91/43 1/9
204/214/155/7
217/167/161
227/221/123 9/11
237/241/123 1/2
247/152/153 1/2
255/147/201 1/49
261/155/186/25
271/183/147/27
287/81/54 3/8
297/203/222 17/30
303/227/1545/154
318/95/142 22/45
323/221/101 4/11
338/153/203 5/9
341/125/147/30
353/225/1421/55
361/124/155/16
372/73/72/3
387/167/105/8
393/101/144 1/5
405/92/92 1/2
417/227/168/11
425/187/185/7
437/241/144 1/12
441/144/1515/56
451/85/99/40
463/203/221 1/10
477/101/149 4/5
487/223/161 23/33
496/71/1815 3/7
507/101/1812 3/5

Arithmetic: Subtraction of Fractions

ProblemMinuendSubtrahendDifference
15/127/12-1/6
25/181/108/45
33/45/71/28
43/105/12-7/60
57/181/2143/126
62/218/15-46/105
77/243/2017/120
82/157/20-13/60
93/223/220
103/221/145/77
118/91/97/9
123/141/2023/140
137/183/2225/99
142/155/14-47/210
151/83/14-5/56
163/101/2431/120
171/127/20-4/15
181/212/15-3/35
193/201/101/20
203/207/24-17/120
217/161/163/8
228/96/72/63
238/153/1683/240
247/241/1437/168
256/73/1039/70
267/108/151/6
271/143/16-13/112
287/125/2129/84
291/92/9-1/9
303/710/21-1/21
317/241/1437/168
327/107/100
336/77/1223/84
347/157/2249/330
357/181/2425/72
365/182/1513/90
375/82/1559/120
388/95/711/63
397/241/1437/168
403/101/148/35
411/127/18-11/36
421/153/10-7/30
435/141/1223/84
447/121/1819/36
457/810/2167/168
467/225/12-13/132
477/245/12-1/8
483/105/181/45
497/181/2061/180
506/74/72/7

Arithmetic: Addition of Fractions

ProblemFirst NumberSecond NumberTotal
11/123/1023/60
25/167/101 1/80
33/148/15157/210
41/243/2023/120
55/145/2495/168
62/157/1847/90
71/167/161/2
88/92/91 1/9
95/161/1591/240
107/105/121 7/60
117/187/20133/180
121/127/122/3
135/221/1597/330
148/151/1237/60
153/221/1013/55
167/85/181 11/72
173/147/1267/84
184/77/101 19/70
194/58/91 31/45
205/247/241/2
217/98/91 2/3
223/165/2273/176
233/223/2063/220
242/158/2118/35
257/121/2019/30
267/161/1871/144
275/217/10197/210
287/91/2459/72
297/94/71 22/63
307/181/1022/45
313/167/1883/144
324/151/1471/210
338/157/22281/330
347/127/247/8
357/161/2423/48
368/158/2132/35
371/211/212/21
387/87/91 47/72
395/241/127/24
407/153/2037/60
415/147/24109/168
423/55/91 7/45
432/155/1211/20
447/165/22117/176
457/121/122/3
461/87/81
471/141/215/42
487/181/1217/36
496/711/241 53/168
501/221/2211/121