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(2,3) P2(-3,8)	sqrt of 50	1/-1
2	P1(7,1) P2(-5,-7)	sqrt of 208	-2/-3
3	P1(9,4) P2(2,7)	sqrt of 58	3/-7
4	P1(7,-6) P2(-9,-9)	sqrt of 265	-3/-16
5	P1(2,1) P2(9,3)	sqrt of 53	2/7
6	P1(-7,1) P2(-4,-9)	sqrt of 109	-10/3
7	P1(-4,5) P2(2,-4)	sqrt of 117	-3/2
8	P1(4,6) P2(5,-9)	sqrt of 226	-15/1
9	P1(9,8) P2(1,5)	sqrt of 73	-3/-8
10	P1(5,7) P2(7,6)	sqrt of 5	-1/2
11	P1(1,6) P2(2,8)	sqrt of 5	2/1
12	P1(5,1) P2(7,2)	sqrt of 5	1/2
13	P1(-3,2) P2(-6,-8)	sqrt of 109	-10/-3
14	P1(7,9) P2(8,3)	sqrt of 37	-6/1
15	P1(7,8) P2(-9,-4)	sqrt of 400	-3/-4
16	P1(1,8) P2(-7,9)	sqrt of 65	1/-8
17	P1(5,9) P2(6,-7)	sqrt of 257	-16/1
18	P1(2,-7) P2(-7,-5)	sqrt of 85	2/-9
19	P1(-3,9) P2(6,-4)	sqrt of 250	-13/9
20	P1(4,3) P2(7,1)	sqrt of 13	-2/3
21	P1(-5,6) P2(1,-2)	sqrt of 100	-4/3
22	P1(8,3) P2(-5,8)	sqrt of 194	5/-13
23	P1(5,5) P2(-7,-4)	sqrt of 225	-3/-4
24	P1(2,8) P2(3,-6)	sqrt of 197	-14/1
25	P1(6,3) P2(8,8)	sqrt of 29	5/2
26	P1(4,9) P2(7,8)	sqrt of 10	-1/3
27	P1(-7,5) P2(-8,-3)	sqrt of 65	-8/-1
28	P1(6,5) P2(3,8)	sqrt of 18	1/-1
29	P1(9,7) P2(3,3)	sqrt of 52	-2/-3
30	P1(8,-4) P2(-3,-9)	sqrt of 146	-5/-11
31	P1(-8,9) P2(6,-6)	sqrt of 421	-15/14
32	P1(5,9) P2(-1,7)	sqrt of 40	-1/-3
33	P1(9,1) P2(-5,-9)	sqrt of 296	-5/-7
34	P1(2,4) P2(7,1)	sqrt of 34	-3/5
35	P1(8,9) P2(2,3)	sqrt of 72	1/1
36	P1(2,9) P2(7,-2)	sqrt of 146	-11/5
37	P1(4,7) P2(2,4)	sqrt of 13	-3/-2
38	P1(-4,3) P2(-1,-7)	sqrt of 109	-10/3
39	P1(7,5) P2(1,9)	sqrt of 52	2/-3
40	P1(7,-2) P2(-5,-3)	sqrt of 145	-1/-12
41	P1(3,5) P2(2,9)	sqrt of 17	4/-1
42	P1(1,6) P2(4,-9)	sqrt of 234	-5/1
43	P1(4,1) P2(5,5)	sqrt of 17	4/1
44	P1(8,-7) P2(-7,-9)	sqrt of 229	-2/-15
45	P1(1,9) P2(-3,7)	sqrt of 20	-1/-2
46	P1(2,2) P2(-7,-8)	sqrt of 181	-10/-9
47	P1(9,2) P2(5,6)	sqrt of 32	1/-1
48	P1(1,8) P2(7,1)	sqrt of 85	-7/6
49	P1(-9,8) P2(4,-2)	sqrt of 269	-10/13
50	P1(-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.

