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Equivalent Fractions with Denominators 200 & 300

Equivalent Fractions with Denominators 200 & 300
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2015-08-19 17:01
PolygonTransformationGeometric ConstructionSlider Animation
This GeoGebra applet visually demonstrates the relationship between equivalent fractions, specifically showing that 20/100, 40/200, and 60/300 are equal, as well as 30/100, 60/200, and 90/300. The core mathematical concept is fraction equivalence, where multiplying the numerator and denominator by the same factor preserves the value. The construction uses polygons to create area models, with commands such as Intersect, Point, Polygon, Midpoint, Segment, OrthogonalLine, and Mirror to divide and transform regions. It is suitable for upper elementary and middle school students learning fractions, and serves as an interactive teaching tool for teachers to illustrate the geometric meaning of equivalent fractions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Midpoint(D, C) → E
  5. Midpoint(C, B) → F
  6. Midpoint(A, B) → G
  7. Midpoint(D, A) → H
  8. Point(c) → I
  9. Point(c) → J
  10. Point(c) → K
  11. Point(c) → L
  12. Point(c) → M
  13. Point(c) → N
  14. Point(c) → O
  15. Point(c) → P
  16. Point(d) → Q
  17. Point(d) → R
  18. Point(d) → S
  19. Point(d) → T
  20. Point(d) → U
  21. Point(d) → V
  22. Point(d) → W
  23. Point(d) → Z
  24. Point(b) → A_1
  25. Point(b) → B_1
  26. Point(b) → C_1
  27. Point(b) → D_1
  28. Point(b) → E_1
  29. Point(b) → F_1
  30. Point(b) → G_1
  31. Point(b) → H_1
  32. Point(a) → I_1
  33. Point(a) → J_1
  34. Point(a) → K_1
  35. Point(a) → L_1
  36. Point(a) → M_1
  37. Point(a) → N_1
  38. Point(a) → O_1
  39. Point(a) → P_1
  40. Segment(I, P_1) → e
  41. Segment(J, O_1) → f
  42. Segment(K, N_1) → g
  43. Segment(L, M_1) → h
  44. Segment(E, G) → i
  45. Segment(M, L_1) → j
  46. Segment(N, K_1) → k
  47. Segment(O, J_1) → l
  48. Segment(P, I_1) → m
  49. Segment(Q, A_1) → n
  50. Segment(R, B_1) → p
  51. Segment(S, C_1) → q
  52. Segment(T, D_1) → r
  53. Segment(H, F) → s
  54. Segment(U, E_1) → t
  55. Segment(V, F_1) → a_1
  56. Segment(W, G_1) → b_1
  57. Segment(Z, H_1) → c_1
  58. Point(yAxis) → Q_1
  59. Point(yAxis) → R_1
  60. Segment(Q_1, R_1) → d_1
  61. OrthogonalLine(R_1, d_1) → e_1
  62. Point(e_1) → Move_1
  63. OrthogonalLine(Move_1, e_1) → f_1
  64. Mirror(poly1, f_1) → poly2
  65. Mirror(I, f_1) → I'
  66. Mirror(P_1, f_1) → T_1
  67. Segment(I', T_1) → e'
  68. Mirror(J, f_1) → J'
  69. Mirror(O_1, f_1) → U_1
  70. Segment(J', U_1) → f'
  71. Mirror(K, f_1) → K'
  72. Mirror(N_1, f_1) → V_1
  73. Segment(K', V_1) → g'
  74. Mirror(L, f_1) → L'
  75. Mirror(M_1, f_1) → W_1
  76. Segment(L', W_1) → h'
  77. Mirror(E, f_1) → E'
  78. Mirror(G, f_1) → G'
  79. Segment(E', G') → i'
  80. Mirror(M, f_1) → M'
  81. Mirror(L_1, f_1) → Z_1
  82. Segment(M', Z_1) → j'
  83. Mirror(N, f_1) → N'
  84. Mirror(K_1, f_1) → A_2
  85. Segment(N', A_2) → k'
  86. Mirror(O, f_1) → O'
  87. Mirror(J_1, f_1) → B_2
  88. Segment(O', B_2) → l'
  89. Mirror(P, f_1) → P'
  90. Mirror(I_1, f_1) → C_2
  91. Segment(P', C_2) → m'
  92. Mirror(Q, f_1) → Q'
  93. Mirror(A_1, f_1) → D_2
  94. Segment(Q', D_2) → n'
  95. Mirror(R, f_1) → R'
  96. Mirror(B_1, f_1) → E_2
  97. Segment(R', E_2) → p'
  98. Mirror(S, f_1) → S'
  99. Mirror(C_1, f_1) → F_2
  100. Segment(S', F_2) → q'
  101. Mirror(T, f_1) → T'
  102. Mirror(D_1, f_1) → G_2
  103. Segment(T', G_2) → r'
  104. Mirror(H, f_1) → H'
  105. Mirror(F, f_1) → F'
  106. Segment(H', F') → s'
  107. Mirror(U, f_1) → U'
  108. Mirror(E_1, f_1) → H_2
  109. Segment(U', H_2) → t'
  110. Mirror(V, f_1) → V'
  111. Mirror(F_1, f_1) → I_2
  112. Segment(V', I_2) → g_1
  113. Mirror(W, f_1) → W'
  114. Mirror(G_1, f_1) → J_2
