Arithmetic: Division of Decimal Numbers

Problem	Dividend	Divisor	Quotient
1	8.488	233.3613	0.0364
2	169.6046	0.4605	368.3053
3	0.0496	3.0711	0.0162
4	0.0945	0.4505	0.2098
5	0.8463	19.2423	0.044
6	98.4193	0.0763	1289.8991
7	7.1581	3.1031	2.3068
8	0.5602	0.0311	18.0129
9	347.3041	0.6389	543.597
10	6.2096	0.3485	17.8181
11	0.1343	591.6728	0.0002
12	14.7355	877.147	0.0168
13	7.9745	0.6545	12.1841
14	8.0954	0.1613	50.1885
15	58.4831	0.0519	1126.842
16	78.3636	0.0208	3767.4808
17	0.0016	866.7104	0
18	0.2518	0.001	251.8
19	3.0491	1.3807	2.2084
20	56.2687	8.0528	6.9875
21	634.4132	15.7736	40.2199
22	4.2809	539.4563	0.0079
23	438.7665	3.5674	122.9934
24	5.5818	62.8657	0.0888
25	0.0877	10.4903	0.0084
26	4.2181	0.053	79.5868
27	0.0872	0.0109	8
28	0.4088	15.8202	0.0258
29	0.0539	0.001	53.9
30	0.3015	1.2759	0.2363
31	194.9015	6.0507	32.2114
32	0.0853	19.1557	0.0045
33	621.8137	318.3101	1.9535
34	5.8954	0.0684	86.1901
35	0.04	8.2063	0.0049
36	1.1275	1.5734	0.7166
37	2.8575	0.0355	80.493
38	87.6861	0.0563	1557.4796
39	89.6882	93.4943	0.9593
40	3.236	0.4342	7.4528
41	0.0543	53.7471	0.001
42	90.1243	411.0571	0.2193
43	542.1571	45.9928	11.7879
44	0.0094	0.0099	0.9495
45	8.3036	0.4716	17.6073
46	0.1738	67.7428	0.0026
47	2.6699	895.3195	0.003
48	1.6401	760.0247	0.0022
49	0.0202	0.6654	0.0304
50	1.4526	81.0638	0.0179

Arithmetic: Multiplication of Decimal Numbers

Problem	Multiplicand	Multiplier	Product
1	0.2092	196.588	41.1262096
2	0.7923	0.9466	0.74999118
3	6.2594	1.2314	7.70782516
4	0.0226	0.0526	0.00118876
5	0.043	3.8815	0.1669045
6	980.4963	0.0568	55.69218984
7	0.0093	0.0352	0.00032736
8	24.5749	0.0272	0.66843728
9	45.532	61.9808	2822.1097856
10	346.4476	33.264	11524.2329664
11	0.1771	0.8461	0.14984431
12	0.001	2.2009	0.0022009
13	95.8318	0.0567	5.43366306
14	0.4508	70.2352	31.66202816
15	0.0264	54.9012	1.44939168
16	0.0667	583.2112	38.90018704
17	9.2183	0.0198	0.18252234
18	0.0327	0.2942	0.00962034
19	0.7415	25.8017	19.13196055
20	89.5714	0.0092	0.82405688
21	5.8683	0.0072	0.04225176
22	2.2585	0.6895	1.55723575
23	0.073	645.402	47.114346
24	25.9454	9.5754	248.43758316
25	1.3689	791.1989	1083.07217421
26	38.3882	0.0885	3.3973557
27	0.6887	0.7672	0.52837064
28	0.0514	3.9018	0.20055252
29	0.0878	2.0567	0.18057826
30	4.4258	509.9977	2257.14782066
31	0.7725	0.9285	0.71726625
32	8.9806	265.8359	2387.36588354
33	3.982	0.0248	0.0987536
34	1.9307	0.8918	1.72179826
35	13.1074	0.2543	3.33321182
36	127.6926	95.7857	12231.12507582
37	8.4808	0.0419	0.35534552
38	57.749	9.3628	540.6923372
39	0.0095	5.4041	0.05133895
40	58.2553	131.2681	7647.06254593
41	0.7637	0.0303	0.02314011
42	443.4442	0.0258	11.44086036
43	0.0091	0.0101	0.00009191
44	7.0079	9.5746	67.09783934
45	9.5315	300.0306	2859.7416639
46	0.0327	79.1454	2.58805458
47	0.0696	0.0327	0.00227592
48	576.1408	0.9258	533.39115264
49	0.8758	8.7065	7.6251527
50	0.7122	887.541	632.1067002

