Algebra: Linear Equations in Two Unknown

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

Problem	Given Equations	Solution
1	6x+2y = 68; 9x+8y = 62	x = 14; y = -8
2	2x-4y = -38; 9x+4y = 93	x = 5; y = 12
3	2x+3y = 60; 9x+3y = 144	x = 12; y = 12
4	9x+3y = 72; x+8y = 77	x = 5; y = 9
5	8x+y = 43; 7x+5y = 83	x = 4; y = 11
6	3x+8y = 95; 9x+3y = 138	x = 13; y = 7
7	6x+6y = 18; 4x+3y = 11	x = 2; y = 1
8	4x+5y = 84; x+9y = 83	x = 11; y = 8
9	6x+y = 38; x+8y = 22	x = 6; y = 2
10	3x+3y = -18; 4x+8y = -60	x = 3; y = -9
11	7x+5y = 47; 4x+7y = 31	x = 6; y = 1
12	8x+7y = 154; 3x+9y = 96	x = 14; y = 6
13	4x+3y = 70; 7x+8y = 161	x = 7; y = 14
14	6x+y = 63; 5x+6y = 99	x = 9; y = 9
15	3x+2y = 61; 2x+2y = 50	x = 11; y = 14
16	7x+4y = 90; 6x+7y = 120	x = 6; y = 12
17	2x+5y = 84; 7x+2y = 77	x = 7; y = 14
18	5x+8y = 23; 8x+5y = -10	x = -5; y = 6
19	6x+5y = 102; 8x+y = 102	x = 12; y = 6
20	x+9y = 20; 2x+7y = 18	x = 2; y = 2
21	6x+2y = 54; 6x+7y = 99	x = 6; y = 9
22	5x-8y = -107; x+y = 15	x = 1; y = 14
23	x+8y = 60; 8x+y = 39	x = 4; y = 7
24	9x+5y = 68; 8x+3y = 46	x = 2; y = 10
25	3x+y = 25; 5x+8y = 10	x = 10; y = -5
26	6x+3y = -9; x+7y = -47	x = 2; y = -7
27	5x+2y = 57; 5x+3y = 68	x = 7; y = 11
28	2x+7y = 36; 4x+y = 20	x = 4; y = 4
29	2x+y = 24; 8x+4y = 96	x = 8; y = 8
30	8x+8y = 176; 5x+y = 70	x = 12; y = 10
31	9x+4y = 10; 6x+5y = -19	x = 6; y = -11
32	3x-3y = 33; 5x+6y = 88	x = 14; y = 3
33	8x+3y = 126; 9x+5y = 158	x = 12; y = 10
34	2x+6y = 48; 4x+y = 30	x = 6; y = 6
35	9x+6y = 195; 8x+8y = 208	x = 13; y = 13
36	3x+8y = 96; 9x+6y = 126	x = 8; y = 9
37	7x+6y = 49; 7x+4y = 35	x = 1; y = 7
38	2x+7y = 25; 6x+8y = 36	x = 2; y = 3
39	9x+9y = 162; 3x+9y = 114	x = 8; y = 10
40	2x+3y = -19; 7x+9y = -50	x = 7; y = -11
41	7x+2y = 33; x+6y = 39	x = 3; y = 6
42	7x+5y = 129; x+8y = 84	x = 12; y = 9
43	5x+8y = 153; 6x+6y = 144	x = 13; y = 11
44	2x+9y = 91; 6x+6y = 126	x = 14; y = 7
45	x+8y = 106; 5x+2y = 36	x = 2; y = 13
46	x+4y = 25; 9x+6y = 75	x = 5; y = 5
47	5x+8y = 174; 6x+5y = 149	x = 14; y = 13
48	7x+3y = -29; 8x+y = -38	x = -5; y = 2
49	9x+y = 63; 9x+9y = 135	x = 6; y = 9
50	3x+5y = 81; 8x+9y = 164	x = 7; y = 12

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.

