2. Operaciones y resolución de problemas con números naturales

Propiedades de la suma y del producto

CONMUTATIVA: el orden de los sumandos (SUMA) o de los factores (PRODUCTO) no altera el resultado.

Ejemplos:

Suma: 4 + 5 = 5 + 4 = 9

Producto: 4 · 5 = 5 · 4 = 20

ASOCIATIVA: el orden en que realizamos la suma o el producto de 3 o más números no altera el resultado.

Ejemplos:

Suma: (5 + 2) + 8 = 5 + (2 + 8) = 15

Producto: (5 · 2) · 8 = 5 · (2 · 8) = 80

Propiedad de la división

La división cumple la siguiente propiedad relacionada con sus términos:

División de números naturales. Propiedades. Selecciona

Realiza, en tu cuaderno de clase, las siguientes operaciones con la división y sus propiedades.

A continuación, selecciona la respuesta correcta y pulsa sobre el botón "responder".

TIEMPO:

Dispones de 3 minutos en los ejercicios 1 y 2.
Dispones de 1 minuto en los ejercicios 3, 4 y 5.

undefined

%E9%B0%F3%E1%FB%F5%FC%F3%E6%E7%E0%F3%B0%A8%B0%B0%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%E7%E6%FA%FD%E0%C4%FB%F6%F7%FD%B0%A8%B0%B0%BE%B0%E6%EB%E2%F7%D5%F3%FF%F7%B0%A8%B0%C1%F7%FE%F7%F1%F1%FB%FD%FC%F3%B0%BE%B0%F7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%FB%F6%C4%FB%F6%F7%FD%B0%A8%B0%B0%BE%B0%E1%E6%F3%E0%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%FB%FC%E1%E6%E0%E7%F1%E6%FB%FD%FC%E1%D7%EA%F7%B0%A8%B0%B7%A1%D1%E2%B7%A1%D7%C0%F7%F3%FE%FB%E8%F3%B7%A0%D1%B7%A0%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%F7%FC%B7%A0%A2%E6%E7%B7%A0%A2%F1%E7%F3%F6%F7%E0%FC%FD%B7%A0%A2%F6%F7%B7%A0%A2%F1%FE%F3%E1%F7%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A0%D1%B7%A0%A2%FE%F3%E1%B7%A0%A2%E1%FB%F5%E7%FB%F7%FC%E6%F7%E1%B7%A0%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%FD%E2%F7%E0%F3%F1%FB%FD%FC%F7%E1%B7%A0%A2%F1%FD%FC%B7%A0%A2%FE%F3%B7%A0%A2%F6%FB%E4%FB%E1%FB%B7%D4%A1%FC%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A0%A2%EB%B7%A0%A2%E1%E7%E1%B7%A0%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%E2%E0%FD%E2%FB%F7%F6%F3%F6%F7%E1%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%BC%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A1%D1%BD%E2%B7%A1%D7%