  115. Segment(W', J_2) → h_1
  116. Mirror(Z, f_1) → Z'
  117. Mirror(H_1, f_1) → K_2
  118. Segment(Z', K_2) → i_1
  119. Point(e_1) → Move_2
  120. OrthogonalLine(Move_2, d_1) → j_1
  121. OrthogonalLine(Move_2, e_1) → k_1
  122. Mirror(poly2, k_1) → poly3
  123. Mirror(I', k_1) → I''
  124. Mirror(T_1, k_1) → M_2
  125. Segment(I'', M_2) → e''
  126. Mirror(J', k_1) → J''
  127. Mirror(U_1, k_1) → N_2
  128. Segment(J'', N_2) → f''
  129. Mirror(K', k_1) → K''
  130. Mirror(V_1, k_1) → O_2
  131. Segment(K'', O_2) → g''
  132. Mirror(L', k_1) → L''
  133. Mirror(W_1, k_1) → P_2
  134. Segment(L'', P_2) → h''
  135. Mirror(E', k_1) → E''
  136. Mirror(G', k_1) → G''
  137. Segment(E'', G'') → i''
  138. Mirror(M', k_1) → M''
  139. Mirror(Z_1, k_1) → Q_2
  140. Segment(M'', Q_2) → j''
  141. Mirror(N', k_1) → N''
  142. Mirror(A_2, k_1) → R_2
  143. Segment(N'', R_2) → k''
  144. Mirror(O', k_1) → O''
  145. Mirror(B_2, k_1) → S_2
  146. Segment(O'', S_2) → l''
  147. Mirror(P', k_1) → P''
  148. Mirror(C_2, k_1) → T_2
  149. Segment(P'', T_2) → m''
  150. Mirror(Q', k_1) → Q''
  151. Mirror(D_2, k_1) → U_2
  152. Segment(Q'', U_2) → n''
  153. Mirror(R', k_1) → R''
  154. Mirror(E_2, k_1) → V_2
  155. Segment(R'', V_2) → p''
  156. Mirror(S', k_1) → S''
  157. Mirror(F_2, k_1) → W_2
  158. Segment(S'', W_2) → q''
  159. Mirror(T', k_1) → T''
  160. Mirror(G_2, k_1) → Z_2
  161. Segment(T'', Z_2) → r''
  162. Mirror(H', k_1) → H''
  163. Mirror(F', k_1) → F''
  164. Segment(H'', F'') → s''
  165. Mirror(U', k_1) → U''
  166. Mirror(H_2, k_1) → A_3
  167. Segment(U'', A_3) → t''
  168. Mirror(V', k_1) → V''
  169. Mirror(I_2, k_1) → B_3
  170. Segment(V'', B_3) → l_1
  171. Mirror(W', k_1) → W''
  172. Mirror(J_2, k_1) → C_3
  173. Segment(W'', C_3) → m_1
  174. Mirror(Z', k_1) → Z''
  175. Mirror(K_2, k_1) → D_3
  176. Segment(Z'', D_3) → n_1
  177. Polygon(S_1, E_3, F_3, G_3) → s60, s_1, e_3, f_3, g_3
  178. Mirror(S_1, f_1) → H_3
  179. Mirror(E_3, f_1) → I_3
  180. Mirror(F_3, f_1) → J_3
  181. Mirror(G_3, f_1) → K_3
  182. Polygon(H_3, I_3, J_3, K_3) → s60', h_3, i_3, j_3, k_3
  183. Mirror(H_3, k_1) → L_3
  184. Mirror(I_3, k_1) → M_3
  185. Mirror(J_3, k_1) → N_3
  186. Mirror(K_3, k_1) → O_3
  187. Polygon(L_3, M_3, N_3, O_3) → s60'', l_3, m_3, n_3, o_3
  188. Polygon(P_3, Q_3, R_3, S_3) → poly4, p_3, q_3, r_3, s_3
  189. Mirror(P_3, f_1) → T_3
  190. Mirror(Q_3, f_1) → U_3
  191. Mirror(R_3, f_1) → V_3
  192. Mirror(S_3, f_1) → W_3
  193. Polygon(T_3, U_3, V_3, W_3) → poly4', t_3, u_3, v_3, w_3
  194. Polygon(Z_3, A_4, B_4, C_4) → poly5, z_3, a_4, b_4, c_4
  195. Mirror(Z_3, f_1) → D_4
  196. Mirror(A_4, f_1) → E_4
  197. Mirror(B_4, f_1) → F_4
  198. Mirror(C_4, f_1) → G_4
  199. Polygon(D_4, E_4, F_4, G_4) → poly5', d_4, e_4, f_4, g_4
  200. Polygon(H_4, I_4, J_4, K_4) → poly6, h_4, i_4, j_4, k_4
  201. Mirror(H_4, f_1) → L_4
  202. Mirror(I_4, f_1) → M_4
  203. Mirror(J_4, f_1) → N_4
  204. Mirror(K_4, f_1) → O_4
  205. Polygon(L_4, M_4, N_4, O_4) → poly6', l_4, m_4, n_4, o_4
  206. Mirror(L_4, k_1) → P_4
  207. Mirror(M_4, k_1) → Q_4
  208. Mirror(N_4, k_1) → R_4
  209. Mirror(O_4, k_1) → S_4
  210. Polygon(P_4, Q_4, R_4, S_4) → poly6'', p_4, q_4, r_4, s_4

AI Drawing Prompt Reference

Draw a square with one vertex at the origin and its base along the x-axis. Divide the top and bottom edges into equal segments, and similarly divide the left and right edges. Connect corresponding division points with straight lines to form a grid. Add midlines horizontally and vertically, plus segments connecting midpoints of opposite sides, creating a symmetric partition. This area model visually represents equivalent fractions by showing proportional subdivisions under different denominators.
The prompt above was compiled from the original drawing commands and is for reference only.