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Fraction Gadget: Common Denominators

Fraction Gadget: Common Denominators
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2017-08-31 07:10
TransformationGeometric Construction
This example demonstrates finding the common denominator of two fractions using geometric transformations. Key mathematical concepts include fractions and similarity transformations. Using commands like Vector, Translate, and Polygon, users can visually understand fraction addition and common denominators. Suitable for upper elementary and middle school students learning fraction operations and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector(B1, F1) → u
  2. Segment(B2, C2) → J2
  3. Segment(D2, E2) → K2
  4. Segment(F2, G2) → L2
  5. Segment(H2, I2) → M2
  6. Segment(B3, C3) → J3
  7. Segment(D3, E3) → K3
  8. Segment(F3, G3) → L3
  9. Segment(H3, I3) → M3
  10. Segment(B4, C4) → J4
  11. Segment(D4, E4) → K4
  12. Segment(F4, G4) → L4
  13. Segment(H4, I4) → M4
  14. Segment(B5, C5) → J5
  15. Segment(D5, E5) → K5
  16. Segment(F5, G5) → L5
  17. Segment(H5, I5) → M5
  18. Segment(B6, C6) → J6
  19. Segment(D6, E6) → K6
  20. Segment(F6, G6) → L6
  21. Segment(H6, I6) → M6
  22. Segment(B7, C7) → J7
  23. Segment(D7, E7) → K7
  24. Segment(F7, G7) → L7
  25. Segment(H7, I7) → M7
  26. Segment(B8, C8) → J8
  27. Segment(D8, E8) → K8
  28. Segment(F8, G8) → L8
  29. Segment(H8, I8) → M8
  30. Segment(B9, C9) → J9
  31. Segment(D9, E9) → K9
  32. Segment(F9, G9) → L9
  33. Segment(H9, I9) → M9
  34. Segment(B10, C10) → J10
  35. Segment(D10, E10) → K10
  36. Segment(F10, G10) → L10
  37. Segment(H10, I10) → M10
  38. Segment(B11, C11) → J11
  39. Segment(D11, E11) → K11
  40. Segment(F11, G11) → L11
  41. Segment(H11, I11) → M11
  42. Segment(B12, C12) → J12
  43. Segment(D12, E12) → K12
  44. Segment(F12, G12) → L12
  45. Segment(H12, I12) → M12
  46. Segment(B13, C13) → J13
  47. Segment(D13, E13) → K13
  48. Segment(F13, G13) → L13
  49. Segment(H13, I13) → M13
  50. Segment(B14, C14) → J14
  51. Segment(D14, E14) → K14
  52. Segment(F14, G14) → L14
  53. Segment(H14, I14) → M14
  54. Segment(B15, C15) → J15
  55. Segment(D15, E15) → K15
  56. Segment(F15, G15) → L15
  57. Segment(H15, I15) → M15
  58. Segment(B16, C16) → J16
  59. Segment(D16, E16) → K16
  60. Segment(F16, G16) → L16
  61. Segment(H16, I16) → M16
  62. Segment(B17, C17) → J17
  63. Segment(D17, E17) → K17
  64. Segment(F17, G17) → L17
  65. Segment(H17, I17) → M17
  66. Segment(B18, C18) → J18
  67. Segment(D18, E18) → K18
  68. Segment(F18, G18) → L18
  69. Segment(H18, I18) → M18
  70. Segment(B19, C19) → J19
  71. Segment(D19, E19) → K19
  72. Segment(F19, G19) → L19
  73. Segment(H19, I19) → M19
  74. Segment(B20, C20) → J20
  75. Segment(D20, E20) → K20
  76. Segment(F20, G20) → L20
  77. Segment(H20, I20) → M20
  78. Segment(B21, C21) → J21
  79. Segment(D21, E21) → K21
  80. Segment(F21, G21) → L21
  81. Segment(H21, I21) → M21
  82. Segment(F22, G22) → L22
  83. Segment(H22, I22) → M22
  84. Segment(F23, G23) → L23