Arithmetic: Subtraction of Decimal Numbers

Problem	Minuend	Subtrahend	Difference
1	0.054	0.0493	0.0047
2	16.1608	0.9381	15.2227
3	428.9793	71.1015	357.8778
4	632.2885	24.5929	607.6956
5	6.5712	0.007	6.5642
6	6.7514	0.0689	6.6825
7	418.3675	0.0096	418.3579
8	30.3243	15.9076	14.4167
9	992.3512	3.5296	988.8216
10	65.0795	6.4159	58.6636
11	786.9899	136.2085	650.7814
12	160.1077	0.6419	159.4658
13	7.1312	0.0095	7.1217
14	204.0917	0.6831	203.4086
15	1.5637	0.0114	1.5523
16	955.7643	0.7823	954.982
17	57.7441	0.0129	57.7312
18	9.4048	0.8092	8.5956
19	1.3303	0.0697	1.2606
20	80.7902	5.5414	75.2488
21	0.0274	0.0009	0.0265
22	981.9702	0.0565	981.9137
23	52.2602	0.0376	52.2226
24	189.9246	0.0584	189.8662
25	47.1731	0.628	46.5451
26	0.2905	0.0307	0.2598
27	996.6277	0.6105	996.0172
28	0.0864	0.0821	0.0043
29	0.7937	0.0009	0.7928
30	0.3147	0.0753	0.2394
31	1.405	0.0807	1.3243
32	7.2464	0.9574	6.289
33	0.7898	0.788	0.0018
34	0.0572	0.0094	0.0478
35	0.7696	0.0866	0.683
36	743.6716	0.0272	743.6444
37	0.0602	0.0464	0.0138
38	684.2305	580.3356	103.8949
39	213.1919	0.0974	213.0945
40	8.5213	0.001	8.5203
41	945.7993	0.3815	945.4178
42	80.5646	0.3437	80.2209
43	27.2151	1.495	25.7201
44	153.7222	7.1016	146.6206
45	5.674	0.4163	5.2577
46	11.4604	0.4903	10.9701
47	2.1944	0.5041	1.6903
48	0.0094	0.001	0.0084
49	3.799	0.0877	3.7113
50	27.2887	0.06	27.2287

Arithmetic: Addition of Decimal Numbers

Problem	First Number	Second Number	Total
1	8.9623	297.7417	306.704
2	701.3934	56.8087	758.2021
3	0.0803	0.0375	0.1178
4	0.2605	0.3988	0.6593
5	92.2453	200.2868	292.5321
6	9.1042	0.0848	9.189
7	55.3875	0.046	55.4335
8	0.8027	4.375	5.1777
9	0.2518	92.2347	92.4865
10	0.1256	14.2466	14.3722
11	0.2597	0.0629	0.3226
12	0.0017	4.8836	4.8853
13	94.992	0.9734	95.9654
14	70.0381	0.8447	70.8828
15	830.4316	591.1617	1421.5933
16	375.1138	897.6198	1272.7336
17	0.0325	635.6434	635.6759
18	0.2136	2.9063	3.1199
19	94.7286	247.4069	342.1355
20	18.6166	0.0095	18.6261
21	3.685	0.0698	3.7548
22	0.0923	0.0745	0.1668
23	1.0355	0.5347	1.5702
24	0.9847	515.7856	516.7703
25	6.6101	7.9197	14.5298
26	0.0092	332.66	332.6692
27	3.1029	0.0766	3.1795
28	0.5722	4.7995	5.3717
29	7.201	0.5759	7.7769
30	296.1494	89.8571	386.0065
31	0.5085	0.2655	0.774
32	95.6671	92.5247	188.1918
33	0.021	0.0678	0.0888
34	3.0109	8.3834	11.3943
35	19.5022	0.0615	19.5637
36	0.0485	6.2722	6.3207
37	82.4537	0.602	83.0557
38	0.5749	4.1111	4.686
39	0.2779	564.1305	564.4084
40	0.8831	0.0392	0.9223
41	0.6283	8.0648	8.6931
42	0.0748	30.2323	30.3071
43	0.419	0.7389	1.1579
44	6.429	643.4785	649.9075
45	60.9713	267.7551	328.7264
46	91.7453	278.0438	369.7891
47	0.1798	0.8098	0.9896
48	5.779	26.4543	32.2333
49	0.0024	0.0512	0.0536
50	9.8455	356.8249	366.6704

Arithmetic: Division of Integers

Problem	Dividend	Divisor	Quotient
1	910	10	91
2	627	57	11
3	750	15	50
4	704	11	64
5	990	30	33
6	520	10	52
7	936	18	52
8	470	10	47
9	770	77	10
10	728	56	13
11	130	13	10
12	451	41	11
13	170	10	17
14	348	12	29
15	190	10	19
16	12402	26	477
17	87688	97	904
18	68780	76	905
19	13860	14	990
20	11857	71	167
21	77812	98	794
22	17813	47	379
23	39259	43	913
24	36782	53	694
25	13032	18	724
26	23894	26	919
27	55260	60	921
28	62790	78	805
29	30294	54	561
30	54448	83	656
31	242	11	22
32	342	18	19
33	546	13	42
34	190	19	10
35	640	32	20
36	780	10	78
37	464	29	16
38	429	11	39
39	726	11	66
40	833	49	17
41	777	37	21
42	940	94	10
43	870	10	87
44	300	12	25
45	825	33	25
46	40296	92	438
47	48412	91	532
48	28310	38	745
49	14782	19	778
50	35760	48	745