Problem	Given Points	Equations of the Line	Slopes of the Line
1	P1(-3,6) P2(4,8); A(8,8) B(1,6)	2x-7y+48=0, 2x-7y+40=0	parallel lines: m1=2/7 m2=-2/-7
2	P1(0,6) P2(7,9); A(0,8) B(3,1)	3x-7y+42=0, 7x+3y-24=0	perpendicular lines: m1=3/7 m2=-7/3
3	P1(3,5) P2(8,1); A(4,2) B(8,7)	4x+5y-37=0, 5x-4y-12=0	perpendicular lines: m1=-4/5 m2=5/4
4	P1(-6,8) P2(2,2); A(2,7) B(10,1)	3x+4y-14=0, 3x+4y-34=0	parallel lines: m1=-3/4 m2=-3/4
5	P1(-3,7) P2(2,1); A(1,6) B(6,0)	6x+5y-17=0, 6x+5y-36=0	parallel lines: m1=-6/5 m2=-6/5
6	P1(7,6) P2(3,0); A(8,3) B(2,7)	3x-2y-9=0, 2x+3y-25=0	perpendicular lines: m1=-3/-2 m2=2/-3
7	P1(-8,1) P2(2,0); A(3,5) B(13,4)	x+10y-2=0, x+10y-53=0	parallel lines: m1=-1/10 m2=-1/10
8	P1(5,8) P2(6,2); A(0,4) B(6,5)	6x+y-38=0, x-6y+24=0	perpendicular lines: m1=-6/1 m2=1/6
9	P1(-9,7) P2(9,4); A(4,10) B(10,9)	x+6y-33=0, x+6y-64=0	parallel lines: m1=-1/6 m2=-1/6
10	P1(0,0) P2(5,3); A(5,5) B(8,0)	3x-5y-0=0, 5x+3y-40=0	perpendicular lines: m1=3/5 m2=-5/3
11	P1(-7,1) P2(1,2); A(13,3) B(5,2)	x-8y+15=0, x-8y+11=0	parallel lines: m1=1/8 m2=-1/-8
12	P1(9,2) P2(1,0); A(5,9) B(7,1)	x-4y-1=0, 4x+y-29=0	perpendicular lines: m1=-1/-4 m2=-4/1
13	P1(-3,7) P2(7,0); A(10,7) B(0,14)	7x+10y-49=0, 7x+10y-140=0	parallel lines: m1=-7/10 m2=7/-10
14	P1(5,8) P2(3,3); A(8,4) B(3,6)	5x-2y-9=0, 2x+5y-36=0	perpendicular lines: m1=-5/-2 m2=2/-5
15	P1(-4,4) P2(8,8); A(3,2) B(6,3)	x-3y+16=0, x-3y+3=0	parallel lines: m1=1/3 m2=1/3
16	P1(4,9) P2(3,0); A(0,8) B(9,7)	9x-y-27=0, x+9y-72=0	perpendicular lines: m1=-9/-1 m2=-1/9
17	P1(-7,6) P2(5,2); A(2,7) B(11,4)	x+3y-11=0, x+3y-23=0	parallel lines: m1=-1/3 m2=-1/3
18	P1(4,4) P2(6,2); A(5,5) B(7,7)	x+y-8=0, x-y-0=0	perpendicular lines: m1=-1/1 m2=1/1
19	P1(2,6) P2(0,3); A(2,2) B(5,0)	3x-2y+6=0, 2x+3y-10=0	perpendicular lines: m1=-3/-2 m2=-2/3
20	P1(-1,5) P2(2,4); A(7,13) B(10,12)	x+3y-14=0, x+3y-46=0	parallel lines: m1=-1/3 m2=-1/3

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.

Problem	Given Points	Equation of the Line
1	P1(-5,2) P2(6,-1)	11x-3y-4=0
2	P1(-1,7) P2(-9,-4)	16x+22y+47=0
3	P1(6,9) P2(8,-2)	4x-22y+49=0
4	P1(1,-3) P2(-4,-6)	5x+3y+21=0
5	P1(6,3) P2(-4,2)	20x+2y-25=0
6	P1(5,9) P2(-2,-1)	14x+20y-101=0
7	P1(5,1) P2(5,-2)	0x-2y-1=0
8	P1(-2,5) P2(3,-5)	2x-4y-1=0
9	P1(4,4) P2(-5,5)	9x-1y+9=0
10	P1(9,-3) P2(-3,-4)	24x+2y-65=0
11	P1(1,8) P2(-9,-2)	1x+1y+1=0
12	P1(-5,7) P2(-1,-1)	1x-2y+9=0
13	P1(-4,1) P2(7,-7)	22x-16y-81=0
14	P1(7,6) P2(-5,1)	24x+10y-59=0
15	P1(1,-1) P2(-3,-4)	8x+6y+23=0
16	P1(6,7) P2(-2,-2)	16x+18y-77=0
17	P1(9,7) P2(1,-8)	16x+30y-65=0
18	P1(-1,7) P2(-7,-4)	12x+22y+15=0
19	P1(-3,3) P2(-2,-5)	2x-16y-11=0
20	P1(6,9) P2(3,-6)	1x+5y-12=0
21	P1(9,-9) P2(-1,-3)	5x-3y-38=0
22	P1(1,7) P2(-7,-7)	4x+7y+12=0
23	P1(5,8) P2(-2,4)	14x+8y-69=0
24	P1(-9,4) P2(3,-4)	3x-2y+9=0
25	P1(4,9) P2(5,-1)	2x-20y+71=0
26	P1(5,-2) P2(-9,-7)	28x+10y+101=0
27	P1(9,9) P2(-3,-5)	6x+7y-32=0
28	P1(3,3) P2(-5,6)	16x-6y+43=0
29	P1(-1,1) P2(-2,-7)	2x+16y+51=0
30	P1(-5,8) P2(2,-5)	7x-13y+30=0