  85. Segment(H23, I23) → M23
  86. Segment(F24, G24) → L24
  87. Segment(H24, I24) → M24
  88. Segment(F25, G25) → L25
  89. Segment(H25, I25) → M25
  90. Segment(F26, G26) → L26
  91. Segment(H26, I26) → M26
  92. Segment(F27, G27) → L27
  93. Segment(H27, I27) → M27
  94. Segment(F28, G28) → L28
  95. Segment(H28, I28) → M28
  96. Segment(F29, G29) → L29
  97. Segment(H29, I29) → M29
  98. Segment(F30, G30) → L30
  99. Segment(H30, I30) → M30
  100. Segment(F31, G31) → L31
  101. Segment(H31, I31) → M31
  102. Segment(F32, G32) → L32
  103. Segment(H32, I32) → M32
  104. Segment(F33, G33) → L33
  105. Segment(H33, I33) → M33
  106. Segment(F34, G34) → L34
  107. Segment(H34, I34) → M34
  108. Segment(F35, G35) → L35
  109. Segment(H35, I35) → M35
  110. Segment(F36, G36) → L36
  111. Segment(H36, I36) → M36
  112. Segment(F37, G37) → L37
  113. Segment(H37, I37) → M37
  114. Segment(F38, G38) → L38
  115. Segment(H38, I38) → M38
  116. Segment(F39, G39) → L39
  117. Segment(H39, I39) → M39
  118. Segment(F40, G40) → L40
  119. Segment(H40, I40) → M40
  120. Segment(F41, G41) → L41
  121. Segment(H41, I41) → M41
  122. Segment(F42, G42) → L42
  123. Segment(H42, I42) → M42
  124. Segment(F43, G43) → L43
  125. Segment(H43, I43) → M43
  126. Segment(F44, G44) → L44
  127. Segment(H44, I44) → M44
  128. Segment(F45, G45) → L45
  129. Segment(H45, I45) → M45
  130. Segment(F46, G46) → L46
  131. Segment(H46, I46) → M46
  132. Segment(F47, G47) → L47
  133. Segment(H47, I47) → M47
  134. Segment(F48, G48) → L48
  135. Segment(H48, I48) → M48
  136. Segment(F49, G49) → L49
  137. Segment(H49, I49) → M49
  138. Segment(F50, G50) → L50
  139. Segment(H50, I50) → M50
  140. Segment(F51, G51) → L51
  141. Segment(H51, I51) → M51
  142. Segment(F52, G52) → L52
  143. Segment(H52, I52) → M52
  144. Segment(F53, G53) → L53
  145. Segment(H53, I53) → M53
  146. Segment(F54, G54) → L54
  147. Segment(H54, I54) → M54
  148. Segment(F55, G55) → L55
  149. Segment(H55, I55) → M55
  150. Segment(F56, G56) → L56
  151. Segment(H56, I56) → M56
  152. Segment(F57, G57) → L57
  153. Segment(H57, I57) → M57
  154. Segment(F58, G58) → L58
  155. Segment(H58, I58) → M58
  156. Segment(F59, G59) → L59
  157. Segment(H59, I59) → M59
  158. Segment(F60, G60) → L60
  159. Segment(H60, I60) → M60
  160. Segment(F61, G61) → L61
  161. Segment(H61, I61) → M61
  162. Segment(F62, G62) → L62
  163. Segment(H62, I62) → M62
  164. Segment(F63, G63) → L63
  165. Segment(H63, I63) → M63
  166. Segment(F64, G64) → L64
  167. Segment(H64, I64) → M64
  168. Segment(F65, G65) → L65
  169. Segment(H65, I65) → M65
  170. Segment(F66, G66) → L66
  171. Segment(H66, I66) → M66
  172. Segment(F67, G67) → L67
  173. Segment(H67, I67) → M67
  174. Segment(F68, G68) → L68
  175. Segment(H68, I68) → M68
  176. Segment(F69, G69) → L69
  177. Segment(H69, I69) → M69
  178. Segment(F70, G70) → L70
  179. Segment(H70, I70) → M70
  180. Segment(F71, G71) → L71
  181. Segment(H71, I71) → M71
  182. Segment(F72, G72) → L72
  183. Segment(H72, I72) → M72
  184. Segment(F73, G73) → L73