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

Greatest Common Divisor (GCD)

Solution Set	Given Numbers	GCD
1	21,18,3	3
2	27,18,12	3
3	50,10,30	10
4	527,62,899	31
5	475,361,437	19
6	30,36,54	6
7	744,961,899	31
8	66,44,55	11
9	40,80,72	8
10	56,80,32	8
11	285,209,513	19
12	348,725,377	29
13	45,90,72	9
14	620,217,434	31
15	30,60,50	10
16	116,580,667	29
17	24,8,56	8
18	15,18,27	3
19	266,437,247	19
20	56,98,70	14
21	299,26,247	13
22	49,28,70	7
23	24,6,18	6
24	70,10,50	10
25	12,20,28	4
26	551,38,589	19
27	40,16,72	8
28	45,40,25	5
29	56,48,8	8
30	14,4,18	2
31	39,299,377	13
32	15,6,27	3
33	77,66,11	11
34	72,56,40	8
35	391,85,119	17
36	551,209,361	19
37	81,54,63	9
38	40,80,48	8
39	558,713,589	31
40	65,143,169	13
41	12,21,15	3
42	87,203,551	29
43	589,93,713	31
44	35,30,20	5
45	221,187,323	17
46	42,14,70	14
47	114,437,589	19
48	63,70,14	7
49	81,36,90	9
50	15,27,9	3

Least Common Multiple (LCM)

Solution Set	Given Numbers	LCM
1	2,21,9	126
2	18,23,13	5382
3	5,14,23	1610
4	24,15,3	120
5	19,9,23	3933
6	8,24,2	24
7	22,21,15	2310
8	5,14,13	910
9	19,2,16	304
10	23,18,21	2898
11	21,19,23	9177
12	7,3,5	105
13	8,13,14	728
14	18,6,12	36
15	15,7,21	105
16	15,10,5	30
17	23,22,8	2024
18	9,6,5	90
19	11,6,4	132
20	24,22,13	3432
21	23,22,24	6072
22	8,11,12	264
23	13,11,10	1430
24	23,12,6	276
25	22,12,13	1716
26	20,16,19	1520
27	13,6,17	1326
28	17,18,22	3366
29	15,7,19	1995
30	24,4,22	264
31	17,8,9	1224
32	2,10,3	30
33	13,24,17	5304
34	21,9,13	819
35	8,3,17	408
36	23,3,4	276
37	9,16,5	720
38	13,8,10	520
39	3,5,8	120
40	13,10,22	1430
41	16,3,21	336
42	21,16,14	336
43	3,19,17	969
44	19,15,13	3705
45	24,3,19	456
46	23,4,9	828
47	22,23,7	3542
48	11,13,18	2574
49	6,19,22	1254
50	2,10,9	90

Algebra: Multiplication of Polynomials

Problem	Given Polynomials	Solution
1	8x+6 and 7x+9	56x2+114x+54
2	7x+12 and 1x-2	7x2-2x-24
3	1x-14 and 2x+3	2x2-25x-42
4	8x-8 and 6x-13	48x2-152x+104
5	5x-3 and 7y-14	35xy-70x-21y+42
6	4x4+4 and 4x2+14	16x6+56x4+16x2+56
7	2x+1 and 5x2-13	10x3-26x1+5x2-13
8	6x3-10 and 5y2+14	30x3y2+84x3-50y2-140
9	1x-12 and 7y2-12	7xy2-12x-84y2+144
10	8x2-11 and 6y3-14	48x2y3-112x2-66y3+154
11	2x2+7y4 and 3x2+7y3	6x4+14x2y3+21x2y4+49y7
12	5x2-5y4 and 4x4+5y2	20x6+25x2y2-20x4y4-25y6
13	3x4+4y2 and 7x2-8y4	21x6-24x4y4+28x2y2-32y6
14	3x2-7y3 and 7x-1y	21x3-3x2y-49xy3+7y4
15	6x+2y3 and 4x	24x2+8xy3
16	3x3+5y4 and 2x	6x4+10xy4
17	5x4-3y and 4x4	20x8-12x4y
18	6x+8 and 2x+3	12x2+34x+24
19	1x+1 and 4x-7	4x2-3x-7
20	1x-14 and 4x+11	4x2-45x-154
21	3x-8 and 7x-8	21x2-80x+64
22	3x-11 and 5y-3	15xy-9x-55y+33
23	4x4+11 and 4x2+1	16x6+4x4+44x2+11
24	6x+4 and 5x2-5	30x3-30x1+20x2-20
25	8x3-13 and 4y2+3	32x3y2+24x3-52y2-39
26	5x-14 and 1y2-14	5xy2-70x-14y2+196
27	1x2-10 and 4y3-8	4x2y3-8x2-40y3+80
28	4x4+2y4 and 8x2+8y2	32x6+32x4y2+16x2y4+16y6
29	5x2-2y and 7x4+4y	35x6+20x2y-14x4y-8y2
30	6x4+2y2 and 1x-1y	6x5-6x4y+2xy2-2y3
31	1x-8y4 and 3x3-2y2	3x4-2xy2-24x3y4+16y6
32	1x+3y2 and 7x3	7x4+21x3y2
33	2x2+4y and 5x3	10x5+20x3y
34	1x-1y3 and 6x	6x2-6xy3
35	8x+14 and 7x+2	56x2+114x+28
36	5x+13 and 3x-10	15x2-11x-130
37	7x-7 and 3x+11	21x2+56x-77
38	6x-12 and 5x-7	30x2-102x+84
39	3x-2 and 3y-8	9xy-24x-6y+16
40	8x4+4 and 1x2+7	8x6+56x4+4x2+28
41	8x+6 and 5x2-1	40x3-8x1+30x2-6
42	3x3-1 and 3y2+9	9x3y2+27x3-3y2-9
43	7x-2 and 8y2-1	56xy2-7x-16y2+2
44	4x2-3 and 6y3-1	24x2y3-4x2-18y3+3
45	6x+4y3 and 2x+6y3	12x2+44x1y3+24y6
46	6x4-6y4 and 2x4+8y	12x8+48x4y-12x4y4-48y5
47	3x2+2y and 3x2-4y3	9x4-12x2y3+6x2y-8y4
48	3x2-1y and 5x3-2y	15x5-6x2y-5x3y+2y2
49	2x2+1y2 and 5x3	10x5+5x3y2
50	3x3+2y3 and 4x2	12x5+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.