Analytic Geometry: Distance Between Two Points

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

Problem	Given Points	Distance	Slope
1	P1(3,7) P2(5,1)	sqrt of 40	-3/1
2	P1(3,2) P2(-8,3)	sqrt of 122	1/-11
3	P1(-3,4) P2(-8,-6)	sqrt of 125	-2/-1
4	P1(7,2) P2(-2,-6)	sqrt of 145	-8/-9
5	P1(5,-9) P2(-8,-1)	sqrt of 233	8/-13
6	P1(6,8) P2(2,4)	sqrt of 32	-1/-1
7	P1(3,6) P2(9,3)	sqrt of 45	-1/2
8	P1(5,6) P2(8,-3)	sqrt of 90	-3/1
9	P1(-5,3) P2(3,-4)	sqrt of 113	-7/8
10	P1(7,2) P2(1,8)	sqrt of 72	1/-1
11	P1(4,1) P2(-6,6)	sqrt of 125	1/-2
12	P1(-8,4) P2(7,-7)	sqrt of 346	-11/15
13	P1(1,3) P2(-7,-1)	sqrt of 80	-1/-2
14	P1(6,9) P2(4,-2)	sqrt of 125	-11/-2
15	P1(8,-7) P2(-7,-9)	sqrt of 229	-2/-15
16	P1(-9,4) P2(-8,-7)	sqrt of 122	-11/1
17	P1(3,2) P2(6,9)	sqrt of 58	7/3
18	P1(5,2) P2(8,5)	sqrt of 18	1/1
19	P1(5,9) P2(9,2)	sqrt of 65	-7/4
20	P1(9,3) P2(7,9)	sqrt of 40	3/-1
21	P1(4,2) P2(-9,-9)	sqrt of 290	-11/-13
22	P1(4,2) P2(9,-8)	sqrt of 125	-2/1
23	P1(1,6) P2(-8,8)	sqrt of 85	2/-9
24	P1(7,6) P2(1,4)	sqrt of 40	-1/-3
25	P1(-9,8) P2(1,-9)	sqrt of 389	-17/10
26	P1(7,8) P2(3,1)	sqrt of 65	-7/-4
27	P1(-9,6) P2(-1,-8)	sqrt of 260	-7/4
28	P1(6,1) P2(9,9)	sqrt of 73	8/3
29	P1(9,9) P2(5,7)	sqrt of 20	-1/-2
30	P1(3,-1) P2(-9,-8)	sqrt of 193	-7/-12
31	P1(4,8) P2(7,1)	sqrt of 58	-7/3
32	P1(9,-9) P2(-8,-2)	sqrt of 338	7/-17
33	P1(2,8) P2(1,4)	sqrt of 17	-4/-1
34	P1(3,2) P2(9,5)	sqrt of 45	1/2
35	P1(3,2) P2(-8,-8)	sqrt of 221	-10/-11
36	P1(9,8) P2(6,-1)	sqrt of 90	-3/-1
37	P1(-5,9) P2(-9,-7)	sqrt of 272	-4/-1
38	P1(5,8) P2(-6,5)	sqrt of 130	-3/-11
39	P1(-8,5) P2(5,-3)	sqrt of 233	-8/13
40	P1(2,9) P2(1,5)	sqrt of 17	-4/-1
41	P1(8,7) P2(6,-5)	sqrt of 148	-6/-1
42	P1(2,8) P2(1,7)	sqrt of 2	-1/-1
43	P1(8,9) P2(4,2)	sqrt of 65	-7/-4
44	P1(4,6) P2(9,3)	sqrt of 34	-3/5
45	P1(-4,2) P2(9,-6)	sqrt of 233	-8/13
46	P1(3,2) P2(4,5)	sqrt of 10	3/1
47	P1(1,4) P2(-7,-7)	sqrt of 185	-11/-8
48	P1(5,3) P2(-9,6)	sqrt of 205	3/-14
49	P1(6,-2) P2(-4,-6)	sqrt of 116	-2/-5
50	P1(-9,2) P2(-1,-4)	sqrt of 100	-3/4