Arithmetic: Multiplication of Integers

Problem	Multiplicand	Multiplier	Product
1	690	59	40710
2	752	80	60160
3	494	55	27170
4	399	41	16359
5	965	27	26055
6	434	37	16058
7	698	48	33504
8	589	51	30039
9	397	97	38509
10	179	89	15931
11	177	67	11859
12	853	46	39238
13	963	68	65484
14	487	78	37986
15	406	65	26390
16	764	826	631064
17	172	873	150156
18	782	221	172822
19	616	420	258720
20	279	231	64449
21	950	616	585200
22	606	527	319362
23	782	179	139978
24	300	331	99300
25	867	439	380613
26	939	793	744627
27	337	500	168500
28	183	899	164517
29	230	782	179860
30	352	705	248160
31	959	95	91105
32	470	65	30550
33	904	25	22600
34	491	90	44190
35	675	85	57375
36	284	36	10224
37	405	33	13365
38	498	73	36354
39	882	49	43218
40	605	27	16335
41	268	70	18760
42	450	79	35550
43	713	81	57753
44	511	33	16863
45	584	42	24528
46	849	291	247059
47	766	595	455770
48	529	725	383525
49	377	896	337792
50	527	633	333591

Arithmetic: Subtraction of Integers

Problem	Minuend	Subtrahend	Difference
1	781	88	693
2	3402	268	3134
3	3400	976	2424
4	724	47	677
5	32	15	17
6	5900	663	5237
7	43	34	9
8	2900	373	2527
9	42	18	24
10	1602	588	1014
11	84	28	56
12	292	76	216
13	804	37	767
14	67	58	9
15	2401	942	1459
16	65	55	10
17	593	97	496
18	96	47	49
19	134	19	115
20	85	83	2
21	1003	576	427
22	2400	133	2267
23	66	59	7
24	74	67	7
25	721	82	639
26	5302	507	4795
27	127	67	60
28	5400	682	4718
29	2300	191	2109
30	2000	579	1421
31	8905	429	8476
32	7000	257	6743
33	447	27	420
34	4305	775	3530
35	1800	193	1607
36	375	59	316
37	9300	146	9154
38	991	99	892
39	175	48	127
40	6705	518	6187
41	707	47	660
42	51	16	35
43	74	37	37
44	73	17	56
45	868	18	850
46	9801	648	9153
47	42	25	17
48	3106	877	2229
49	26	19	7
50	841	17	824

Arithmetic: Addition of Integers

Problem	First Number	Second Number	Sum
1	340	489	829
2	372	293	665
3	374	854	1228
4	229	807	1036
5	598	104	702
6	618	950	1568
7	171	541	712
8	927	298	1225
9	904	264	1168
10	168	293	461
11	360	440	800
12	304	772	1076
13	825	768	1593
14	927	525	1452
15	609	962	1571
16	603	744	1347
17	100	638	738
18	456	881	1337
19	451	704	1155
20	577	212	789
21	242	907	1149
22	924	306	1230
23	714	118	832
24	647	130	777
25	315	100	415
26	667	675	1342
27	634	396	1030
28	265	971	1236
29	199	976	1175
30	631	531	1162
31	680	66	746
32	968	13	981
33	139	72	211
34	977	84	1061
35	463	96	559
36	800	12	812
37	712	84	796
38	840	88	928
39	676	17	693
40	871	38	909
41	777	81	858
42	417	78	495
43	976	89	1065
44	220	45	265
45	690	67	757
46	821	46	867
47	152	71	223
48	207	97	304
49	912	95	1007
50	531	65	596

Arithmetic: Division of Fractions

Problem	Dividend	Divisor	Quotient
1	7/8	15/16	14/15
2	4/21	3/14	8/9
3	1/18	5/21	7/30
4	7/8	1/8	7
5	7/16	3/10	1 11/24
6	7/18	1/15	5 5/6
7	5/22	1/20	4 6/11
8	7/24	3/14	1 13/36
9	7/12	7/12	1
10	7/20	1/14	4 9/10
11	2/3	7/8	16/21
12	2/15	5/18	12/25
13	5/14	4/15	1 19/56
14	1/18	5/14	7/45
15	3/22	2/21	1 19/44
16	3/22	7/12	18/77
17	1/18	1/18	1
18	8/9	3/20	5 25/27
19	1/15	3/10	2/9
20	7/24	3/22	2 5/36
21	7/8	1/18	15 3/4
22	4/21	7/18	24/49
23	7/15	7/16	1 1/15
24	5/8	7/8	5/7
25	1/10	7/12	6/35
26	7/16	3/16	2 1/3
27	8/21	1/22	8 8/21
28	7/9	7/8	8/9
29	5/21	7/10	50/147
30	7/12	5/24	2 4/5
31	7/24	5/12	7/10
32	4/9	10/21	14/15
33	8/9	3/20	5 25/27
34	1/12	1/20	1 2/3
35	8/9	7/9	1 1/7
36	5/12	7/22	1 13/42
37	7/10	7/10	1
38	6/7	8/9	27/28
39	5/24	1/14	2 11/12
40	7/12	1/15	8 3/4
41	5/16	5/21	1 5/16
42	5/14	7/18	45/49
43	7/9	4/7	1 13/36
44	1/22	3/20	10/33
45	7/20	1/24	8 2/5
46	4/21	1/20	3 17/21
47	7/20	2/21	3 27/40
48	7/24	5/16	14/15
49	8/9	5/9	1 3/5
50	1/14	1/24	1 5/7