  185. Segment(H73, I73) → M73
  186. Segment(F74, G74) → L74
  187. Segment(H74, I74) → M74
  188. Segment(F75, G75) → L75
  189. Segment(H75, I75) → M75
  190. Segment(F76, G76) → L76
  191. Segment(H76, I76) → M76
  192. Segment(F77, G77) → L77
  193. Segment(H77, I77) → M77
  194. Segment(F78, G78) → L78
  195. Segment(H78, I78) → M78
  196. Segment(F79, G79) → L79
  197. Segment(H79, I79) → M79
  198. Segment(F80, G80) → L80
  199. Segment(H80, I80) → M80
  200. Segment(F81, G81) → L81
  201. Segment(H81, I81) → M81
  202. Segment(F82, G82) → L82
  203. Segment(H82, I82) → M82
  204. Segment(F83, G83) → L83
  205. Segment(H83, I83) → M83
  206. Segment(F84, G84) → L84
  207. Segment(H84, I84) → M84
  208. Segment(F85, G85) → L85
  209. Segment(H85, I85) → M85
  210. Segment(F86, G86) → L86
  211. Segment(H86, I86) → M86
  212. Segment(F87, G87) → L87
  213. Segment(H87, I87) → M87
  214. Segment(F88, G88) → L88
  215. Segment(H88, I88) → M88
  216. Segment(F89, G89) → L89
  217. Segment(H89, I89) → M89
  218. Segment(F90, G90) → L90
  219. Segment(H90, I90) → M90
  220. Segment(F91, G91) → L91
  221. Segment(H91, I91) → M91
  222. Segment(F92, G92) → L92
  223. Segment(H92, I92) → M92
  224. Segment(F93, G93) → L93
  225. Segment(H93, I93) → M93
  226. Segment(F94, G94) → L94
  227. Segment(H94, I94) → M94
  228. Segment(F95, G95) → L95
  229. Segment(H95, I95) → M95
  230. Segment(F96, G96) → L96
  231. Segment(H96, I96) → M96
  232. Segment(F97, G97) → L97
  233. Segment(H97, I97) → M97
  234. Segment(F98, G98) → L98
  235. Segment(H98, I98) → M98
  236. Segment(F99, G99) → L99
  237. Segment(H99, I99) → M99
  238. Segment(F100, G100) → L100
  239. Segment(H100, I100) → M100
  240. Segment(F101, G101) → L101
  241. Segment(H101, I101) → M101
  242. Segment(F102, G102) → L102
  243. Segment(H102, I102) → M102
  244. Segment(F103, G103) → L103
  245. Segment(H103, I103) → M103
  246. Segment(F104, G104) → L104
  247. Segment(H104, I104) → M104
  248. Segment(F105, G105) → L105
  249. Segment(H105, I105) → M105
  250. Segment(F106, G106) → L106
  251. Segment(H106, I106) → M106
  252. Segment(F107, G107) → L107
  253. Segment(H107, I107) → M107
  254. Segment(F108, G108) → L108
  255. Segment(H108, I108) → M108
  256. Segment(F109, G109) → L109
  257. Segment(H109, I109) → M109
  258. Segment(F110, G110) → L110
  259. Segment(H110, I110) → M110
  260. Segment(F111, G111) → L111
  261. Segment(H111, I111) → M111
  262. Segment(F112, G112) → L112
  263. Segment(H112, I112) → M112
  264. Segment(F113, G113) → L113
  265. Segment(H113, I113) → M113
  266. Segment(F114, G114) → L114
  267. Segment(H114, I114) → M114
  268. Segment(F115, G115) → L115
  269. Segment(H115, I115) → M115
  270. Segment(F116, G116) → L116
  271. Segment(H116, I116) → M116
  272. Segment(F117, G117) → L117
  273. Segment(H117, I117) → M117
  274. Segment(F118, G118) → L118
  275. Segment(H118, I118) → M118
  276. Segment(F119, G119) → L119
  277. Segment(H119, I119) → M119
  278. Segment(F120, G120) → L120
  279. Segment(H120, I120) → M120