Arithmetic: Division of Decimal Numbers

Problem	Dividend	Divisor	Quotient
1	44.784	56.7892	0.7886
2	44.5097	67.5208	0.6592
3	7888.9234	892.604	8.8381
4	65098.6465	692.8491	93.9579
5	786.7735	2.1861	359.8982
6	64.873	924.1173	0.0702
7	6.6735	7.7284	0.8635
8	59.3669	8.0468	7.3777
9	430.599	76.7433	5.6109
10	0.0016	0.0621	0.0264
11	20.4644	33.6585	0.608
12	0.0015	0.8061	0.0019
13	436.7363	798.5671	0.5469
14	23503.1479	436.0073	53.9054
15	3279.8532	8.5102	385.4026
16	0.156	21.9669	0.0071
17	0.2264	5.7467	0.0394
18	197.5916	76.9318	2.5684
19	26.3738	6.5734	4.0122
20	0.0628	62.7709	0.001
21	6675.0322	85.6386	77.9442
22	181824.5404	631.6969	287.8351
23	0	0.0009	0.0169
24	3.5173	0.0854	41.1864
25	688.9783	0.8178	842.4777
26	6214.5181	69.0601	89.9871
27	0.0195	0.8937	0.0218
28	20.6037	35.6403	0.5781
29	27839.2215	44.1776	630.166
30	562.9067	0.8819	638.2886
31	9035.2309	93.6974	96.4299
32	4389.1909	51.2218	85.6899
33	0.0109	0.0763	0.1431
34	104.512	144.1147	0.7252
35	0.2406	4.2352	0.0568
36	81.2819	12.7477	6.3762
37	7573.4771	181.2986	41.7735
38	3705.9026	453.9767	8.1632
39	29.7328	0.1367	217.5041
40	10.2486	14.0469	0.7296
41	965.5841	116.2934	8.303
42	31.0689	502.7334	0.0618
43	1951.7555	272.0558	7.1741
44	379.0092	7.2848	52.0274
45	20.5656	2.6399	7.7903
46	42017.6013	575.0369	73.0694
47	15.3743	174.5096	0.0881
48	2089.4177	424.3334	4.924
49	197.343	1.3559	145.5439
50	0.0182	0.0653	0.2785

Arithmetic: Multiplication of Decimal Numbers

Problem	Multiplicand	Multiplier	Product
1	0.5094	309.0038	157.40653572
2	40.9598	5.4809	224.49656782
3	0.6049	79.7741	48.25535309
4	0.2195	0.0343	0.00752885
5	688.0884	0.0617	42.45505428
6	51.4242	2.8335	145.7104707
7	915.6447	0.4908	449.39841876
8	0.1063	3.9918	0.42432834
9	978.1362	4.7387	4635.09401094
10	95.5147	1.1155	106.54664785
11	642.5188	754.4554	484751.77826152
12	255.8015	55.6871	14244.84371065
13	0.0372	0.0971	0.00361212
14	1.6275	0.0326	0.0530565
15	889.822	0.0685	60.952807
16	0.3795	483.0143	183.30392685
17	189.7927	0.5984	113.57195168
18	0.7188	1.1769	0.84595572
19	0.1073	8.3671	0.89778983
20	47.1719	83.6382	3945.37280658
21	8.6757	8.69	75.391833
22	0.0749	8.4114	0.63001386
23	0.061	59.9761	3.6585421
24	0.054	876.9499	47.3552946
25	0.0374	0.0055	0.0002057
26	0.0001	75.6288	0.00756288
27	8.9716	0.7492	6.72152272
28	3.3164	0.0353	0.11706892
29	69.1712	0.2635	18.2266112
30	14.2166	6.5364	92.92538424
31	541.0089	0.046	24.8864094
32	506.637	0.0568	28.7769816
33	0.4379	3.3688	1.47519752
34	0.001	0.1454	0.0001454
35	0.001	426.3851	0.4263851
36	0.0379	0.8039	0.03046781
37	12.7783	3.4847	44.52854201
38	380.1181	0.0475	18.05560975
39	0.0457	0.0213	0.00097341
40	33.3423	0.8558	28.53434034
41	0.3592	0.0119	0.00427448
42	5.6339	0.2669	1.50368791
43	107.3717	8.7067	934.85318039
44	0.0847	78.862	6.6796114
45	873.4683	45.9648	40148.79571584
46	0.9698	5.8509	5.67420282
47	0.0626	773.8705	48.4442933
48	0.0537	76.8209	4.12528233
49	7.6381	0.0061	0.04659241
50	0.0699	0.0799	0.00558501