Multiplication of Fractions

Problem	Multiplicand	Multiplier	Product
1	2/7	4/9	8/63
2	1/16	5/21	5/336
3	5/7	5/14	25/98
4	5/24	5/24	25/576
5	5/9	4/9	20/81
6	5/16	5/18	25/288
7	7/12	7/12	49/144
8	1/18	7/12	7/216
9	1/14	1/12	1/168
10	8/15	3/10	4/25
11	8/9	5/18	20/81
12	3/22	7/10	21/220
13	8/9	1/9	8/81
14	8/15	1/24	1/45
15	7/15	7/22	49/330
16	7/12	7/18	49/216
17	7/8	3/5	21/40
18	7/10	4/15	14/75
19	1/24	1/10	1/240
20	1/15	7/24	7/360
21	4/21	8/21	32/441
22	5/16	3/16	15/256
23	6/7	9/20	27/70
24	1/21	7/18	1/54
25	1/24	4/15	1/90
26	7/24	7/20	49/480
27	7/20	3/20	21/400
28	5/16	1/12	5/192
29	1/22	8/15	4/165
30	1/18	1/21	1/378
31	1/10	7/18	7/180
32	3/10	5/18	1/12
33	1/24	1/16	1/384
34	1/12	7/20	7/240
35	1/16	5/22	5/352
36	7/24	7/16	49/384
37	3/22	1/22	3/484
38	7/10	7/18	49/180
39	2/3	2/3	4/9
40	3/5	3/4	9/20
41	1/4	7/4	7/16
42	7/12	8/15	14/45
43	3/20	7/24	7/160
44	5/14	7/20	1/8
45	7/20	1/22	7/440
46	7/24	5/12	35/288
47	1/18	7/10	7/180
48	4/5	5/18	2/9
49	1/14	7/12	1/24
50	4/15	7/20	7/75

Arithmetic: Subtraction of Fractions

Problem	Minuend	Subtrahend	Difference
1	1/12	7/12	-1/2
2	5/12	1/18	13/36
3	7/22	7/10	-21/55
4	1/16	5/18	-31/144
5	5/12	7/24	1/8
6	5/12	7/22	13/132
7	5/22	7/16	-37/176
8	6/7	5/8	13/56
9	1/24	2/15	-11/120
10	8/9	1/16	119/144
11	1/22	8/15	-161/330
12	5/8	3/8	1/4
13	3/14	5/12	-17/84
14	7/22	7/10	-21/55
15	3/5	4/5	-1/5
16	5/21	5/12	-5/28
17	5/18	1/10	8/45
18	5/21	7/22	-37/462
19	4/21	1/18	17/126
20	3/20	1/15	1/12
21	7/12	1/21	15/28
22	8/15	3/16	83/240
23	3/16	1/14	13/112
24	2/3	8/9	-2/9
25	1/12	1/14	1/84
26	3/20	1/14	11/140
27	5/12	8/15	-7/60
28	3/5	11/12	-19/60
29	3/14	1/12	11/84
30	3/5	5/24	47/120
31	7/18	1/14	20/63
32	3/14	3/16	3/112
33	4/9	5/24	17/72
34	8/21	1/14	13/42
35	6/7	3/7	3/7
36	2/3	1/12	7/12
37	7/10	3/20	11/20
38	5/12	7/18	1/36
39	8/9	10/21	26/63
40	5/7	5/9	10/63
41	1/16	5/14	-33/112
42	7/24	7/18	-7/72
43	5/18	3/14	4/63
44	2/21	7/10	-127/210
45	5/22	7/12	-47/132
46	7/18	3/20	43/180
47	7/20	7/16	-7/80
48	1/20	3/20	-1/10
49	3/14	3/14	0
50	5/24	1/15	17/120

Arithmetic: Addition of Fractions

Problem	First Number	Second Number	Total
1	5/24	3/10	61/120
2	1/21	3/14	11/42
3	4/9	1/22	97/198
4	5/12	7/24	17/24
5	1/20	1/22	21/220
6	5/12	8/21	67/84
7	1/10	5/24	37/120
8	5/16	5/14	75/112
9	6/7	4/9	1 19/63
10	7/20	7/12	14/15
11	2/9	7/9	1
12	7/18	1/10	22/45
13	3/16	7/15	157/240
14	3/22	1/22	22/121
15	5/14	1/12	37/84
16	7/16	5/21	227/336
17	5/14	1/21	17/42
18	7/15	1/12	11/20
19	1/22	2/15	59/330
20	1/2	1/2	1
21	7/20	5/21	247/420
22	1/24	7/15	61/120
23	3/14	3/22	27/77
24	1/10	7/22	23/55
25	8/9	1/24	67/72
26	8/9	21/22	1 167/198
27	5/14	4/15	131/210
28	8/21	7/12	27/28
29	7/10	3/10	1
30	4/7	2/5	34/35
31	7/10	1/18	34/45
32	4/15	3/22	133/330
33	1/7	8/9	1 2/63
34	7/10	1/10	4/5
35	7/10	1/20	3/4
36	2/3	10/21	1 1/7
37	7/18	5/18	2/3
38	1/3	3/10	19/30
39	7/16	7/18	119/144
40	2/21	4/15	38/105
41	7/16	7/10	1 11/80
42	6/7	8/9	1 47/63
43	3/4	1/4	1
44	5/22	1/12	41/132
45	5/16	5/24	25/48
46	5/9	5/14	115/126
47	3/22	7/10	46/55
48	5/16	1/16	3/8
49	1/15	5/21	32/105
50	1/15	5/14	89/210

