Suma de fracciones propias
Author: Alfredo Ramos

Se pueden sumar dos cantidades fraccionarias para obtener otro número fraccionario

¿Es posible que la suma de dos fracciones no sea una fracción?

¿Bajo que condiciones de los sumandos puede ocurrir?

+

=

Suma de fracciones propias

Selecciona los sumandos
moviendo los deslizadores

b = 7 (slider from 2 to 10, step 1)
a = 3 (slider from 1 to b - 1, step 1)
d = 7 (slider from 2 to 10, step 1)
c = 5 (slider from 1 to d - 1, step 1)
A = (1, 2)
B = (5, 2)
C = (5, 4.98)
D = (1, 4.98)
polígono1, a_1, b_1, c_1, d_1 = Polygon(A, B, C, D)
lista1 = Sequence(A + ((B - A) / b * t), t, 0, b)
lista2 = Sequence(D + ((C - D) / b * t), t, 0, b)
lista3 = Sequence(Segment[Element[lista1, t], Element[lista2, t]], t, 1, b)
polígono2, e, f, g, h = Polygon(A, D, D + ((a * 4 / b), 0), A + ((a * 4 / b), 0))
E = (6, 2)
F = (10, 2)
G = (10, 5)
H = (6, 5)
polígono3, e_1, f_1, g_1, h_1 = Polygon(E, F, G, H)
lista4 = Sequence(E + ((F - E) / d * t), t, 0, d)
lista5 = Sequence(H + ((G - H) / d * t), t, 0, d)
lista6 = Sequence(Segment[Element[lista4, t], Element[lista5, t]], t, 1, d)
polígono4, e_2, h_2, i, j = Polygon(E, H, H + ((c * 4 / d), 0), E + ((c * 4 / d), 0))
k = LCM(b, d)
I = (11, 2)
J = (15, 2)
K = (15, 5)
L = (11, 5)
polígono5, i_1, j_1, k_1, l = Polygon(I, J, K, L)
lista7 = Sequence(I + ((J - I) / k * t), t, 0, k)
lista8 = Sequence(L + ((K - L) / k * t), t, 0, k)
lista9 = Sequence(Segment[Element[lista7, t], Element[lista8, t]], t, 1, k)
polígono6, i_2, l_1, m, n = Polygon(I, L, L + ((((k / b * a) + (k / d * c)) * 4 / k), 0), I + ((((k / b * a) + (k / d * c)) * 4 / k), 0))
texto3: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}"
texto4: "\frac{" + (LaTeX[c]) + "}{" + (LaTeX[d]) + "}"
texto6 = FractionText(((k / b * a) + (k / d * c)) / k)
M = (11, 2)
N = (11, 5)
O = (15, 5)
P = (15, 2)
polígono7, m_1, n_1, o, p = Polygon(M, N, O, P)
lista10 = Sequence(M + ((P - M) / k * t), t, 0, k)
lista11 = Sequence(N + ((O - N) / k * t), t, 0, k)
lista12 = Sequence(Segment[Element[lista10, t], Element[lista11, t]], t, 1, k)
Q = (16, 2)
R = (20, 2)
S = (20, 5)
T = (16, 5)
polígono8, q, r, s, t = Polygon(Q, R, S, T)
lista13 = Sequence(Q + ((R - Q) / k * t), t, 0, k)
lista14 = Sequence(T + ((S - T) / k * t), t, 0, k)
lista15 = Sequence(Segment[Element[lista13, t], Element[lista14, t]], t, 1, k)
polígono9, q_1, t_1, p_1, r_1 = Polygon(Q, T, T + ((((k / b * a) + (k / d * c) - k) * 4 / k), 0), Q + ((((k / b * a) + (k / d * c) - k) * 4 / k), 0))
texto7: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}+\frac{" + (LaTeX[c]) + "}{" + (LaTeX[d]) + "}=\frac{" + (LaTeX[(k / b * a)]) + "+" + (LaTeX[(k / d * c)]) + "}{" + (LaTeX[k]) + "}=\frac{" + (LaTeX[(k / b * a) + (k / d * c)]) + "}{" + (LaTeX[k]) + "}"
k_2 = LCM(b, d)
texto7_1: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}+\frac{" + (LaTeX[c]) + "}{" + (LaTeX[d]) + "}=\frac{" + (LaTeX[(k_2 / b * a)]) + "+" + (LaTeX[(k_2 / d * c)]) + "}{" + (LaTeX[k_2]) + "}=\frac{" + (LaTeX[(k_2 / b * a) + (k_2 / d * c)]) + "}{" + (LaTeX[k_2]) + "}=1\frac{" + (LaTeX[(k_2 / b * a) + (k_2 / d * c) - k]) + "}{" + (LaTeX[k]) + "}"
k_3 = LCM(b, d)
k_4 = LCM(b, d)
texto7_2: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}+\frac{" + (LaTeX[c]) + "}{" + (LaTeX[d]) + "}=\frac{" + (LaTeX[(k_4 / b * a)]) + "+" + (LaTeX[(k_4 / d * c)]) + "}{" + (LaTeX[k_4]) + "}=\frac{" + (LaTeX[(k_4 / b * a) + (k_4 / d * c)]) + "}{" + (LaTeX[k_4]) + "}=1"
U = (22, 2)
V = (26, 2)
W = (22, 5)
Z = (21.21321860465116, 1.708734883720929)
A_1 = (29.5098, 1.9636)
B_1 = (21.18901860465116, 8.218534883720931)