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

Problem	Given Equations	Solution
1	6x+3y = 45; 8x+4y = 60	x = 14; y = -13
2	3x-9y = -114; 7x+4y = 84	x = 4; y = 14
3	4x+8y = 104; 5x+y = 76	x = 14; y = 6
4	4x+3y = 59; 2x+9y = 97	x = 8; y = 9
5	6x+y = 21; 2x+5y = 49	x = 2; y = 9
6	3x+3y = 30; x+3y = 14	x = 8; y = 2
7	5x+7y = 139; 4x+5y = 104	x = 11; y = 12
8	6x+7y = 125; 7x+4y = 100	x = 8; y = 11
9	5x+2y = 60; x+8y = 50	x = 10; y = 5
10	9x+y = 16; 4x+9y = -10	x = 2; y = -2
11	x+8y = 63; 6x+4y = 70	x = 7; y = 7
12	8x+4y = 44; 6x+y = 31	x = 5; y = 1
13	2x+6y = 96; 3x+6y = 102	x = 6; y = 14
14	7x+4y = 63; 5x+8y = 117	x = 1; y = 14
15	8x+5y = 102; 6x+8y = 102	x = 9; y = 6
16	6x+y = 11; 5x+7y = 40	x = 1; y = 5
17	x+8y = 41; 8x+6y = 38	x = 1; y = 5
18	x+2y = 0; 5x+7y = -12	x = -8; y = 4
19	6x+4y = 20; 6x+4y = 20	x = 2; y = 2
20	x+3y = 22; 6x+3y = 42	x = 4; y = 6
21	5x+5y = 95; x+2y = 29	x = 9; y = 10
22	5x-8y = 52; 8x+y = 97	x = 12; y = 1
23	9x+9y = 234; 8x+y = 124	x = 14; y = 12
24	9x+6y = 93; 8x+6y = 88	x = 5; y = 8
25	7x+4y = 41; 5x+7y = -8	x = 11; y = -9
26	2x+6y = -48; 7x+9y = -24	x = 12; y = -12
27	3x+3y = 33; 7x+9y = 89	x = 5; y = 6
28	3x+9y = 96; 3x+9y = 96	x = 5; y = 9
29	9x+2y = 62; 5x+3y = 59	x = 4; y = 13
30	x+6y = 72; 7x+8y = 164	x = 12; y = 10
31	7x+4y = 43; 8x+4y = 44	x = 1; y = 9
32	4x+6y = 88; 3x-5y = -29	x = 7; y = 10
33	7x+4y = 18; 6x+3y = 15	x = 2; y = 1
34	7x+2y = 32; 8x+8y = 88	x = 2; y = 9
35	x+3y = 53; 4x+3y = 95	x = 14; y = 13
36	6x+9y = 87; 2x+6y = 38	x = 10; y = 3
37	3x+9y = 36; 4x+2y = 18	x = 3; y = 3
38	4x+5y = 93; 6x+6y = 120	x = 7; y = 13
39	2x+5y = 51; 8x+5y = 69	x = 3; y = 9
40	3x+9y = 126; 5x+9y = 138	x = 6; y = 12
41	8x+7y = 124; 2x+7y = 94	x = 5; y = 12
42	3x+2y = 2; 7x+6y = -10	x = 8; y = -11
43	9x+6y = 135; 8x+7y = 140	x = 7; y = 12
44	7x+y = 34; 4x+2y = 28	x = 4; y = 6
45	9x+6y = 33; 8x+7y = 46	x = -3; y = 10
46	8x+y = 54; 3x+5y = -26	x = 8; y = -10
47	4x+7y = 116; 5x+7y = 124	x = 8; y = 12
48	2x+4y = 38; 2x+5y = 42	x = 11; y = 4
49	5x+5y = 75; 6x-8y = -64	x = 4; y = 11
50	9x+8y = 126; 6x+2y = 54	x = 6; y = 9

