Subtraction of Fractions with the Same Denominator by Anthony OR 柯志明

GeoGebra Commands & Parameters

1. If(c > b, m - n - 1, m - n) → ansinteger'
2. If(c > b, (a + b - c) / a, (b - c) / a) → ansfraction'
3. Point(yAxis) → C
4. Point(yAxis) → B
5. Vector((0, 0), (-2.2, 0)) → u
6. Point(yAxis) → A
7. Polygon({A, A + (2, 0), A + (2, 1), A + (0, 1)}) → q1
8. Polygon({B, B + (2, 0), B + (2, 1), B + (0, 1)}) → q2
9. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_1
10. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_2
11. Polygon({A, A + ((2 * b / a), 0), A + ((2 * b / a), 1), A + (0, 1)}) → q3
12. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_5
13. Polygon({B, B + ((2 * c / a), 0), B + ((2 * c / a), 1), B + (0, 1)}) → q4
14. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_6
15. Sequence(Segment[A + ((i * 2 / a), 0), A + ((i * 2 / a), 1)], i, 1, a - 1) → L_3
16. Sequence(Segment[B + ((i * 2 / a), 0), B + ((i * 2 / a), 1)], i, 1, a - 1) → L_4
17. Polygon({C, C + (2, 0), C + (2, 1), C + (0, 1)}) → q5
18. Translate(C, Vector[(m * u)]) → C'
19. Sequence(Segment[C + ((i * 2 / a), 0), C + ((i * 2 / a), 1)], i, 1, a - 1) → L_{18}
20. Segment(H, I) → f
21. If(b ≤ c, m - 1, m) → nmax
22. If(n < m, a - 1, b - 1) → cmax
23. Sequence(A1 + (i * v) + ((-0.5 * 2 / a), 0.5), i, 0, If[c > b, Min[t2, b] - 1, t2 - 1]) → L_9
24. Sequence(Segment[J + ((i * 2 / a), 1 - t1), J + ((i * 2 / a), 1)], i, 1, a - 1) → L_7
25. Sequence(B1 + (i * v) + ((-0.5 * 2 / a), 0.5), i, 0, t2' - 1) → L_8
26. Sequence(A1 + (i * v) + ((-0.5 * 2 / a), 0.5) + (If[c > b ∧ i > b - 1, -0.2, 0], 0), i, 0, t2' - 1) → L_{10}
27. Sequence(L + (1, 0.5) - (i * u), i, 0, n - 1) → L_{11}
28. Sequence(K + (1, 0.5) - (i * u), i, 0, n - 1) → L_{12}
29. Translate(J, Vector[(t4 * Vector[J, C])]) → J'
30. Polygon({J', J' + (((a + b - c) * 2 / a), 0), J' + (((a + b - c) * 2 / a), 1), J' + (0, 1)}) → q6
31. Sequence(Segment[J' + ((i * 2 / a), 0), J' + ((i * 2 / a), 1)], i, 0, a + b - c) → L_{13}
32. Sequence(Segment[J' + (0, i), J' + (((a + b - c) * 2 / a), i)], i, 0, 1) → L_{14}
33. Translate(K, Vector[(t4 * Vector[K, E])]) → K'
34. Polygon({K', K' + (2, 0), K' + (2, 1), K' + (0, 1)}) → q7
35. Polygon({K', K' + (2, 0), K' + (2, 1), K' + (0, 1)}) → q8
36. Translate(A, Vector[(t4 * Vector[A, C])]) → A'
37. Polygon({A', A' + (((b - c) * 2 / a), 0), A' + (((b - c) * 2 / a), 1), A' + (0, 1)}) → q9
38. Sequence(Segment[A' + ((i * 2 / a), 0), A' + ((i * 2 / a), 1)], i, 0, b - c) → L_{15}
39. Sequence(Segment[A' + (0, i), A' + (((b - c) * 2 / a), i)], i, 0, 1) → L_{16}
40. Sequence(Polygon[{A' + (i * u), A' + (i * u) + (2, 0), A' + (i * u) + (2, 1), A' + (i * u) + (0, 1)}], i, 1, m - n) → L_{17}
41. Sequence(Polygon[{A' + (i * u), A' + (i * u) + (2, 0), A' + (i * u) + (2, 1), A' + (i * u) + (0, 1)}], i, 1, m - n) → L_{19}
42. If(c > b, 1, 0) → s1
43. If(b > 0 ∨ c > 0, 1, 0) → s2
44. If(n > 0, 1, 0) → s3
45. If(t1 + t2 + t3 + t4 ≥ s1 + s2 + s3 + s4, true, false) → finished
46. Sequence({Segment[B1 + (i * v), B1 + ((i + 1) * v) + (0, 1)], Segment[B1 + (i * v) + (0, 1), B1 + ((i + 1) * v)]}, i, 0, t2' - 1) → L_8'
47. Sequence({Segment[A1 + (i * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 0), A1 + ((i + 1) * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 1)], Segment[A1 + (i * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 1), A1 + ((i + 1) * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 0)]}, i, 0, t2' - 1) → L_{10}'
48. Sequence({Segment[L - (i * u), L - (i * u) + (2, 1)], Segment[L - (i * u) + (0, 1), L - (i * u) + (2, 0)]}, i, 0, n - 1) → L_{11}'
49. Sequence({Segment[K - (i * u), K - (i * u) + (2, 1)], Segment[K - (i * u) + (0, 1), K - (i * u) + (2, 0)]}, i, 0, n - 1) → L_{12}'