Arithmetic: Subtraction of Decimal Numbers

Problem	Minuend	Subtrahend	Difference
1	55.5831	0.0938	55.4893
2	97.3977	0.0119	97.3858
3	2.9727	0.0253	2.9474
4	77.9792	0.071	77.9082
5	663.8993	0.8293	663.07
6	68.2815	0.841	67.4405
7	91.5115	7.5429	83.9686
8	75.2968	0.0382	75.2586
9	95.925	0.0409	95.8841
10	0.4075	0.0736	0.3339
11	0.8718	0.302	0.5698
12	64.858	0.6873	64.1707
13	9.5118	0.01	9.5018
14	77.6452	2.0874	75.5578
15	0.8926	0.0931	0.7995
16	123.4639	0.4006	123.0633
17	68.9763	0.0095	68.9668
18	335.351	8.3938	326.9572
19	0.8847	0.6093	0.2754
20	751.2624	0.0741	751.1883
21	0.0712	0.0092	0.062
22	0.013	0.0009	0.0121
23	92.259	19.3473	72.9117
24	0.9896	0.0858	0.9038
25	0.8896	0.6365	0.2531
26	479.5022	4.3652	475.137
27	915.9891	0.0166	915.9725
28	0.8726	0.0286	0.844
29	842.7037	9.3765	833.3272
30	34.519	1.8296	32.6894
31	53.3587	4.2871	49.0716
32	553.897	0.7819	553.1151
33	0.243	0.0488	0.1942
34	46.9253	9.5407	37.3846
35	167.0183	6.9835	160.0348
36	6.4248	0.0335	6.3913
37	0.9673	0.0775	0.8898
38	1.0272	0.085	0.9422
39	0.0716	0.0352	0.0364
40	9.9647	3.717	6.2477
41	16.2975	5.9343	10.3632
42	487.3001	38.9786	448.3215
43	55.1973	0.0026	55.1947
44	75.6277	75.1861	0.4416
45	828.1208	0.0229	828.0979
46	0.0134	0.0006	0.0128
47	31.6996	27.2697	4.4299
48	539.5189	37.5577	501.9612
49	664.7314	0.0032	664.7282
50	641.7394	34.9651	606.7743

Arithmetic: Addition of Decimal Numbers

Problem	First Number	Second Number	Total
1	0.0026	981.2654	981.268
2	0.0208	42.6029	42.6237
3	0.0634	44.5964	44.6598
4	793.6952	830.9936	1624.6888
5	0.0662	622.8985	622.9647
6	8.0414	0.0324	8.0738
7	63.0108	0.0631	63.0739
8	711.5169	0.1995	711.7164
9	0.9275	0.4569	1.3844
10	54.8677	2.5913	57.459
11	2.1705	43.5898	45.7603
12	651.9181	80.7507	732.6688
13	47.7874	257.3152	305.1026
14	0.0778	33.5236	33.6014
15	0.079	0.0566	0.1356
16	71.6728	0.0081	71.6809
17	12.2747	567.3753	579.65
18	0.0562	0.2013	0.2575
19	4.9568	210.9177	215.8745
20	86.2756	9.2923	95.5679
21	774.662	765.2909	1539.9529
22	607.6213	8.2403	615.8616
23	0.0101	5.7655	5.7756
24	0.6504	9.5634	10.2138
25	0.0117	260.0548	260.0665
26	0.9758	29.3103	30.2861
27	340.8141	508.5107	849.3248
28	0.875	0.3414	1.2164
29	0.0034	0.0364	0.0398
30	1.1171	0.4417	1.5588
31	0.0861	25.1032	25.1893
32	0.1595	0.0663	0.2258
33	75.8952	0.4997	76.3949
34	0.001	2.3697	2.3707
35	154.5753	82.012	236.5873
36	0.0549	9.3232	9.3781
37	5.8314	6.1639	11.9953
38	94.4763	677.1486	771.6249
39	0.9663	167.5815	168.5478
40	735.6252	6.2167	741.8419
41	1.9531	404.8249	406.778
42	9.1271	586.0576	595.1847
43	0.0095	0.2098	0.2193
44	1.448	0.0275	1.4755
45	0.2775	588.0124	588.2899
46	544.8598	0.0221	544.8819
47	0.9052	9.8625	10.7677
48	0.5704	5.6942	6.2646
49	0.4421	984.7867	985.2288
50	0.036	10.5488	10.5848