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(-4,5) P2(0,3); A(7,11) B(11,9)	x+2y-6=0, x+2y-29=0	parallel lines: m1=-1/2 m2=-1/2
2	P1(-3,1) P2(1,5); A(4,12) B(2,10)	x-y+4=0, x-y+8=0	parallel lines: m1=1/1 m2=1/1
3	P1(6,5) P2(4,3); A(4,4) B(2,6)	x-y-1=0, x+y-8=0	perpendicular lines: m1=1/1 m2=1/-1
4	P1(6,1) P2(8,4); A(3,3) B(6,1)	3x-2y-16=0, 2x+3y-15=0	perpendicular lines: m1=3/2 m2=-2/3
5	P1(9,7) P2(5,0); A(0,6) B(7,2)	7x-4y-35=0, 4x+7y-42=0	perpendicular lines: m1=-7/-4 m2=-4/7
6	P1(-3,8) P2(7,2); A(9,10) B(14,7)	3x+5y-31=0, 3x+5y-77=0	parallel lines: m1=-3/5 m2=-3/5
7	P1(4,5) P2(8,1); A(5,1) B(9,5)	x+y-9=0, x-y-4=0	perpendicular lines: m1=-1/1 m2=1/1
8	P1(-2,0) P2(4,8); A(14,14) B(8,6)	4x-3y+8=0, 4x-3y-14=0	parallel lines: m1=4/3 m2=-4/-3
9	P1(7,3) P2(4,5); A(7,4) B(9,7)	2x+3y-23=0, 3x-2y-13=0	perpendicular lines: m1=2/-3 m2=3/2
10	P1(4,3) P2(5,8); A(2,1) B(7,0)	5x-y-17=0, x+5y-7=0	perpendicular lines: m1=5/1 m2=-1/5
11	P1(-4,1) P2(0,5); A(2,3) B(5,6)	x-y+5=0, x-y+1=0	parallel lines: m1=1/1 m2=1/1
12	P1(-1,0) P2(9,3); A(14,3) B(4,0)	3x-10y+3=0, 3x-10y-12=0	parallel lines: m1=3/10 m2=-3/-10
13	P1(-2,9) P2(6,7); A(12,3) B(8,4)	x+4y-34=0, x+4y-24=0	parallel lines: m1=-1/4 m2=1/-4
14	P1(7,7) P2(6,9); A(7,7) B(9,8)	2x+y-21=0, x-2y+7=0	perpendicular lines: m1=2/-1 m2=1/2
15	P1(-1,4) P2(8,9); A(2,8) B(11,13)	5x-9y+41=0, 5x-9y+62=0	parallel lines: m1=5/9 m2=5/9
16	P1(7,8) P2(3,4); A(8,1) B(4,5)	x-y+1=0, x+y-9=0	perpendicular lines: m1=1/1 m2=1/-1
17	P1(-6,9) P2(3,6); A(6,8) B(0,10)	x+3y-21=0, x+3y-30=0	parallel lines: m1=-1/3 m2=1/-3
18	P1(-8,2) P2(4,5); A(8,1) B(4,0)	x-4y+16=0, x-4y-4=0	parallel lines: m1=1/4 m2=-1/-4
19	P1(3,9) P2(7,7); A(3,0) B(5,4)	x+2y-21=0, 2x-y-6=0	perpendicular lines: m1=-1/2 m2=2/1
20	P1(6,7) P2(0,0); A(7,0) B(0,6)	7x-6y+0=0, 6x+7y-42=0	perpendicular lines: m1=-7/-6 m2=6/-7