B7%A2%D3%B7%A1%D1%E2%B7%A1%D7%D3%B7%A0%A2%F1%FD%FC%E6%FB%FC%E7%F3%F1%FB%B7%D4%A1%FC%B7%A0%D1%B7%A0%A2%E1%F7%FE%F7%F1%F1%FB%FD%FC%F3%B7%A0%A2%FE%F3%B7%A0%A2%E0%F7%E1%E2%E7%F7%E1%E6%F3%B7%A0%A2%F1%FD%E0%E0%F7%F1%E6%F3%B7%A0%A2%EB%B7%D3%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%E2%E7%FE%E1%F3%B7%A0%A2%E1%FD%F0%E0%F7%B7%A0%A2%F7%FE%B7%A0%A2%F0%FD%E6%B7%D4%A1%FC%B7%A0%A2%B7%A0%A0%E0%F7%E1%E2%FD%FC%F6%F7%E0%B7%A0%A0%BC%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A1%D1%BD%E2%B7%A1%D7%B7%A2%D3%B7%A1%D1%E2%B7%A1%D7%C6%DB%D7%DF%C2%DD%B7%A1%D3%B7%D3%A2%B7%A1%D1%BD%E2%B7%A1%D7%B7%A2%D3%B7%A1%D1%E7%FE%B7%A1%D7%B7%A2%D3%B7%A1%D1%FE%FB%B7%A1%D7%D6%FB%E1%E2%FD%FC%F7%E1%B7%D3%A2%B7%A0%A2%F6%F7%B7%A0%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A1%D7%A1%B7%A0%A2%FF%FB%FC%E7%E6%FD%E1%B7%A0%A2%F7%FC%B7%A0%A2%FE%FD%E1%B7%A0%A2%F7%F8%F7%E0%F1%FB%F1%FB%FD%E1%B7%A0%A2%A3%B7%A0%A2%EB%B7%A0%A2%A0%BC%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A1%D1%BD%FE%FB%B7%A1%D7%B7%A2%D3%B7%A1%D1%FE%FB%B7%A1%D7%D6%FB%E1%E2%FD%FC%F7%E1%B7%A0%A2%F6%F7%B7%D3%A2%B7%A1%D1%E1%E6%E0%FD%FC%F5%B7%A0%A2%E1%E6%EB%FE%F7%B7%A1%D6%B7%A0%A0%F4%FD%FC%E6%BF%E1%FB%E8%F7%B7%A1%D3%B7%A0%A2%A3%BC%A2%A7%F7%FF%B7%A1%D0%B7%A0%A0%B7%A1%D7%A3%B7%A0%A2%FF%FB%FC%E7%E6%FD%B7%A0%A2%F7%FC%B7%A0%A2%FE%FD%E1%B7%A0%A2%F7%F8%F7%E0%F1%FB%F1%FB%FD%E1%B7%A0%A2%A1%B7%A0%D1%B7%A0%A2%A6%B7%A0%A2%EB%B7%A0%A2%A7%BC%B7%A1%D1%BD%E1%E6%E0%FD%FC%F5%B7%A1%D7%B7%A1%D1%BD%FE%FB%B7%A1%D7%B7%A2%D3%B7%A1%D1%BD%E7%FE%B7%A1%D7%B7%A2%D3%B7%A1%D1%E2%B7%A1%D7%B7%A1%D1%BD%E2%B7%A1%D7%B0%BE%B0%FB%FC%E1%E6%E0%E7%F1%E6%FB%FD%FC%E1%B0%A8%B0%C1%F7%FE%F7%F1%F1%FB%FD%FC%F3%B2%FE%F3%E1%B2%E0%F7%E1%E2%E7%F7%E1%E6%F3%E1%B2%F1%FD%E0%E0%F7%F1%E6%F3%E1%B2%EB%B2%E2%E7%FE%E1%F3%B2%E1%FD%F0%E0%F7%B2%F7%FE%B2%F0%FD%E6a%FC%B2%CE%B0%E0%F7%E1%E2%FD%FC%F6%F7%E0%CE%B0%B2%B0%BE%B0%E1%FA%FD%E5%DF%FB%FC%FB%FF%FB%E8%F7%B0%A8%F4%F3%FE%E1%F7%BE%B0%FD%E2%E6%FB%FD%FC%E1%C0%F3%FF%F6%FD%FC%B0%A8%F4%F3%FE%E1%F7%BE%B0%F3%FC%E1%E5%F7%E0%E1%C0%F3%FF%F6%FD%FC%B0%A8%F4%F3%FE%E1%F7%BE%B0%E1%FA%FD%E5%C1%FD%FE%E7%E6%FB%FD%FC%B0%A8%E6%E0%E7%F7%BE%B0%E6%FB%FF%F7%C1%FA%FD%E5%C1%FD%FE%E7%E6%FB%FD%FC%B0%A8%A1%BE