Arithmetic: Division of Fractions

Problem	Dividend	Divisor	Quotient
1	1/18	2/21	7/12
2	1/20	5/12	3/25
3	5/24	7/12	5/14
4	5/16	4/21	1 41/64
5	7/20	1/20	7
6	7/22	1/18	5 8/11
7	4/7	15/16	64/105
8	1/18	7/16	8/63
9	3/20	3/10	1/2
10	5/18	5/24	1 1/3
11	3/10	7/20	6/7
12	5/18	2/15	2 1/12
13	7/20	3/20	2 1/3
14	3/4	2/5	1 7/8
15	5/7	8/7	5/8
16	7/12	7/16	1 1/3
17	2/7	8/7	1/4
18	1/14	3/22	11/21
19	1/16	3/14	7/24
20	1/24	3/22	11/36
21	7/18	5/22	1 32/45
22	1/14	5/24	12/35
23	5/16	5/16	1
24	7/12	1/10	5 5/6
25	4/15	5/21	1 3/25
26	8/21	1/15	5 5/7
27	3/5	11/20	1 1/11
28	6/7	2/9	3 6/7
29	1/14	8/21	3/16
30	7/9	7/12	1 1/3
31	7/12	7/24	2
32	4/21	7/16	64/147
33	4/21	1/24	4 4/7
34	7/10	5/24	3 9/25
35	2/15	1/18	2 2/5
36	3/20	1/16	2 2/5
37	3/5	1/24	14 2/5
38	7/15	1/10	4 2/3
39	7/18	1/18	7
40	7/12	1/14	8 1/6
41	7/16	1/12	5 1/4
42	3/14	7/10	15/49
43	8/9	1/10	8 8/9
44	1/5	5/24	24/25
45	8/9	2/9	4
46	4/7	1/5	2 6/7
47	7/18	1/14	5 4/9
48	4/7	3/5	20/21
49	1/18	7/12	2/21
50	4/15	3/20	1 7/9

Arithmetic: Multiplication of Fractions

Problem	Multiplicand	Multiplier	Product
1	7/8	8/9	7/9
2	5/12	2/15	1/18
3	3/5	1/12	1/20
4	4/7	11/12	11/21
5	5/22	8/21	20/231
6	5/24	8/21	5/63
7	7/20	7/24	49/480
8	1/12	1/18	1/216
9	3/22	7/16	21/352
10	1/4	5/4	5/16
11	1/14	2/21	1/147
12	5/24	1/15	1/72
13	7/20	5/22	7/88
14	1/18	7/10	7/180
15	5/21	1/15	1/63
16	6/7	8/9	16/21
17	5/22	1/21	5/462
18	7/15	7/12	49/180
19	7/8	3/8	21/64
20	7/20	3/10	21/200
21	8/21	2/15	16/315
22	7/20	1/14	1/40
23	1/18	3/16	1/96
24	7/20	3/14	3/40
25	3/16	1/24	1/128
26	1/18	1/14	1/252
27	1/14	5/12	5/168
28	4/7	11/18	22/63
29	7/18	7/20	49/360
30	7/15	1/14	1/30
31	4/15	1/24	1/90
32	7/10	3/20	21/200
33	7/8	10/21	5/12
34	3/20	8/21	2/35
35	1/12	8/21	2/63
36	5/16	7/22	35/352
37	6/7	4/7	24/49
38	4/5	7/8	7/10
39	5/12	8/21	10/63
40	3/20	7/10	21/200
41	5/9	10/21	50/189
42	8/9	3/7	8/21
43	7/18	1/10	7/180
44	7/10	1/14	1/20
45	7/18	1/24	7/432
46	2/15	7/22	7/165
47	3/14	3/10	9/140
48	7/16	1/14	1/32
49	5/21	7/10	1/6
50	5/22	5/14	25/308