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(-3,5) P2(-2,-5)	2x-20y+5=0
2	P1(9,7) P2(1,-1)	1x+1y-8=0
3	P1(3,7) P2(-9,-4)	24x+22y+39=0
4	P1(4,8) P2(-1,5)	5x+3y-27=0
5	P1(9,-6) P2(-4,-9)	13x+3y-10=0
6	P1(-8,7) P2(7,-5)	10x-8y+13=0
7	P1(3,4) P2(-6,-8)	6x+8y+25=0
8	P1(4,-3) P2(-8,-4)	24x+2y+55=0
9	P1(1,8) P2(3,-9)	4x-34y-25=0
10	P1(-1,3) P2(8,-7)	18x-20y-103=0
11	P1(-3,4) P2(-8,-4)	10x+16y+55=0
12	P1(9,1) P2(-9,6)	36x-10y+35=0
13	P1(-5,9) P2(-8,-3)	2x+8y-11=0
14	P1(-2,2) P2(3,-1)	5x-3y-1=0
15	P1(2,1) P2(2,-4)	0x-2y-3=0
16	P1(8,7) P2(-3,-9)	22x+32y-23=0
17	P1(5,-3) P2(-8,-8)	13x+5y+47=0
18	P1(7,1) P2(-5,5)	3x-1y-0=0
19	P1(-9,1) P2(3,-5)	2x-1y+4=0
20	P1(1,3) P2(8,-1)	14x-8y-55=0
21	P1(3,-5) P2(-4,-9)	14x+8y+63=0
22	P1(-3,6) P2(-6,-6)	2x+8y+9=0
23	P1(5,7) P2(-5,-7)	5x+7y-0=0
24	P1(4,9) P2(-9,1)	26x+16y-15=0
25	P1(4,1) P2(-5,-4)	9x+5y+12=0
26	P1(5,6) P2(-3,9)	16x-6y+29=0
27	P1(-8,4) P2(-4,-7)	8x-22y+15=0
28	P1(-1,3) P2(4,-2)	1x-1y-1=0
29	P1(3,5) P2(6,-1)	2x-4y-1=0
30	P1(6,-2) P2(-7,-3)	13x+1y+9=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(2,4) P2(7,8)	sqrt of 41	4/5
2	P1(8,6) P2(4,7)	sqrt of 17	1/-4
3	P1(1,-3) P2(-3,-6)	sqrt of 25	-3/-4
4	P1(-6,7) P2(5,-6)	sqrt of 290	-13/11
5	P1(-1,5) P2(-8,-2)	sqrt of 98	1/1
6	P1(1,7) P2(9,-3)	sqrt of 164	-5/4
7	P1(5,6) P2(-2,-7)	sqrt of 218	-13/-7
8	P1(9,8) P2(4,9)	sqrt of 26	1/-5
9	P1(3,9) P2(-2,1)	sqrt of 89	-8/-5
10	P1(4,1) P2(3,9)	sqrt of 65	8/-1
11	P1(6,3) P2(-8,4)	sqrt of 197	1/-14
12	P1(7,6) P2(2,2)	sqrt of 41	-4/-5
13	P1(4,-2) P2(-6,-9)	sqrt of 149	-7/-10
14	P1(8,4) P2(2,2)	sqrt of 40	-1/-3
15	P1(3,3) P2(8,-4)	sqrt of 74	-7/5
16	P1(-2,8) P2(-1,-9)	sqrt of 290	-17/1
17	P1(2,5) P2(7,9)	sqrt of 41	4/5
18	P1(3,8) P2(-4,-5)	sqrt of 218	-13/-7
19	P1(6,4) P2(8,8)	sqrt of 20	2/1
20	P1(-4,3) P2(5,-6)	sqrt of 162	-1/1
21	P1(-9,3) P2(-5,-8)	sqrt of 137	-11/4
22	P1(4,3) P2(1,5)	sqrt of 13	2/-3
23	P1(4,-6) P2(-5,-7)	sqrt of 82	-1/-9
24	P1(4,4) P2(1,-9)	sqrt of 178	-13/-3
25	P1(-4,8) P2(8,-6)	sqrt of 340	-7/6
26	P1(5,2) P2(1,9)	sqrt of 65	7/-4
27	P1(8,7) P2(-1,-4)	sqrt of 202	-11/-9
28	P1(1,8) P2(9,3)	sqrt of 89	-5/8
29	P1(1,9) P2(-6,5)	sqrt of 65	-4/-7
30	P1(8,2) P2(2,8)	sqrt of 72	1/-1
31	P1(8,-3) P2(-2,-5)	sqrt of 104	-1/-5
32	P1(3,3) P2(-4,-2)	sqrt of 74	-5/-7
33	P1(8,8) P2(5,9)	sqrt of 10	1/-3
34	P1(8,3) P2(2,5)	sqrt of 40	1/-3
35	P1(9,6) P2(-6,4)	sqrt of 229	-2/-15
36	P1(8,6) P2(1,-2)	sqrt of 113	-8/-7
37	P1(5,3) P2(7,5)	sqrt of 8	1/1
38	P1(-8,8) P2(-3,-3)	sqrt of 146	-11/5
39	P1(-4,7) P2(1,-9)	sqrt of 281	-16/5
40	P1(7,9) P2(1,7)	sqrt of 40	-1/-3
41	P1(-4,8) P2(-9,-3)	sqrt of 146	-11/-5
42	P1(-3,3) P2(7,-7)	sqrt of 200	-1/1
43	P1(8,2) P2(-7,7)	sqrt of 250	1/-3
44	P1(2,1) P2(3,9)	sqrt of 65	8/1
45	P1(8,2) P2(4,9)	sqrt of 65	7/-4
46	P1(1,7) P2(8,8)	sqrt of 50	1/7
47	P1(3,-8) P2(-1,-4)	sqrt of 32	1/-1
48	P1(9,7) P2(1,4)	sqrt of 73	-3/-8
49	P1(2,7) P2(5,-3)	sqrt of 109	-10/3
50	P1(7,4) P2(-3,-8)	sqrt of 244	-6/-5

Algebra: Least Common Multiple (LCM)