%B0%E7%E1%F7%DE%FB%E4%F7%E1%B0%A8%E6%E0%E7%F7%BE%B0%FC%E7%FF%F0%F7%E0%DE%FB%E4%F7%E1%B0%A8%A1%BE%B0%FB%E6%FB%FC%F7%E0%F3%E0%EB%B0%A8%E9%B0%E1%FA%FD%E5%D1%FE%E7%F7%B0%A8%F4%F3%FE%E1%F7%BE%B0%F1%FE%E7%F7%D5%F3%FF%F7%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%D1%FE%E7%F7%B0%A8%A6%A2%BE%B0%E1%FA%FD%E5%D1%FD%F6%F7%D3%F1%F1%F7%E1%E1%B0%A8%E6%E0%E7%F7%BE%B0%F1%FD%F6%F7%D3%F1%F1%F7%E1%E1%B0%A8%B0%D6%FB%E4%FB%E1%FBa%FC%B0%BE%B0%FF%F7%E1%E1%F3%F5%F7%D1%FD%F6%F7%D3%F1%F1%F7%E1%E1%B0%A8%B0-%DC%FD%FF%F0%E0%F7%B2%F6%F7%B2%FE%F3%B2%FD%E2%F7%E0%F3%F1%FBa%FC%AD%B0%EF%BE%B0%E1%F7%FE%F7%F1%E6%E1%D5%F3%FF%F7%B0%A8%C9%E9%B0%E6%EB%E2%F7%B0%A8%A3%BE%B0%E6%FB%FF%F7%B0%A8%A1%BE%B0%FC%E7%FF%F0%F7%E0%DD%E2%E6%FB%FD%FC%E1%B0%A8%A6%BE%B0%E6%EB%E2%F7%C1%F7%FE%F7%F1%E6%B0%A8%A2%BE%B0%EA%B0%A8%A2%BE%B0%EB%B0%A8%A2%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%FE%E6%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%A3%BE%B0%E7%E0%FE%B0%A8%B0%E0%F7%E1%FD%E7%E0%F1%F7%E1%BD%F7%F8%F7%E0%F1%FB%F1%FB%FD%CD%F6%FB%E4%FB%E1%FB%FD%FC%BC%F8%E2%F5%B0%BE%B0%F3%E7%F6%FB%FD%B0%A8%B0%B0%BE%B0%FA%FB%E6%B0%A8%BF%A3%BE%B0%F7%E0%E0%FD%E0%B0%A8%BF%A3%BE%B0%FF%E1%F5%DA%FB%E6%B0%A8%B0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%B0%A8%B0%B0%BE%B0%E1%FD%E7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%FF%F3%F5%F7%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F4%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E6%C1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F7%C6%F7%EA%E6%B0%A8%B0%B0%BE%B0%E3%E7%F7%EA%E6%FB%FD%FC%B0%A8%B0%A3%BC%B2%C0%F7%F3%FE%FB%E8%F3%B2%FE%F3%B2%E1%FB%F5%E7%FB%F7%FC%E6%F7%B2%F6%FB%E4%FB%E1%FBa%FC%B2%F7%B2%FB%FC%F6%FB%F1%F3%B2%F7%FE%B2%F1%FD%F1%FB%F7%FC%E6%F7%B2%EB%B2%F7%FE%B2%E0%F7%E1%E6%FD%B2%FD%F0%E6%F7%FC%FB%F6%FD%E1%BC%B0%BE%B0%FD%E2%E6%FB%FD%FC%E1%B0%A8%C9%B0%D1%B2%AF%B2%A1%A6%A6%B2%EB%B2%C0%B2%AF%B2%A6%A4%B0%BE%B0%D1%B2%AF%B2%A1%A7%A1%B2%EB%B2%C0%B2%AF%B2%A4%A6%B0%BE%B0%D1%B2%AF%B2%A1%A6%A6%B2%EB%B2%B2%C0%B2%AF%B2%A4%A6%B0%BE%B0%D1%B2%AF%B2%A1%A7%A1%B2%EB%B2%C0%B2%AF%B2%A6%A4%B0%CF%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%B0%A8%B0%D1%B0%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