Arithmetic: Subtraction of Fractions

Problem	Minuend	Subtrahend	Difference
1	1/16	8/15	-113/240
2	2/5	1/5	1/5
3	8/21	8/21	0
4	2/15	1/16	17/240
5	7/18	1/12	11/36
6	2/9	6/7	-40/63
7	3/5	11/12	-19/60
8	1/9	8/9	-7/9
9	8/9	6/7	2/63
10	8/15	5/22	101/330
11	8/21	1/24	19/56
12	7/24	1/18	17/72
13	5/24	7/20	-17/120
14	5/7	3/20	79/140
15	8/15	1/16	113/240
16	4/21	7/24	-17/168
17	1/21	4/15	-23/105
18	1/14	7/20	-39/140
19	7/9	11/18	1/6
20	1/15	4/21	-13/105
21	3/14	4/21	1/42
22	5/12	2/21	9/28
23	5/18	5/24	5/72
24	3/10	1/12	13/60
25	1/12	1/14	1/84
26	8/21	5/12	-1/28
27	1/16	5/22	-29/176
28	7/12	3/10	17/60
29	5/16	5/24	5/48
30	7/20	1/24	37/120
31	3/14	7/12	-31/84
32	5/18	1/12	7/36
33	7/12	7/24	7/24
34	7/8	3/14	37/56
35	3/5	10/21	13/105
36	1/12	5/18	-7/36
37	7/8	8/9	-1/72
38	3/20	4/21	-17/420
39	5/24	1/20	19/120
40	1/8	3/4	-5/8
41	7/24	8/21	-5/56
42	3/20	8/21	-97/420
43	3/10	1/10	1/5
44	1/22	1/24	1/264
45	3/20	7/18	-43/180
46	3/22	7/18	-25/99
47	1/10	5/18	-8/45
48	2/3	8/3	-2
49	1/16	7/18	-47/144
50	1/24	1/10	-7/120

Arithmetic: Addition of Fractions

Problem	First Number	Second Number	Total
1	1/10	4/21	61/210
2	3/16	7/16	5/8
3	5/14	1/15	89/210
4	8/9	1/6	1 1/18
5	3/7	7/24	121/168
6	1/24	5/14	67/168
7	7/10	4/15	29/30
8	7/8	1/8	1
9	1/18	1/20	19/180
10	7/18	7/22	70/99
11	1/22	2/21	65/462
12	1/4	2/3	11/12
13	3/14	7/24	85/168
14	7/24	1/20	41/120
15	7/10	1/15	23/30
16	3/10	1/12	23/60
17	3/20	1/18	37/180
18	5/18	8/15	73/90
19	2/15	7/24	17/40
20	3/16	7/18	83/144
21	6/7	7/12	1 37/84
22	1/10	5/24	37/120
23	1/24	7/16	23/48
24	5/22	3/10	29/55
25	7/9	5/9	1 1/3
26	7/24	7/12	7/8
27	3/16	1/18	35/144
28	1/20	7/20	2/5
29	1/6	15/16	1 5/48
30	7/18	1/12	17/36
31	7/16	1/24	23/48
32	3/10	7/22	34/55
33	3/16	1/12	13/48
34	4/21	1/16	85/336
35	1/8	7/8	1
36	7/18	7/18	7/9
37	3/5	5/14	67/70
38	7/16	5/12	41/48
39	7/16	8/21	275/336
40	3/20	7/20	1/2
41	2/21	3/20	103/420
42	7/16	7/18	119/144
43	2/21	5/16	137/336
44	5/7	1/20	107/140
45	7/9	2/5	1 8/45
46	5/14	1/15	89/210
47	7/8	1/18	67/72
48	7/16	7/24	35/48
49	4/21	4/21	8/21
50	8/21	5/14	31/42