Solution Set	Given Numbers	LCM
1	5,13,10	130
2	28,9,20	1260
3	10,15,3	30
4	22,12,17	2244
5	3,2,12	12
6	8,10,21	840
7	12,3,16	48
8	10,8,11	440
9	21,19,15	1995
10	18,24,8	72
11	17,16,12	816
12	19,17,20	6460
13	19,18,12	684
14	17,15,18	1530
15	22,2,7	154
16	6,7,13	546
17	17,14,22	2618
18	22,9,13	2574
19	18,23,13	5382
20	16,12,20	240
21	19,17,5	1615
22	3,5,12	60
23	18,14,24	504
24	4,23,17	1564
25	22,13,23	6578
26	21,15,17	1785
27	15,7,19	1995
28	20,14,15	420
29	7,14,6	42
30	13,21,8	2184
31	15,21,6	210
32	14,22,16	1232
33	16,17,15	4080
34	9,6,2	18
35	19,5,7	665
36	7,12,20	420
37	24,6,4	24
38	17,20,6	1020
39	22,18,13	2574
40	11,23,9	2277
41	13,17,20	4420
42	22,2,6	66
43	13,4,9	468
44	2,3,18	18
45	3,20,4	60
46	3,21,6	42
47	21,11,17	3927
48	13,23,21	6279
49	12,2,13	156
50	15,14,2	210

Algebra: Greatest Common Divisor (GCD)

Solution Set	Given Numbers	GCD
1	54,48,60	6
2	8,48,40	8
3	598,322,713	23
4	40,80,48	8
5	20,40,32	4
6	70,10,50	10
7	87,493,667	29
8	15,18,30	3
9	195,91,65	13
10	42,48,12	6
11	70,30,60	10
12	8,10,14	2
13	341,93,217	31
14	44,33,77	11
15	28,40,32	4
16	620,155,341	31
17	28,40,24	4
18	207,115,322	23
19	115,621,391	23
20	60,50,30	10
21	49,70,63	7
22	42,18,54	6
23	45,20,50	5
24	290,377,493	29
25	35,25,5	5
26	49,70,63	7
27	48,72,36	12
28	266,475,551	19
29	403,155,434	31
30	49,28,56	7
31	54,60,12	6
32	667,87,638	29
33	3,15,12	3
34	84,36,72	12
35	459,51,289	17
36	32,8,48	8
37	95,209,551	19
38	24,8,32	8
39	27,6,15	3
40	221,91,247	13
41	187,51,323	17
42	16,24,20	4
43	11,66,33	11
44	63,56,28	7
45	21,18,30	3
46	63,18,81	9
47	48,12,84	12
48	72,12,48	12
49	30,60,40	10
50	11,33,66	11

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	7x+5y = 38; 6x+3y = 30	x = 4; y = 2
2	4x+7y = 18; 6x+9y = 24	x = 1; y = 2
3	x+8y = 29; 6x+8y = 94	x = 13; y = 2
4	6x+4y = -26; 3x+7y = -68	x = 3; y = -11
5	9x+y = 101; x+9y = 29	x = 11; y = 2
6	3x+7y = 51; 2x+9y = 60	x = 3; y = 6
7	x+4y = 47; 7x+4y = 89	x = 7; y = 10
8	3x-3y = -72; x+9y = 96	x = -12; y = 12
9	x+2y = 33; x+4y = 61	x = 5; y = 14
10	x+8y = 78; 8x+y = 120	x = 14; y = 8
11	5x+2y = 57; 5x+4y = 79	x = 7; y = 11
12	x+y = 20; 9x+y = 108	x = 11; y = 9
13	5x+7y = 102; 8x+6y = 132	x = 12; y = 6
14	5x+7y = 133; 8x+9y = 193	x = 14; y = 9
15	7x+3y = 43; 3x+y = 15	x = 1; y = 12
16	4x+3y = 43; 9x+4y = 61	x = 1; y = 13
17	9x+8y = 150; 4x+y = 59	x = 14; y = 3
18	9x+2y = 19; 7x+6y = -43	x = 5; y = -13
19	5x+y = 24; 4x+7y = 106	x = 2; y = 14
20	5x+9y = 83; 8x+2y = 46	x = 4; y = 7
21	x+4y = -44; 2x+8y = -88	x = 8; y = -13
22	9x+9y = 216; 5x+4y = 107	x = 11; y = 13
23	6x+y = 74; 5x+8y = 76	x = 12; y = 2
24	3x+9y = 72; 4x+4y = 64	x = 12; y = 4
25	4x+7y = -65; 2x+4y = -38	x = 3; y = -11
26	5x+y = 62; 2x+y = 32	x = 10; y = 12
27	4x+y = 18; 3x+2y = 21	x = 3; y = 6
28	8x+5y = 18; 9x+2y = -16	x = -4; y = 10
29	9x+9y = 216; 9x+6y = 174	x = 10; y = 14
30	x+4y = 17; 8x+5y = 82	x = 9; y = 2
31	5x+2y = 24; 8x+y = 34	x = 4; y = 2
32	9x+7y = 166; x+y = 20	x = 13; y = 7
33	3x+7y = 104; 5x+9y = 144	x = 9; y = 11
34	7x+7y = 0; 8x+8y = 0	x = 4; y = -4
35	4x+7y = 94; 2x+7y = 68	x = 13; y = 6
36	7x+2y = 34; 2x+3y = 34	x = 2; y = 10
37	8x+8y = 104; 9x+9y = 117	x = 2; y = 11
38	x+9y = 128; 3x+3y = 72	x = 11; y = 13
39	5x+8y = 22; 7x-9y = -50	x = -2; y = 4
40	9x+6y = 54; 6x+9y = -24	x = 14; y = -12
41	5x+4y = 65; 3x+9y = 105	x = 5; y = 10
42	2x+9y = 56; 6x+5y = 36	x = 1; y = 6
43	7x+6y = 59; 6x+6y = 54	x = 5; y = 4
44	8x+5y = 85; 2x+7y = 73	x = 5; y = 9
45	3x+8y = 41; 3x+2y = 35	x = 11; y = 1
46	7x+y = 71; 7x+2y = 72	x = 10; y = 1
47	5x+9y = 79; 2x+y = 16	x = 5; y = 6
48	9x+8y = -93; 6x+2y = -72	x = -13; y = 3
49	9x+y = 85; x+4y = 25	x = 9; y = 4
50	9x+6y = 156; 8x+8y = 152	x = 14; y = 5