Addition of Fractions

Problem	First Number	Second Number	Total
1	7/24	7/18	49/72
2	1/20	5/18	59/180
3	7/8	1/24	11/12
4	7/24	7/22	161/264
5	6/7	5/8	1 27/56
6	7/20	2/15	29/60
7	3/5	8/9	1 22/45
8	3/14	1/20	37/140
9	1/20	4/15	19/60
10	1/9	11/24	41/72
11	1/24	5/21	47/168
12	3/5	7/10	1 3/10
13	4/21	5/16	169/336
14	7/18	5/18	2/3
15	5/22	7/10	51/55
16	6/7	4/7	1 3/7
17	4/21	3/10	103/210
18	1/15	1/15	2/15
19	7/18	7/16	119/144
20	5/14	7/12	79/84
21	5/12	1/10	31/60
22	7/24	8/21	113/168
23	5/18	7/16	103/144
24	8/9	4/9	1 1/3
25	5/24	1/20	31/120
26	3/16	5/12	29/48
27	1/14	5/18	22/63
28	1/14	7/20	59/140
29	8/21	8/21	16/21
30	7/15	3/14	143/210
31	7/12	7/18	35/36
32	7/12	7/24	7/8
33	1/10	1/14	6/35
34	7/18	3/22	52/99
35	5/16	1/20	29/80
36	8/21	5/24	33/56
37	7/18	7/20	133/180
38	1/14	3/14	2/7
39	6/7	1/7	1
40	8/15	7/18	83/90
41	5/24	5/18	35/72
42	3/4	14/15	1 41/60
43	4/5	7/8	1 27/40
44	1/16	4/21	85/336
45	1/21	2/21	1/7
46	5/16	5/14	75/112
47	5/24	7/20	67/120
48	3/10	7/18	31/45
49	8/9	4/9	1 1/3
50	1/16	7/24	17/48

Subtraction of Fractions

Problem	Minuend	Subtrahend	Difference
1	7/15	3/10	1/6
2	1/18	1/16	-1/144
3	5/21	7/15	-8/35
4	1/18	1/10	-2/45
5	5/14	1/14	2/7
6	6/7	1/7	5/7
7	1/16	7/15	-97/240
8	7/10	5/16	31/80
9	7/10	1/24	79/120
10	6/7	8/9	-2/63
11	1/14	5/24	-23/168
12	6/7	2/7	4/7
13	7/12	1/12	1/2
14	7/20	7/12	-7/30
15	3/16	8/21	-65/336
16	7/8	6/7	1/56
17	1/21	1/14	-1/42
18	1/12	7/12	-1/2
19	2/7	3/16	11/112
20	1/3	11/12	-7/12
21	2/15	8/15	-2/5
22	1/24	1/10	-7/120
23	3/20	5/14	-29/140
24	3/14	5/18	-4/63
25	5/12	7/10	-17/60
26	7/24	2/21	11/56
27	6/7	1/15	83/105
28	3/10	7/16	-11/80
29	7/24	7/24	0
30	7/10	5/12	17/60
31	7/22	5/21	37/462
32	4/21	7/18	-25/126
33	3/4	5/4	-1/2
34	7/24	1/10	23/120
35	7/9	7/18	7/18
36	7/24	3/22	41/264
37	5/18	7/24	-1/72
38	6/7	11/15	13/105
39	7/16	5/18	23/144
40	7/16	5/14	9/112
41	5/18	4/15	1/90
42	7/24	4/21	17/168
43	3/14	7/22	-8/77
44	1/15	1/14	-1/210
45	7/16	1/16	3/8
46	3/16	7/18	-29/144
47	7/24	7/18	-7/72
48	7/24	5/24	1/12
49	7/18	3/14	11/63
50	8/9	7/24	43/72