  280. Segment(F121, G121) → L121
  281. Segment(H121, I121) → M121
  282. Segment(F122, G122) → L122
  283. Segment(H122, I122) → M122
  284. Segment(F123, G123) → L123
  285. Segment(H123, I123) → M123
  286. Segment(F124, G124) → L124
  287. Segment(H124, I124) → M124
  288. Segment(F125, G125) → L125
  289. Segment(H125, I125) → M125
  290. Segment(F126, G126) → L126
  291. Segment(H126, I126) → M126
  292. Segment(F127, G127) → L127
  293. Segment(H127, I127) → M127
  294. Segment(F128, G128) → L128
  295. Segment(H128, I128) → M128
  296. Segment(F129, G129) → L129
  297. Segment(H129, I129) → M129
  298. Segment(F130, G130) → L130
  299. Segment(H130, I130) → M130
  300. Segment(F131, G131) → L131
  301. Segment(H131, I131) → M131
  302. Segment(F132, G132) → L132
  303. Segment(H132, I132) → M132
  304. Segment(F133, G133) → L133
  305. Segment(H133, I133) → M133
  306. Segment(F134, G134) → L134
  307. Segment(H134, I134) → M134
  308. Segment(F135, G135) → L135
  309. Segment(H135, I135) → M135
  310. Segment(F136, G136) → L136
  311. Segment(H136, I136) → M136
  312. Segment(B1, C1) → J1
  313. Segment(D1, E1) → K1
  314. Segment(F1, G1) → L1
  315. Segment(H1, I1) → M1
  316. Segment(B22, C22) → J22
  317. Segment(D22, E22) → K22
  318. Segment(D22, D1) → K23
  319. Segment(E22, E1) → K24
  320. Segment(B1, B22) → J23
  321. Segment(C1, C22) → J24
  322. Translate(C1, u) → P1
  323. Translate(B1, u) → O1
  324. Segment(O1, P1) → N1
  325. Translate(B2, u) → O2
  326. Translate(C2, u) → P2
  327. Segment(O2, P2) → N2
  328. Translate(B3, u) → O3
  329. Translate(C3, u) → P3
  330. Segment(O3, P3) → N3
  331. Translate(B4, u) → O4
  332. Translate(C4, u) → P4
  333. Segment(O4, P4) → N4
  334. Translate(B5, u) → O5
  335. Translate(C5, u) → P5
  336. Segment(O5, P5) → N5
  337. Translate(B6, u) → O6
  338. Translate(C6, u) → P6
  339. Segment(O6, P6) → N6
  340. Translate(B7, u) → O7
  341. Translate(C7, u) → P7
  342. Segment(O7, P7) → N7
  343. Translate(B8, u) → O8
  344. Translate(C8, u) → P8
  345. Segment(O8, P8) → N8
  346. Translate(B9, u) → O9
  347. Translate(C9, u) → P9
  348. Segment(O9, P9) → N9
  349. Translate(B10, u) → O10
  350. Translate(C10, u) → P10
  351. Segment(O10, P10) → N10
  352. Translate(B11, u) → O11
  353. Translate(C11, u) → P11
  354. Segment(O11, P11) → N11
  355. Translate(B12, u) → O12
  356. Translate(C12, u) → P12
  357. Segment(O12, P12) → N12
  358. Translate(B13, u) → O13
  359. Translate(C13, u) → P13
  360. Segment(O13, P13) → N13
  361. Translate(B14, u) → O14
  362. Translate(C14, u) → P14
  363. Segment(O14, P14) → N14
  364. Translate(B15, u) → O15
  365. Translate(C15, u) → P15
  366. Segment(O15, P15) → N15
  367. Translate(B16, u) → O16
  368. Translate(C16, u) → P16
  369. Segment(O16, P16) → N16
  370. Translate(B17, u) → O17
  371. Translate(C17, u) → P17
  372. Segment(O17, P17) → N17
  373. Translate(B18, u) → O18
  374. Translate(C18, u) → P18
  375. Segment(O18, P18) → N18
  376. Translate(B19, u) → O19
  377. Translate(C19, u) → P19
  378. Segment(O19, P19) → N19