%C1%FA%FD%E5%B0%A8%A1%A7%EF%BE%E9%B0%E6%EB%E2%F7%B0%A8%A3%BE%B0%E6%FB%FF%F7%B0%A8%A1%BE%B0%FC%E7%FF%F0%F7%E0%DD%E2%E6%FB%FD%FC%E1%B0%A8%A6%BE%B0%E6%EB%E2%F7%C1%F7%FE%F7%F1%E6%B0%A8%A2%BE%B0%EA%B0%A8%A2%BE%B0%EB%B0%A8%A2%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%FE%E6%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%A3%BE%B0%E7%E0%FE%B0%A8%B0%E0%F7%E1%FD%E7%E0%F1%F7%E1%BD%F7%F8%F7%E0%F1%FB%F1%FB%FD%CD%F6%FB%E4%FB%E1%FB%FD%FC%CD%A3%BC%F8%E2%F5%B0%BE%B0%F3%E7%F6%FB%FD%B0%A8%B0%B0%BE%B0%FA%FB%E6%B0%A8%BF%A3%BE%B0%F7%E0%E0%FD%E0%B0%A8%BF%A3%BE%B0%FF%E1%F5%DA%FB%E6%B0%A8%B0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%B0%A8%B0%B0%BE%B0%E1%FD%E7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%FF%F3%F5%F7%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F4%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E6%C1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F7%C6%F7%EA%E6%B0%A8%B0%B0%BE%B0%E3%E7%F7%EA%E6%FB%FD%FC%B0%A8%B0%A0%BC%B2%C0%F7%F3%FE%FB%E8%F3%B2%FE%F3%B2%E1%FB%F5%E7%FB%F7%FC%E6%F7%B2%F6%FB%E4%FB%E1%FBa%FC%B2%F7%B2%FB%FC%F6%FB%F1%F3%B2%F7%FE%B2%F1%FD%F1%FB%F7%FC%E6%F7%B2%EB%B2%F7%FE%B2%E0%F7%E1%E6%FD%B2%FD%F0%E6%F7%FC%FB%F6%FD%E1%BC%B0%BE%B0%FD%E2%E6%FB%FD%FC%E1%B0%A8%C9%B0%D1%B2%AF%B2%A3%BC%AB%A7%A4%B2%EB%B2%C0%B2%AF%B2%A0%AB%A7%B0%BE%B0%D1%B2%AF%B2%A3%BC%AB%A4%A7%B2%EB%B2%C0%B2%AF%B2%A0%AB%A7%B0%BE%B0%D1%B2%AF%B2%A3%BC%AA%A1%A7%B2%EB%B2%B2%C0%B2%AF%B2%A0%A5%A0%B0%BE%B0%D1%B2%AF%B2%A3%BC%AA%A7%A1%B2%EB%B2%C0%B2%AF%B2%A0%A0%A5%B0%CF%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%B0%A8%B0%D6%B0%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%C1%FA%FD%E5%B0%A8%A1%A7%EF%BE%E9%B0%E6%EB%E2%F7%B0%A8%A3%BE%B0%E6%FB%FF%F7%B0%A8%A0%BE%B0%FC%E7%FF%F0%F7%E0%DD%E2%E6%FB%FD%FC%E1%B0%A8%A6%BE%B0%E6%EB%E2%F7%C1%F7%FE%F7%F1%E6%B0%A8%A2%BE%B0%EA%B0%A8%A2%BE%B0%EB%B0%A8%A2%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%FE%E6%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%A3%BE%B0%E7%E0%FE%B0%A8%B0%E0%F7%E1%FD%E7%E0%F1%F7%E1%BD%F6%FB%E4%FB%E1%FB%FD%FC%CD%E6%F7%E0%FF%FB%FC%FD%CD%F4%F3%FE%E6%F3%BC%F8%E2%F5%B0%BE%B0%F3%E7%F6%FB%FD%B0%A8%B0%B0%BE%B0%FA%FB%E6%B0%A8%BF%A3%BE%B0%F7%E0%E0%FD%E0%B0%A8%BF%A3%BE%B0%FF%E1%F5%DA%FB%E6%B0%A8%B0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%B0%A8%B0%B0%BE%B0%E1%FD%E7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%FF%F3%F5%F7%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F4%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E6%C1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F7%C6%F7%EA%E6%B0%A8%B0%B0%BE%B0%E3%E7%F7%EA%E6%FB%FD%FC%B0%A8%B0%A1%BC%B2%D1%F3%FE%F1%E7%FE%F3%B2%F7%FE%B2%E6%7B%E0%FF%FB%FC%FD%B2%E3%E7%F7%B2%F4%F3%FE%E6%F3%B2%BA%F7%FE%B2%E0%F7%E1%E6%FD%BB%B2%F7%FC%B2%FE%F3%B2%E1%FB%F5%E7%FB%F7%FC%E6%F7%B2%F6%FB%E4%FB%E1%FBa%FC%B2%F3%B2%E2%F3%E0%E6%FB%E0%B2%F6%F7%B2%FE%FD%E1%B2%F6%F3%E6%FD%E1%B2%FB%FC%F6%FB%F1%F3%F6%FD%E1%BC%B0%BE%B0%FD%E2%E6%FB%FD%FC%E1%B0%A8%C9%B0%C0%B2%AF%B2%A0%A3%B0%BE%B0%C0%B2%AF%B2%A0%A4%B0%BE%B0%C0%B2%AF%B2%A0%A0%B0%BE%B0%C0%B2%AF%B2%A0%A6%B0%CF%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%B0%A8%B0%D3%B0%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%C1%FA%FD%E5%B0%A8%A1%A7%EF%BE%E9%B0%E6%EB%E2%F7%B0%A8%A3%BE%B0%E6%FB%FF%F7%B0%A8%A0%BE%B0%FC%E7%FF%F0%F7%E0%DD%E2%E6%FB%FD%FC%E1%B0%A8%A6%BE%B0%E6%EB%E2%F7%C1%F7%FE%F7%F1%E6%B0%A8%A2%BE%B0%EA%B0%A8%A2%BE%B0%EB%B0%A8%A2%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%FE%E6%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%A3%BE%B0%E7%E0%FE%B0%A8%B0%E0%F7%E1%FD%E7%E0%F1%F7%E1%BD%F6%FB%E4%FB%E1%FB%FD%FC%CD%E6%F7%E0%FF%FB%FC%FD%CD%F4%F3%FE%E6%F3%CD%A3%BC%F8%E2%F5%B0%BE%B0%F3%E7%F6%FB%FD%B0%A8%B0%B0%BE%B0%FA%FB%E6%B0%A8%BF%A3%BE%B0%F7%E0%E0%FD%E0%B0%A8%BF%A3%BE%B0%FF%E1%F5%DA%FB%E6%B0%A8%B0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%B0%A8%B0%B0%BE%B0%E1%FD%E7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%FF%F3%F5%F7%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F4%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E6%C1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F7%C6%F7%EA%E6%B0%A8%B0%B0%BE%B0%E3%E7%F7%EA%E6%FB%FD%FC%B0%A8%B0%A6%BC%B2%D1%F3%FE%F1%E7%FE%F3%B2%F7%FE%B2%E6%7B%E0%FF%FB%FC%FD%B2%E3%E7%F7%B2%F4%F3%FE%E6%F3%B2%BA%F7%FE%B2%F6%FB%E4%FB%F6%F7%FC%F6%FD%BB%B2%F7%FC%B2%FE%F3%B2%E1%FB%F5%E7%FB%F7%FC%E6%F7%B2%F6%FB%E4%FB%E1%FBa%FC%B2%F3%B2%E2%F3%E0%E6%FB%E0%B2%F6%F7%B2%FE%FD%E1%B2%F6%F3%E6%FD%E1%B2%FB%FC%F6%FB%F1%F3%F6%FD%E1%BC%B0%BE%B0%FD%E2%E6%FB%FD%FC%E1%B0%A8%C9%B0%D6%B2%AF%B2%A3%A2%A6%B0%BE%B0%D6%B2%AF%B2%A3%A2%AB%B0%BE%B0%D6%B2%AF%B2%A7%A1%B0%BE%B0%D6%B2%AF%B2%A7%A7%B0%CF%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%B0%A8%B0%D0%B0%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%C1%FA%FD%E5%B0%A8%A1%A7%EF%BE%E9%B0%E6%EB%E2%F7%B0%A8%A3%BE%B0%E6%FB%FF%F7%B0%A8%A0%BE%B0%FC%E7%FF%F0%F7%E0%DD%E2%E6%FB%FD%FC%E1%B0%A8%A6%BE%B0%E6%EB%E2%F7%C1%F7%FE%F7%F1%E6%B0%A8%A2%BE%B0%EA%B0%A8%A2%BE%B0%EB%B0%A8%A2%BE%B0%F3%E7%E6%FA%FD%E0%B0%A8%B0%B0%BE%B0%F3%FE%E6%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%A3%BE%B0%E7%E0%FE%B0%A8%B0%E0%F7%E1%FD%E7%E0%F1%F7%E1%BD%F6%FB%E4%FB%E1%FB%FD%FC%CD%E6%F7%E0%FF%FB%FC%FD%CD%F4%F3%FE%E6%F3%CD%A0%BC%F8%E2%F5%B0%BE%B0%F3%E7%F6%FB%FD%B0%A8%B0%B0%BE%B0%FA%FB%E6%B0%A8%BF%A3%BE%B0%F7%E0%E0%FD%E0%B0%A8%BF%A3%BE%B0%FF%E1%F5%DA%FB%E6%B0%A8%B0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%B0%A8%B0%B0%BE%B0%E1%FD%E7%FC%F6%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%FF%F3%F5%F7%C4%FB%F6%F7%FD%B0%A8%A3%BE%B0%FB%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F4%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%E6%C1%FB%FE%F7%FC%E6%C4%FB%F6%F7%FD%B0%A8%A2%BE%B0%F7%C6%F7%EA%E6%B0%A8%B0%B0%BE%B0%E3%E7%F7%EA%E6%FB%FD%FC%B0%A8%B0%A7%BC%B2%D1%F3%FE%F1%E7%FE%F3%B2%F7%FE%B2%E6%7B%E0%FF%FB%FC%FD%B2%E3%E7%F7%B2%F4%F3%FE%E6%F3%B2%BA%F7%FE%B2%F6%FB%E4%FB%E1%FD%E0%BB%B2%F7%FC%B2%FE%F3%B2%E1%FB%F5%E7%FB%F7%FC%E6%F7%B2%F6%FB%E4%FB%E1%FBa%FC%B2%F3%B2%E2%F3%E0%E6%FB%E0%B2%F6%F7%B2%FE%FD%E1%B2%F6%F3%E6%FD%E1%B2%FB%FC%F6%FB%F1%F3%F6%FD%E1%BC%B0%BE%B0%FD%E2%E6%FB%FD%FC%E1%B0%A8%C9%B0%F6%B2%AF%B2%AA%B0%BE%B0%F6%B2%AF%B2%AB%B0%BE%B0%F6%B2%AF%B2%A4%B0%BE%B0%F6%B2%AF%B2%A5%B0%CF%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%B0%A8%B0%D6%B0%BE%B0%E1%FD%FE%E7%E6%FB%FD%FC%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%B0%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F5%F7%C1%FA%FD%E5%B0%A8%A1%A7%EF%