Multiplication of Fractions

Problem	Multiplicand	Multiplier	Product
1	3/7	2/7	6/49
2	1/20	7/10	7/200
3	2/5	1/20	1/50
4	7/22	3/10	21/220
5	1/12	2/15	1/90
6	7/18	1/10	7/180
7	8/9	1/7	8/63
8	7/24	7/18	49/432
9	3/10	7/10	21/100
10	1/16	3/20	3/320
11	1/7	6/7	6/49
12	3/22	7/16	21/352
13	7/15	3/14	1/10
14	7/22	7/15	49/330
15	7/22	1/24	7/528
16	1/3	1/12	1/36
17	3/20	5/22	3/88
18	5/24	7/20	7/96
19	1/15	7/20	7/300
20	7/22	7/12	49/264
21	5/12	5/16	25/192
22	3/4	9/14	27/56
23	2/15	7/12	7/90
24	3/14	1/22	3/308
25	7/20	7/10	49/200
26	3/10	7/16	21/160
27	3/22	3/22	9/484
28	8/9	7/8	7/9
29	5/12	7/20	7/48
30	5/12	3/14	5/56
31	1/16	5/12	5/192
32	7/9	5/9	35/81
33	2/21	3/14	1/49
34	7/18	1/14	1/36
35	8/9	7/18	28/81
36	1/20	7/22	7/440
37	5/18	1/15	1/54
38	1/18	7/10	7/180
39	1/18	3/10	1/60
40	8/9	10/21	80/189
41	8/9	4/9	32/81
42	4/15	1/16	1/60
43	3/22	7/20	21/440
44	7/16	7/22	49/352
45	1/10	5/12	1/24
46	1/15	2/15	2/225
47	5/9	9/22	5/22
48	5/24	5/14	25/336
49	1/22	1/12	1/264
50	5/7	5/8	25/56

Division of Fractions

Problem	Dividend	Divisor	Quotient
1	3/4	6/7	7/8
2	5/18	1/21	5 5/6
3	7/9	1/9	7
4	1/20	7/10	1/14
5	1/20	3/14	7/30
6	5/7	5/22	3 1/7
7	3/20	3/22	1 1/10
8	1/21	5/12	4/35
9	5/12	1/12	5
10	2/21	7/16	32/147
11	1/21	7/20	20/147
12	1/22	5/24	12/55
13	5/14	7/15	75/98
14	1/14	1/24	1 5/7
15	7/16	7/22	1 3/8
16	1/22	5/12	6/55
17	3/10	5/22	1 8/25
18	5/22	4/15	75/88
19	6/7	4/7	1 1/2
20	3/22	7/16	24/77
21	5/22	7/15	75/154
22	1/22	5/16	8/55
23	7/20	5/14	49/50
24	8/9	1/20	17 7/9
25	7/24	7/24	1
26	5/18	7/20	50/63
27	3/14	3/16	1 1/7
28	1/16	3/10	5/24
29	4/7	11/24	1 19/77
30	5/8	1/7	4 3/8
31	2/15	7/12	8/35
32	2/21	1/12	1 1/7
33	2/21	1/24	2 2/7
34	5/8	8/9	45/64
35	1/12	3/16	4/9
36	3/5	8/9	27/40
37	8/21	1/15	5 5/7
38	1/4	1/4	1
39	7/9	11/24	1 23/33
40	1/16	7/18	9/56
41	5/24	5/14	7/12
42	3/20	1/15	2 1/4
43	7/8	11/10	35/44
44	3/16	1/20	3 3/4
45	7/15	1/15	7
46	1/18	8/21	7/48
47	7/24	3/10	35/36
48	7/12	1/18	10 1/2
49	6/7	4/7	1 1/2
50	5/12	1/14	5 5/6

