addfraction
Author: Daniel Mentrard
Date: 14 Octobre 2014

voir

Les deux fractions à additionner

La réduction au même dénominateur

Résultats de l'addition

+

T = (16, 0)
q = 3 (slider from 1 to p, step 1)
p = 11 (slider from -5 to 20, step 1)
m = 9 (slider from -5 to 20, step 1)
qq = Mod(q * m, p)
pp: (q * m - qq) / p
w = 5 (slider from 1 to 10, step 1)
A = (10, 0)
B: A + (w, 0)
a = Segment(A, B)
D: A + (0, w)
C: A + (w, w)
b = Segment(A, D)
c = Segment(D, C)
d = Segment(C, B)
E = (10.03179560260592, 7.945136363636386)
F = Translate(E, Vector[A, B])
H = Rotate(F, 90*°, E)
G = Rotate(E, 90*°, H)
e = Segment(E, F)
f = Segment(F, G)
g = Segment(G, H)
h = Segment(H, E)
n = 1 (slider from 1 to m, step 1)
list1 = Sequence(Segment[A + (i * w / p, 0), A + (i * w / p, w)], i, 1, p - 1)
list2 = Sequence(Segment[E + (i * w / p, 0), E + (i * w / p, w)], i, 1, p - 1)
list3 = Sequence(Segment[A + (0, i * w / m), A + (w, i * w / m)], i, 1, m - 1)
list4 = Sequence(Segment[E + (0, i * w / m), E + (w, i * w / m)], i, 1, m - 1)
poly1, e_1, i, j, k = Polygon(E, E + (w, 0), E + (w, n / m * w), E + (0, n / m * w))
poly2, a_1, l, r, s_1 = Polygon(A, A + (q / p * w, 0), A + (q / p * w, w), A + (0, w))
o = true
text3: "$ \frac{" + (LaTeX[n]) + "}{" + (LaTeX[m]) + "} $"
text4: "\frac{" + (LaTeX[q]) + "}{" + (LaTeX[p]) + "}"
I = (4.087954915605596, 7.808772727272749)
poly3, i_1, s, t, b_1 = Polygon(I, I + (w, 0), I + (w, n / m * w), I + (0, n / m * w))
J: I + (w, 0)
K: I + (w, w)
L: I + (0, w)
liste1 = Sequence(Segment[I + (0, i * w / m), I + (w, i * w / m)], i, 1, m - 1)
M = (3.8153016730826446, 0.11786363636366243)
N: M + (w, 0)
O: M + (w, w)
P: M + (0, w)
liste2 = Sequence(Segment[M + (i * w / p, 0), M + (i * w / p, w)], i, 1, p - 1)
poly4, i_2, j_1, k_1, l_1 = Polygon(I, J, K, L)
poly5, m_1, c_1, d_1, f_1 = Polygon(M, M + (q / p * w, 0), M + (q / p * w, w), M + (0, w))
poly6, m_2, n_1, o_1, p_1 = Polygon(M, N, O, P)
Q = (25.51849977790952, 5.436045454545478)
u = Vector(E, Q)
G' = Translate(G, u)
H' = Translate(H, u)
g' = Segment(G', H')
list2' = Translate(list2, u)
F' = Translate(F, u)
G'_1 = Translate(G, u)
f' = Segment(F', G'_1)
H'_1 = Translate(H, u)
E' = Translate(E, u)
h' = Segment(H'_1, E')
E'_1 = Translate(E, u)
F'_1 = Translate(F, u)
e' = Segment(E'_1, F'_1)
poly1' = Translate(poly1, u)
list4' = Translate(list4, u)
R: Q + (0, n / m * w)
rr: p / q * w
v = Vector(A, T)
C' = Translate(C, v)
B' = Translate(B, v)
d' = Segment(C', B')
list3' = Translate(list3, v)
A' = Translate(A, v)
B'_1 = Translate(B, v)
a' = Segment(A', B'_1)
list1' = Translate(list1, v)
D' = Translate(D, v)
C'_1 = Translate(C, v)
c' = Segment(D', C'_1)
A'_1 = Translate(A, v)
D'_1 = Translate(D, v)
