Fracciones propias e impropias/ Proper and Improper Fraction
Author: Leopoldo Aranda Murcia

Cuando dividimos algo en partes iguales lo estamos fraccionando. El número de trozos en que están divididas las unidades se llama denominador. El número de trozos que cogemos es el denominador.

Para pasar una fracción a forma mixta hay que dividir el numerador entre el denominador. La fracción es igual al cociente de la división más
una fracción con numerador el resto de la división y el denominador anterior.

Pizza

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Deslizadores

Numerador

Denominador

Botones

a = 19 (slider from 0 to If[g ≟ 1, 120, (32 * b)], step 1)
b = 6 (slider from 1 to If[g ≟ 1, 20, 40], step 1)
d = If(a / b > 1, 0, 0.75)
ncir: ceil(a / b)
col = 8
radio = If(ncir  <  3, 0.5, 9 / ((10 * Min[col, ncir]) - 2))
e = If(ncir ≤ col, 0.5, 1 - radio)
A: (d, e)
B: A + (radio, 0)
c = Circle(B, radio)
separaciones = Sequence(Segment[B, B + (radio; ((2 * π) * i / b))], i, 0, b - 1)
lista3 = Sequence(Translate[c, Vector[((2.25 * radio) * (Mod[i, col], (-floor(i / col))))]], i, 1, ncir - 1)
lista2 = Sequence(Translate[separaciones, Vector[((2.25 * radio) * (Mod[i, col], (-floor(i / col))))]], i, 1, ncir - 1)
circulos = Sequence(Translate[c, Vector[((2.25 * radio) * (Mod[i, col], (-floor(i / col))))]], i, 0, ncir - 1)
B' = Translate(B, Vector[((2.25 * radio) * (Mod[ncir - 1, col], (-floor((ncir - 1) / col))))])
f = CircleSector(B', B' + (radio; ((2 * π) * a / b)), B' + (radio; 0))
E_1: B + (radio * (-1, -1))
E_2: B + (radio * (1, -1))
imagenes: {pizza, tarta_1, tortilla}
opción = 1 (slider from 0 to 3, step 1)
lista1 = Sequence(Translate[Element[imagenes, opción], Vector[((2.25 * radio) * (Mod[i, col], (-floor(i / col))))]], i, 0, ncir - 1)
ncir_1: ceil(a / b)
texto2: "=" + (LaTeX[floor(a / b)]) + "+\frac{" + LaTeX[Mod[a, b]] + "}{" + LaTeX[b] + "}"
texto2_1: "=" + (LaTeX[floor(a / b)]) + ""
texto1: "$ \frac{" + (LaTeX[a]) + "}{" + LaTeX[b] + "} $"
texto3 = If(a / b  <  1, "Fracción propia", If[a ≟ b, "Fracción unidad", "Fracción impropia"])
texto4 = If(Mod[a, b] ≟ 0, "entera", "no entera")
idioma = 1 (slider from 0 to 1, step 1)
texto9 = If(idioma ≟ 1, "Tortilla", "Omelette")
texto13 = If(idioma ≟ 1, "Tarta", "Cake")
denominadores: {"unidades", "medio", "tercio", "cuarto", "quinto", "sexto", "séptimo", "octavo", "noveno", "décimo", "onceavo", "doceavo", "treceavo", "catorceavo", "quinceavo", "dieciseisavo", "diecisieteavo", "dieciochoavo", "diecinueveavo", "veinteavo", "veintunavo", "veintidosavo", "ventitresavo", "venticuatroavo", "venticincoavo", "ventiseisavo", "ventisieteavo", "ventiochoavo", "ventinueveavo", "treintaavo", "treintaiunavo", "treintaidosavo", "treintaitresavo", "treintaicuatroavo", "treintaicincoavo", "treintaiseisavo", "treintaisieteavo", "treintaiochoavo", "treintainueveavo", "cuarentaavo"}
numeradores: {"Cero", "Un", "Dos", "Tres", "Cuatro", "Cinco", "Seis", "Siete", "Ocho", "Nueve", "Diez", "Once", "Doce", "Trece", "Catorce", "Quince", "Dieciséis", "Diecisiete", "Dieciocho", "Diecinueve", "Veinte", "Veintiuno", "Veintidos", "Veintitrés", "Veinticuatro", "Veinticinco", "Veintiseis", "Veintisiete", "Veintiocho", "Ventinueve", "Treinta", "Treintaiuno", "Treintaidos", "Treintaitres", "Treintaicuatro", "Treintaicinco", "Treintaiseis", "Treintaisiete", "Treintaiocho", "Treintainueve"}
texto15: " " + (Element[numeradores, a + 1]) + "
 " + Element[denominadores, b] + "" + If[a ≠ 1, "s", ""] + ""
denominators: {"unit", "half", "third", "quarter", "fifth", "sixth", "seventh", "eighth", "ninth", "tenth", "eleventh", "twelfth", "thirteenth", "fourteenth", "fifteenth", "sixteenth", "seventeenth", "eighteenth", "nineteenth", "twentieth", "twenty-first", "twenty-second", "twenty-third", "twenty-fourth", "twenty-fifth", "twenty-sixth", "twenty-seventh", "twenty-eight", "twenty-ninth", "thirtieth", "thirty-first", "thirty-second", "thirty-third", "thirty-fourth", "thirty-fifth", "thirty-sixth", "thirty-seventh", "thirty-eight", "thirty-ninth", "fortieth"}
numerators: {"Zero", "One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten", "Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen", "Sixteen", "Seventeen", "Eighteen", "Nineteen", "Twenty", "Twenty-one", "Twenty-two", "Twenty-three", "Twenty-four", "Twenty-five", "Twenty-six", "Twenty-seven", "Twenty-eight", "Twenty-nine", "Thirty", "Thirty-one", "Thirty-two", "Thirty-three", "Thirty-four", "Thirty-five", "Thirty-six", "Thirty-seven", "Thirty-eight", "Thirty-nine", "Fourty"}
texto14 = If(idioma ≟ 1, "Círculo", "Circle")
E_4: B + (radio * (-1, 1))
g = 1 (slider from 0 to 1, step 1)
idioma_1 = 0 (slider from 0 to 1, step 1)