Algebra: Multiplication of Polynomials

Problem	Given Polynomials	Solution
1	2x+12 and 7x+9	14x2+102x+108
2	1x+13 and 7x-13	7x2+78x-169
3	8x-2 and 8x+5	64x2+24x-10
4	1x-12 and 5x-11	5x2-71x+132
5	1x-11 and 5y-11	5xy-11x-55y+121
6	5x4+7 and 1x2+8	5x6+40x4+7x2+56
7	5x+4 and 7x2-7	35x3-35x1+28x2-28
8	7x3-1 and 2y2+12	14x3y2+84x3-2y2-12
9	6x-13 and 2y2-2	12xy2-12x-26y2+26
10	4x2-10 and 3y3-1	12x2y3-4x2-30y3+10
11	3x3+5y4 and 1x+2y	3x4+6x3y+5xy4+10y5
12	2x2-2y4 and 4x2+3y3	8x4+6x2y3-8x2y4-6y7
13	1x+7y2 and 4x-1y3	4x2-1xy3+28xy2-7y5
14	1x2-3y2 and 5x3-1y	5x5-1x2y-15x3y2+3y3
15	5x+2y3 and 3x3	15x4+6x3y3
16	4x2+5y4 and 2x	8x3+10xy4
17	6x4-7y2 and 1x4	6x8-7x4y2
18	7x+13 and 4x+5	28x2+87x+65
19	7x+12 and 8x-14	56x2-2x-168
20	3x-6 and 8x+1	24x2-45x-6
21	8x-9 and 5x-3	40x2-69x+27
22	3x-2 and 4y-3	12xy-9x-8y+6
23	5x4+12 and 6x2+8	30x6+40x4+72x2+96
24	8x+6 and 4x2-9	32x3-72x1+24x2-54
25	4x3-14 and 3y2+1	12x3y2+4x3-42y2-14
26	5x-3 and 4y2-12	20xy2-60x-12y2+36
27	8x2-11 and 2y3-14	16x2y3-112x2-22y3+154
28	4x2+3y4 and 6x4+5y3	24x6+20x2y3+18x4y4+15y7
29	5x4-6y2 and 2x+2y2	10x5+10x4y2-12xy2-12y4
30	2x2+6y and 8x3-3y2	16x5-6x2y2+48x3y-18y3
31	2x2-7y4 and 1x-1y	2x3-2x2y-7xy4+7y5
32	2x4+1y4 and 1x	2x5+1xy4
33	5x4+2y and 1x4	5x8+2x4y
34	4x4-2y3 and 1x3	4x7-2x3y3
35	4x+4 and 2x+2	8x2+16x+8
36	1x+10 and 8x-8	8x2+72x-80
37	8x-1 and 1x+14	8x2+111x-14
38	7x-12 and 5x-1	35x2-67x+12
39	6x-12 and 4y-11	24xy-66x-48y+132
40	7x4+13 and 6x2+4	42x6+28x4+78x2+52
41	3x+3 and 7x2-2	21x3-6x1+21x2-6
42	4x3-1 and 7y2+7	28x3y2+28x3-7y2-7
43	3x-10 and 2y2-2	6xy2-6x-20y2+20
44	2x2-5 and 1y3-11	2x2y3-22x2-5y3+55
45	5x4+4y4 and 8x3+4y4	40x7+20x4y4+32x3y4+16y8
46	7x3-6y2 and 2x+1y2	14x4+7x3y2-12xy2-6y4
47	1x2+3y2 and 3x2-3y	3x4-3x2y+9x2y2-9y3
48	5x2-4y and 8x4-2y4	40x6-10x2y4-32x4y+8y5
49	1x2+8y2 and 7x	7x3+56xy2
50	2x4+6y3 and 2x4	4x8+12x4y3