Addition of Decimal Numbers

Problem	First Number	Second Number	Total
1	0.0506	1.587	1.6376
2	390.4383	5.9718	396.4101
3	0.0602	0.14	0.2002
4	0.0081	942.8246	942.8327
5	29.7178	0.0073	29.7251
6	6.8056	353.6796	360.4852
7	0.9054	0.0413	0.9467
8	931.1829	7.5214	938.7043
9	584.983	264.8744	849.8574
10	81.7623	403.2804	485.0427
11	21.4113	0.0201	21.4314
12	94.0603	941.2649	1035.3252
13	0.023	0.7856	0.8086
14	0.057	0.1799	0.2369
15	901.6578	82.5607	984.2185
16	601.3541	823.9487	1425.3028
17	4.4858	0.0206	4.5064
18	8.7102	7.596	16.3062
19	6.4131	0.7263	7.1394
20	2.7574	3.9388	6.6962
21	85.4156	0.2945	85.7101
22	942.2289	8.7778	951.0067
23	0.2051	448.9193	449.1244
24	8.3661	0.0511	8.4172
25	6.5286	906.484	913.0126
26	14.4538	650.3442	664.798
27	3.9325	0.0136	3.9461
28	0.0479	1.5994	1.6473
29	0.0171	2.4268	2.4439
30	0.4751	0.2458	0.7209
31	256.8323	97.9562	354.7885
32	423.1792	0.0025	423.1817
33	0.433	0.0138	0.4468
34	26.8661	0.8419	27.708
35	2.7442	18.9363	21.6805
36	0.1747	738.0352	738.2099
37	8.3352	38.5703	46.9055
38	0.6048	473.8623	474.4671
39	9.032	0.0371	9.0691
40	0.4805	0.2649	0.7454
41	0.5736	94.2592	94.8328
42	20.8031	3.8512	24.6543
43	0.4118	479.4381	479.8499
44	5.5113	0.1387	5.65
45	9.6122	0.0156	9.6278
46	0.0813	0.1025	0.1838
47	38.1558	0.5095	38.6653
48	0.0732	0.0009	0.0741
49	8.4623	7.8377	16.3
50	0.089	370.4226	370.5116

Subtraction of Decimal Numbers

Problem	Minuend	Subtrahend	Difference
1	418.6141	0.0311	418.583
2	5.8263	4.1995	1.6268
3	58.3098	0.6929	57.6169
4	15.9232	0.6256	15.2976
5	73.1806	61.5638	11.6168
6	15.1579	0.0009	15.157
7	56.4055	30.0123	26.3932
8	0.0334	0.001	0.0324
9	5.5864	0.463	5.1234
10	901.2809	1.6911	899.5898
11	7.824	6.0996	1.7244
12	8.6479	0.6711	7.9768
13	6.911	0.0715	6.8395
14	9.6117	7.9917	1.62
15	0.0117	0.0086	0.0031
16	76.59	0.08	76.51
17	9.5027	0.7827	8.72
18	0.9569	0.7477	0.2092
19	4.1203	0.9858	3.1345
20	67.1054	0.0927	67.0127
21	61.432	7.3619	54.0701
22	0.6839	0.2668	0.4171
23	376.7248	0.646	376.0788
24	63.1288	62.1517	0.9771
25	0.479	0.0652	0.4138
26	5.4296	0.5246	4.905
27	77.6816	8.2821	69.3995
28	0.0874	0.0359	0.0515
29	0.0976	0.0095	0.0881
30	0.5273	0.0745	0.4528
31	0.8362	0.0042	0.832
32	39.6108	0.8939	38.7169
33	8.9235	0.0098	8.9137
34	4.1035	0.5621	3.5414
35	736.3137	4.5167	731.797
36	156.9821	0.081	156.9011
37	3.8537	0.0119	3.8418
38	9.9834	0.4172	9.5662
39	8.9758	0.0783	8.8975
40	24.8848	4.8286	20.0562
41	45.4084	8.7019	36.7065
42	29.9791	0.0397	29.9394
43	591.4327	41.2007	550.232
44	0.0939	0.0097	0.0842
45	4.6183	1.4754	3.1429
46	0.8513	0.022	0.8293
47	24.4672	0.0094	24.4578
48	74.4092	31.7624	42.6468
49	49.0878	13.5679	35.5199
50	151.0122	0.0078	151.0044