CF%BE%B0%FB%E1%C1%F1%FD%E0%FF%B0%A8%A2%BE%B0%E6%F7%EA%E6%D0%E7%E6%E6%FD%FC%C1%F1%FD%E0%FF%B0%A8%B0%D5%E7%F3%E0%F6%F3%E0%B2%FE%F3%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B0%BE%B0%E0%F7%E2%F7%F3%E6%D3%F1%E6%FB%E4%FB%E6%EB%B0%A8%F4%F3%FE%E1%F7%BE%B0%E6%FB%E6%FE%F7%B0%A8%B0%B0%BE%B0%F1%E7%E1%E6%FD%FF%C1%F1%FD%E0%F7%B0%A8%F4%F3%FE%E1%F7%BE%B0%E6%F7%EA%E6%D3%F4%E6%F7%E0%B0%A8%B0%B0%BE%B0%E6%F7%EA%E6%D4%F7%F7%F6%D0%F3%F1%F9%B0%A8%B0%B0%BE%B0%F5%F3%FF%F7%DF%FD%F6%F7%B0%A8%A3%BE%B0%F4%F7%F7%F6%D0%F3%F1%F9%B0%A8%F4%F3%FE%E1%F7%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F8%F7%D4%D0%B0%A8%A3%A2%A2%BE%B0%FD%E0%F6%F7%E0%B0%A8%A2%BE%B0%F1%E7%E1%E6%FD%FF%DF%F7%E1%E1%F3%F5%F7%E1%B0%A8%F4%F3%FE%E1%F7%BE%B0%E4%F7%E0%E1%FB%FD%FC%B0%A8%A1%BC%A3%BE%B0%E2%F7%E0%F1%F7%FC%E6%F3%F8%F7%C3%E7%F7%E1%E6%FB%FD%FC%E1%B0%A8%A3%A2%A2%BE%B0%F3%E7%F6%FB%FD%D4%F7%F7%F6%D0%F3%F1%FA%B0%A8%F4%F3%FE%E1%F7%BE%B0%FF%FD%F6%F7%D0%FD%F3%E0%F6%B0%A8%F4%F3%FE%E1%F7%BE%B0%FF%E1%F5%E1%B0%A8%E9%B0%FF%E1%F5%C0%F7%F3%F6%EB%B0%A8%B0-%C2%E0%F7%E2%F3%E0%F3%F6%FD%AD%B0%BE%B0%FF%E1%F5%C1%E6%F3%E0%E6%D5%F3%FF%F7%B0%A8%B0%C2%E7%FE%E1%F7%B2%F3%E3%E7%7F%B2%E2%F3%E0%F3%B2%F7%FF%E2%F7%E8%F3%E0%B0%BE%B0%FF%E1%F5%C1%E7%F0%FF%FB%E6%B0%A8%B0%D7%FC%E4%FB%F3%E0%B0%BE%B0%FF%E1%F5%D7%FC%E6%F7%E0%D1%FD%F6%F7%B0%A8%B0%DB%FC%E6%E0%FD%F6%E7%E8%F1%F3%B2%F7%FE%B2%F1a%F6%FB%F5%FD%B2%F6%F7%B2%F3%F1%F1%F7%E1%FD%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%D1%FD%F6%F7%B0%A8%B0%D7%FE%B2%F1a%F6%FB%F5%FD%B2%F6%F7%B2%F3%F1%F1%F7%E1%FD%B2%FC%FD%B2%F7%E1%B2%F1%FD%E0%E0%F7%F1%E6%FD%B0%BE%B0%FF%E1%F5%D5%F3%FF%F7%DD%E4%F7%E0%B0%A8%B03%D4%FB%FC%B2%F6%F7%B2%FE%F3%B2%E2%F3%E0%E6%FB%F6%F3%B3%B0%BE%B0%FF%E1%F5%D1%FE%E7%F7%B0%A8%B03%D5%F7%FC%FB%F3%FE%B3%B2%DE%F3%B2%E2%FB%E1%E6%F3%B2%F7%E1%A8%B0%BE%B0%FF%E1%F5%DC%F7%E5%D5%F3%FF%F7%B0%A8%B0%C2%E7%FE%E1%F7%B2%F3%E3%E7%7F%B2%E2%F3%E0%F3%B2%F7%FF%E2%F7%E8%F3%E0%B2%FD%E6%E0%F3%B2%E2%F3%E0%E6%FB%F6%F3%B0%BE%B0%FF%E1%F5%CB%FD%E7%DA%F3%E1%B0%A8%B0%C6%FB%F7%FC%F7%B2%B7%A3%B2%F3%F1%FB%F7%E0%E6%FD%E1%B2%EB%B2%B7%A0%B2%F4%F3%FE%FE%FD%E1%B0%BE%B0%FF%E1%F5%D1%FD%F6%F7%D3%F1%F1%F7%E1%E1%B0%A8%B0%D1a%F6%FB%F5%FD%B2%F6%F7%B2%F3%F1%F1%F7%E1