  379. Translate(B20, u) → O20
  380. Translate(C20, u) → P20
  381. Segment(O20, P20) → N20
  382. Translate(B21, u) → O21
  383. Translate(C21, u) → P21
  384. Segment(O21, P21) → N21
  385. Translate(B22, u) → O22
  386. Translate(C22, u) → P22
  387. Segment(O22, P22) → N22
  388. Segment(O1, O22) → O23
  389. Segment(P1, P22) → P23
  390. Translate(D1, u) → R1
  391. Translate(E1, u) → S1
  392. Segment(R1, S1) → Q1
  393. Translate(D2, u) → R2
  394. Translate(E2, u) → S2
  395. Segment(R2, S2) → Q2
  396. Translate(D3, u) → R3
  397. Translate(E3, u) → S3
  398. Segment(R3, S3) → Q3
  399. Translate(D4, u) → R4
  400. Translate(E4, u) → S4
  401. Segment(R4, S4) → Q4
  402. Translate(D5, u) → R5
  403. Translate(E5, u) → S5
  404. Segment(R5, S5) → Q5
  405. Translate(D6, u) → R6
  406. Translate(E6, u) → S6
  407. Segment(R6, S6) → Q6
  408. Translate(D7, u) → R7
  409. Translate(E7, u) → S7
  410. Segment(R7, S7) → Q7
  411. Translate(D8, u) → R8
  412. Translate(E8, u) → S8
  413. Segment(R8, S8) → Q8
  414. Translate(D9, u) → R9
  415. Translate(E9, u) → S9
  416. Segment(R9, S9) → Q9
  417. Translate(D10, u) → R10
  418. Translate(E10, u) → S10
  419. Segment(R10, S10) → Q10
  420. Translate(D11, u) → R11
  421. Translate(E11, u) → S11
  422. Segment(R11, S11) → Q11
  423. Translate(D12, u) → R12
  424. Translate(E12, u) → S12
  425. Segment(R12, S12) → Q12
  426. Translate(D13, u) → R13
  427. Translate(E13, u) → S13
  428. Segment(R13, S13) → Q13
  429. Translate(D14, u) → R14
  430. Translate(E14, u) → S14
  431. Segment(R14, S14) → Q14
  432. Translate(D15, u) → R15
  433. Translate(E15, u) → S15
  434. Segment(R15, S15) → Q15
  435. Translate(D16, u) → R16
  436. Translate(E16, u) → S16
  437. Segment(R16, S16) → Q16
  438. Translate(D17, u) → R17
  439. Translate(E17, u) → S17
  440. Segment(R17, S17) → Q17
  441. Translate(D18, u) → R18
  442. Translate(E18, u) → S18
  443. Segment(R18, S18) → Q18
  444. Translate(D19, u) → R19
  445. Translate(E19, u) → S19
  446. Segment(R19, S19) → Q19
  447. Translate(E20, u) → S20
  448. Translate(E21, u) → S21
  449. Translate(D22, u) → R22
  450. Translate(E22, u) → S22
  451. Segment(R22, S22) → Q22
  452. Translate(D20, u) → R20
  453. Translate(D21, u) → R21
  454. Segment(R20, S20) → Q20
  455. Segment(R21, S21) → Q21
  456. Segment(R1, R22) → R23
  457. Segment(S1, S22) → S23
  458. Polygon(B1, C1, C22, B22) → B23, C23, D23, E23, F23_1
  459. Polygon(D1, E1, E22, D22) → B24, C24, D24, E24, F24_1
  460. Polygon(O1, O22, P22, P1) → O24, P24, Q24, R24, S24
  461. Polygon(R1, R22, S22, S1) → O25, P25, Q25, R25, S25

AI Drawing Prompt Reference

Draw the common denominator of two fractions by first drawing the numerator line segments, then translating these segments to find their common endpoint, forming a new segment representing the common denominator. Next, draw parallel lines to these segments to create geometric shapes, helping to understand fraction addition and common denominators.
The prompt above was compiled from the original drawing commands and is for reference only.