Multiplication of Decimal Numbers

Problem	Multiplicand	Multiplier	Product
1	45.888	0.859	39.417792
2	0.0706	4.9556	0.34986536
3	0.0585	20.5939	1.20474315
4	5.7695	0.7884	4.5486738
5	0.0096	772.53	7.416288
6	0.1487	0.0497	0.00739039
7	573.5382	915.5287	525090.68264634
8	0.1296	8.8878	1.15185888
9	459.4131	553.384	254231.8589304
10	0.0767	781.929	59.9739543
11	0.0301	0.0281	0.00084581
12	13.6811	0.0098	0.13407478
13	8.2884	0.001	0.0082884
14	0.0887	7.171	0.6360677
15	0.0753	336.2077	25.31643981
16	491.774	527.6509	259484.9936966
17	0.0009	0.0323	0.00002907
18	2.5648	0.8228	2.11031744
19	0.3003	0.906	0.2720718
20	618.0001	5.6335	3481.50356335
21	261.2421	57.0368	14900.41340928
22	55.1606	539.7617	29773.57922902
23	58.8791	0.0009	0.05299119
24	22.1171	5.5005	121.65510855
25	0.3952	0.1891	0.07473232
26	11.0999	0.3251	3.60857749
27	869.0035	5.1597	4483.79735895
28	627.1198	5.4497	3417.61477406
29	93.1607	42.7163	3979.48040941
30	32.9792	0.7189	23.70874688
31	0.0111	497.1066	5.51788326
32	670.2927	1.1393	763.66447311
33	55.3392	28.5182	1578.17437344
34	5.8665	0.0379	0.22234035
35	0.0092	0.0994	0.00091448
36	0.3025	7.0804	2.141821
37	282.0921	9.1824	2590.28249904
38	72.5864	0.0217	1.57512488
39	39.8267	0.0196	0.78060332
40	498.4997	0.0651	32.45233047
41	0.0871	58.0219	5.05370749
42	1.0017	4.5429	4.55062293
43	0.0157	1.2899	0.02025143
44	0.2788	54.1616	15.10025408
45	5.5809	190.9168	1065.48756912
46	0.0114	0.538	0.0061332
47	0.0251	1.3752	0.03451752
48	0.9801	0.2434	0.23855634
49	212.2965	49.4011	10487.68062615
50	95.6189	32.2752	3086.11912128

Division of Decimal Numbers

Problem	Dividend	Divisor	Quotient
1	0.0504	392.7541	0.0001
2	700.5557	0.0504	13899.9147
3	0.0111	0.6054	0.0183
4	0.5149	96.4196	0.0053
5	0.5385	96.7612	0.0056
6	1.7428	71.9476	0.0242
7	0.0536	0.0513	1.0448
8	99.961	0.0659	1516.8589
9	863.9551	0.6869	1257.7596
10	0.5789	3.7927	0.1526
11	0.4591	619.0738	0.0007
12	8.9347	281.077	0.0318
13	0.7325	0.3745	1.9559
14	0.784	7.4198	0.1057
15	9.9243	0.0732	135.5779
16	829.7192	816.9251	1.0157
17	0.0548	0.4442	0.1234
18	363.7341	0.4215	862.9516
19	8.4255	0.0173	487.0231
20	0.0923	0.8687	0.1063
21	9.9789	42.3955	0.2354
22	9.4893	253.4445	0.0374
23	691.5085	240.4305	2.8761
24	0.8595	0.0557	15.4309
25	820.1939	9.2086	89.0683
26	198.0009	0.0096	20625.0938
27	6.1586	0.0126	488.7778
28	0.8394	7.4535	0.1126
29	0.4444	51.2001	0.0087
30	80.9695	32.5665	2.4863
31	0.1343	56.0309	0.0024
32	146.2976	0.0291	5027.4089
33	0.3405	6.6448	0.0512
34	0.3401	88.2121	0.0039
35	628.7561	427.9234	1.4693
36	6.5295	0.0002	32647.5
37	211.5547	0.0725	2917.9959
38	67.1754	39.252	1.7114
39	20.6832	845.8308	0.0245
40	7.3449	0.1929	38.0762
41	0.4001	0.8963	0.4464
42	0.4171	0.076	5.4882
43	16.8962	0.2255	74.9277
44	23.8758	0.406	58.8074
45	0.0054	3.5467	0.0015
46	86.4589	0.0091	9500.978
47	0.2345	0.1328	1.7658
48	68.9996	6.4346	10.7232
49	0.7346	5.0004	0.1469
50	0.3275	52.3661	0.0063