Arithmetic: Division of Integers

Problem	Dividend	Divisor	Quotient
1	624	16	39
2	868	62	14
3	440	10	44
4	736	46	16
5	250	10	25
6	608	16	38
7	520	10	52
8	816	68	12
9	200	20	10
10	950	38	25
11	800	10	80
12	130	10	13
13	170	10	17
14	190	10	19
15	580	10	58
16	28832	32	901
17	46300	50	926
18	44660	58	770
19	13944	83	168
20	6148	29	212
21	16910	95	178
22	65010	66	985
23	21584	71	304
24	29810	55	542
25	18216	44	414
26	15162	21	722
27	26255	89	295
28	34086	78	437
29	4884	37	132
30	19383	39	497
31	869	79	11
32	680	10	68
33	414	23	18
34	350	35	10
35	341	11	31
36	903	43	21
37	600	60	10
38	264	12	22
39	648	12	54
40	620	10	62
41	640	32	20
42	297	11	27
43	460	46	10
44	731	43	17
45	247	19	13
46	4290	30	143
47	43362	66	657
48	15470	17	910
49	11377	31	367
50	28149	33	853

Arithmetic: Multiplication of Integers

Problem	Multiplicand	Multiplier	Product
1	688	61	41968
2	598	16	9568
3	543	78	42354
4	266	53	14098
5	904	20	18080
6	106	43	4558
7	987	33	32571
8	516	62	31992
9	819	26	21294
10	290	32	9280
11	622	51	31722
12	265	61	16165
13	978	45	44010
14	298	79	23542
15	108	10	1080
16	723	806	582738
17	189	150	28350
18	148	599	88652
19	305	348	106140
20	495	351	173745
21	923	203	187369
22	218	296	64528
23	537	543	291591
24	449	760	341240
25	826	812	670712
26	447	338	151086
27	711	781	555291
28	291	896	260736
29	531	984	522504
30	856	760	650560
31	139	68	9452
32	735	41	30135
33	355	87	30885
34	601	60	36060
35	643	64	41152
36	957	74	70818
37	499	23	11477
38	364	94	34216
39	953	61	58133
40	502	91	45682
41	337	67	22579
42	534	59	31506
43	821	88	72248
44	566	57	32262
45	852	56	47712
46	302	840	253680
47	921	690	635490
48	291	788	229308
49	450	696	313200
50	652	846	551592

Arithmetic: Subtraction of Integers

Problem	Minuend	Subtrahend	Difference
1	2600	385	2215
2	81	44	37
3	7701	333	7368
4	495	98	397
5	65	28	37
6	1908	299	1609
7	6503	298	6205
8	1301	583	718
9	677	49	628
10	851	83	768
11	7702	226	7476
12	4203	707	3496
13	3000	278	2722
14	9406	537	8869
15	4100	446	3654
16	4003	157	3846
17	6700	669	6031
18	2400	618	1782
19	157	78	79
20	5805	615	5190
21	6605	567	6038
22	55	35	20
23	84	44	40
24	91	73	18
25	91	55	36
26	6402	843	5559
27	111	53	58
28	9504	967	8537
29	7402	177	7225
30	74	45	29
31	5000	377	4623
32	823	54	769
33	812	27	785
34	61	29	32
35	747	59	688
36	7100	286	6814
37	4800	813	3987
38	343	38	305
39	41	24	17
40	4705	639	4066
41	3202	654	2548
42	71	25	46
43	4500	623	3877
44	8700	149	8551
45	1904	174	1730
46	6505	348	6157
47	3802	739	3063
48	7701	986	6715
49	5106	246	4860
50	1401	588	813

Arithmetic: Addition of Integers

Problem	First Number	Second Number	Total
1	391	72	463
2	387	72	459
3	634	65	699
4	670	11	681
5	601	96	697
6	132	32	164
7	729	38	767
8	691	17	708
9	221	66	287
10	907	21	928
11	245	63	308
12	617	32	649
13	763	96	859
14	660	92	752
15	826	22	848
16	792	72	864
17	811	16	827
18	866	11	877
19	287	45	332
20	688	14	702
21	174	56	230
22	239	69	308
23	596	25	621
24	583	25	608
25	512	77	589
26	805	74	879
27	860	71	931
28	826	49	875
29	873	97	970
30	726	87	813
31	401	95	496
32	243	39	282
33	226	39	265
34	763	60	823
35	544	22	566
36	665	60	725
37	551	25	576
38	753	88	841
39	576	30	606
40	992	18	1010
41	326	70	396
42	550	25	575
43	151	81	232
44	732	93	825
45	641	56	697
46	468	96	564
47	498	37	535
48	863	38	901
49	453	77	530
50	770	35	805