b' = Segment(A'_1, D'_1)
U = (26.422345276873042, 1.3525)
r1: q * m
r2: r1 - p
W: B'_1 + (0, pp * w / m)
V: T + (0, pp * w / m)
Z: V + (0, w / m)
A_1: V + (qq / p * w, 0)
B_1: A_1 + (0, w / m)
poly8, v_1, w_1, b'_1, t_1 = Polygon(V, W, B', T)
poly9, z, b_2, a_2, v_2 = Polygon(Z, B_1, A_1, V)
texte1: "" + qq + ""
u_1 = Vector(T, R)
V' = Translate(V, u_1)
W' = Translate(W, u_1)
B'' = Translate(B', u_1)
T' = Translate(T, u_1)
poly8', v', w', b'', t' = Polygon(V', W', B'', T')
Z' = Translate(Z, u_1)
S = Translate(B_1, u_1)
C_1 = Translate(A_1, u_1)
V'_1 = Translate(V, u_1)
poly9', z', s_2, c_2, v'_1 = Polygon(Z', S, C_1, V'_1)
text1: " \left\{
\begin{array}{l}
\frac{" + (LaTeX[n]) + "}{" + (LaTeX[m]) + "} =\frac{" + (LaTeX[n]) + "×" + (LaTeX[p]) + " }{ " + (LaTeX[m]) + "×" + (LaTeX[p]) + "}=\frac{" + (LaTeX[n * p]) + " }{" + (LaTeX[m * p]) + " }  \\
\frac{" + (LaTeX[q]) + " }{ " + (LaTeX[p]) + "} =\frac{ " + (LaTeX[q]) + "×" + (LaTeX[m]) + "  }{  " + (LaTeX[p]) + "× " + (LaTeX[m]) + "}=\frac{ " + (LaTeX[q * m]) + " }{" + (LaTeX[p * m]) + "  }
\end{array}
\right.
⇒
 \left\{
\begin{array}{l}
\frac{" + (LaTeX[n]) + " }{" + (LaTeX[m]) + " } +\frac{" + (LaTeX[q]) + "}{" + (LaTeX[p]) + " }=\frac{ " + (LaTeX[n * p + q * m]) + " }{ " + (LaTeX[m * p]) + " } \\
 }
\end{array}
\right."
texte2: "\frac{ " + (LaTeX[n * p]) + "}{" + (LaTeX[m * p]) + "  } "
mq: m * q
"\frac{ " + (LaTeX[n]) + "" + (LaTeX[p]) + "}{  } ": "\frac{ " + (LaTeX[mq]) + "}{" + (LaTeX[m * p]) + "  } "
texte3: "\frac{ " + (LaTeX[mq + n * p]) + " }{ " + (LaTeX[m * p]) + "  } "
D_1 = (12.376613488303272, 5.245136363636386)
E_1 = (15.103145913532774, 6.172409090909113)
F_1 = (17.502494447734737, 5.163318181818204)
g_1 = CircumcircleArc(D_1, E_1, F_1)
G_1 = Point(g_1)
z_1 = Vector(G_1, F_1)
H_1 = (9.568285090316897, 13.836045454545472)
I_1 = (9.486489117560012, -0.8094090909090642)
h_1 = Line(H_1, I_1)
J_1 = (22.87376332543688, 13.399681818181818)
K_1 = (22.955559298193766, -0.45486363636361016)
q_1 = Line(J_1, K_1)
r_1 = Segment(W', B'')
d_2 = Segment(V', W')
f_2 = Segment(W', B'')
g_2 = Segment(V'_1, T')
h_2 = Segment(V'_1, Z')
j_2 = Segment(S, C_1)
L_1 = (17.61155574474395, 11.163318181818202)
M_1 = (24.318825510808534, 9.608772727272749)
u_2 = Vector(L_1, M_1)
N_1 = (21.319639843056077, 4.372409090909114)
O_1 = (24.482417456322306, 6.663318181818204)
w_2 = Vector(N_1, O_1)
liste42 = Sequence(Segment[V'_1 + (i * w / p, 0), Z' + (i * w / p, 0)], i, 1, p)
liste41 = Sequence(Segment[T' + (i * w / p, 0), V' + (i * w / p, 0)], i, 1, p)
P_1: W + (0, w / m)
Q_1 = Translate(P_1, u_1)
e_2 = Segment(Z', Q_1)
k_2 = Segment(W', G')
liste40 = Sequence(Segment[T' + (0, i * w / m), T' + (w, i * w / m)], i, 1, pp)