Division of Integers

Problem	Dividend	Divisor	Quotient
1	799	47	17
2	696	29	24
3	858	66	13
4	720	72	10
5	736	32	23
6	627	57	11
7	792	66	12
8	624	26	24
9	561	11	51
10	330	10	33
11	840	10	84
12	230	10	23
13	855	57	15
14	810	27	30
15	648	36	18
16	2640	24	110
17	6670	23	290
18	9112	34	268
19	62092	86	722
20	9550	25	382
21	46463	97	479
22	43150	50	863
23	5232	12	436
24	7414	11	674
25	5700	30	190
26	45214	94	481
27	13298	61	218
28	24284	26	934
29	47568	48	991
30	7448	49	152
31	806	62	13
32	504	18	28
33	700	35	20
34	820	41	20
35	610	61	10
36	825	55	15
37	782	46	17
38	726	11	66
39	780	65	12
40	504	24	21
41	470	10	47
42	767	59	13
43	450	45	10
44	529	23	23
45	350	10	35
46	22239	63	353
47	39237	87	451
48	15796	22	718
49	18315	55	333
50	3267	27	121

Multiplication of Integers

Problem	Multiplicand	Multiplier	Product
1	434	43	18662
2	909	98	89082
3	822	73	60006
4	180	75	13500
5	430	12	5160
6	299	56	16744
7	933	94	87702
8	189	95	17955
9	819	38	31122
10	342	75	25650
11	776	55	42680
12	334	78	26052
13	366	31	11346
14	934	60	56040
15	199	44	8756
16	617	216	133272
17	520	954	496080
18	444	675	299700
19	733	518	379694
20	514	331	170134
21	904	346	312784
22	988	403	398164
23	299	618	184782
24	902	951	857802
25	772	339	261708
26	188	299	56212
27	711	835	593685
28	359	405	145395
29	486	511	248346
30	282	352	99264
31	812	15	12180
32	303	12	3636
33	380	51	19380
34	726	34	24684
35	317	21	6657
36	199	31	6169
37	811	95	77045
38	125	51	6375
39	480	23	11040
40	735	14	10290
41	378	74	27972
42	761	38	28918
43	370	65	24050
44	821	33	27093
45	679	15	10185
46	892	394	351448
47	377	186	70122
48	327	933	305091
49	885	387	342495
50	656	306	200736

Subtraction of Integers

Problem	Minuend	Subtrahend	Difference
1	88	88	0
2	4500	338	4162
3	47	29	18
4	7700	544	7156
5	231	75	156
6	82	66	16
7	9502	505	8997
8	6103	897	5206
9	277	59	218
10	75	28	47
11	1403	833	570
12	41	11	30
13	83	82	1
14	84	58	26
15	6700	723	5977
16	65	47	18
17	5401	888	4513
18	813	64	749
19	86	85	1
20	31	17	14
21	5303	459	4844
22	422	38	384
23	5900	779	5121
24	7100	739	6361
25	486	58	428
26	81	66	15
27	84	47	37
28	6200	421	5779
29	373	95	278
30	9002	478	8524
31	871	36	835
32	91	84	7
33	582	44	538
34	83	75	8
35	2203	118	2085
36	7400	771	6629
37	813	44	769
38	7508	859	6649
39	493	74	419
40	2800	636	2164
41	8400	984	7416
42	97	18	79
43	452	96	356
44	36	26	10
45	88	28	60
46	4800	956	3844
47	41	22	19
48	84	19	65
49	8500	566	7934
50	7301	109	7192

Addition of Integers

Problem	First Number	Second Number	Total
1	469	485	954
2	681	543	1224
3	412	645	1057
4	495	933	1428
5	365	400	765
6	421	784	1205
7	457	807	1264
8	102	540	642
9	339	779	1118
10	355	458	813
11	574	254	828
12	225	322	547
13	557	502	1059
14	604	750	1354
15	697	966	1663
16	189	524	713
17	210	531	741
18	238	758	996
19	881	356	1237
20	165	530	695
21	827	364	1191
22	249	283	532
23	904	623	1527
24	555	263	818
25	876	964	1840
26	121	172	293
27	797	119	916
28	850	939	1789
29	206	797	1003
30	396	821	1217
31	278	508	786
32	113	426	539
33	361	307	668
34	301	786	1087
35	342	442	784
36	419	418	837
37	452	577	1029
38	670	583	1253
39	966	628	1594
40	256	426	682
41	933	745	1678
42	186	840	1026
43	896	695	1591
44	496	287	783
45	932	984	1916
46	412	723	1135
47	172	131	303
48	123	994	1117
49	535	218	753
50	412	831	1243