%FD%B0%BE%B0%FF%E1%F5%C2%FE%F3%EB%D3%F5%F3%FB%FC%B0%A8%B0%D8%E7%F5%F3%E0%B2%FD%E6%E0%F3%B2%E4%F7%E8%B0%BE%B0%FF%E1%F5%C0%F7%E3%E7%FB%E0%F7%F6%D3%F1%F1%F7%E1%E1%D9%F7%EB%B0%A8%B0%D7%E1%B2%FC%F7%F1%F7%E1%F3%E0%FB%FD%B2%F7%FE%B2%F1a%F6%FB%F5%FD%B2%F6%F7%B2%F3%F1%F1%F7%E1%FD%B0%BE%B0%FF%E1%F5%DB%FC%F4%FD%E0%FF%F3%E6%FB%FD%FC%DE%FD%FD%F9%FB%FC%F5%B0%A8%B03%D5%F7%FC%FB%F3%FE%B3%B2%DE%F3%B2%FB%FC%F4%FD%E0%FF%F3%F1%FBa%FC%B2%E3%E7%F7%B2%F7%E1%E6%F3%F0%F3%B2%F0%E7%E1%F1%F3%FC%F6%FD%B0%BE%B0%FF%E1%F5%C2%FE%F3%EB%C1%E6%F3%E0%E6%B0%A8%B0%C2%E7%FE%E1%F7%B2%F3%E3%E7%7F%B2%E2%F3%E0%F3%B2%F8%E7%F5%F3%E0%B0%BE%B0%FF%E1%F5%D7%E0%E0%FD%E0%E1%B0%A8%B0%D7%E0%E0%FD%E0%F7%E1%B0%BE%B0%FF%E1%F5%DA%FB%E6%E1%B0%A8%B0%D3%F1%FB%F7%E0%E6%FD%E1%B0%BE%B0%FF%E1%F5%C1%F1%FD%E0%F7%B0%A8%B0%C2%E7%FC%E6%E7%F3%F1%FBa%FC%B0%BE%B0%FF%E1%F5%DF%FB%FC%FB%FF%FB%E8%F7%B0%A8%B0%DF%FB%FC%FB%FF%FB%E8%F3%E0%B0%BE%B0%FF%E1%F5%DF%F3%EA%FB%FF%FB%E8%F7%B0%A8%B0%DF%F3%EA%FB%FF%FB%E8%F3%E0%B0%BE%B0%FF%E1%F5%C6%FB%FF%F7%B0%A8%B0%C6%FB%F7%FF%E2%FD%B2%E2%FD%E0%B2%E2%E0%F7%F5%E7%FC%E6%F3%B0%BE%B0%FF%E1%F5%DE%FB%E4%F7%B0%A8%B0%C4%FB%F6%F3%B0%BE%B0%FF%E1%F5%D4%E7%FE%FE%C1%F1%E0%F7%F7%FC%B0%A8%B0%C2%F3%FC%E6%F3%FE%FE%F3%B2%D1%FD%FF%E2%FE%F7%E6%F3%B0%BE%B0%FF%E1%F5%D7%EA%FB%E6%D4%E7%FE%FE%C1%F1%E0%F7%F7%FC%B0%A8%B0%C1%F3%FE%FB%E0%B2%F6%F7%FE%B2%FF%FD%F6%FD%B2%E2%F3%FC%E6%F3%FE%FE%F3%B2%F1%FD%FF%E2%FE%F7%E6%F3%B0%BE%B0%FF%E1%F5%DC%E7%FF%C3%E7%F7%E1%E6%FB%FD%FC%E1%B0%A8%B0%DCh%FF%F7%E0%FD%B2%F6%F7%B2%E2%E0%F7%F5%E7%FC%E6%F3%E1%B0%BE%B0%FF%E1%F5%DC%FD%DB%FF%F3%F5%F7%B0%A8%B0%C2%E0%F7%F5%E7%FC%E6%F3%B2%E1%FB%FC%B2%FB%FFs%F5%F7%FC%F7%E1%B0%BE%B0%FF%E1%F5%D1%FD%FD%FE%B0%A8%B03%D0%FB%F7%FC%B3%B0%BE%B0%FF%E1%F5%DE%FD%E1%F7%C6%B0%A8%B0%DA%F3%B2%E2%F7%E0%F6%FB%F6%FD%B2%A1%A1%A2%B2%E2%E7%FC%E6%FD%E1%B0%BE%B0%FF%E1%F5%DE%FD%E1%F7%DE%FB%E4%F7%B0%A8%B0%DA%F3%B2%E2%F7%E0%F6%FB%F6%FD%B2%E7%FC%F3%B2%E4%FB%F6%F3%B0%BE%B0%FF%E1%F5%DE%FD%E1%E6%DE%FB%E4%F7%E1%B0%A8%B03%DA%F3%B2%E2%F7%E0%F6%FB%F6%FD%B2%E6%FD%F6%F3%E1%B2%E1%E7%E1%B2%E4%FB%F6%F3%E1%B3%B0%BE%B0%FF%E1%F5%D3%FE%FE%C3%E7%F7%E1%E6%FB%FD%FC%E1%B0%A8%B03%D1%FD%FF%E2%FE%F7%E6%F3%F6%F3%E1%B2%FE%F3%E1%B2%E2%E0%F7%F5%E7%FC%E6%F3%E1%B3%B0%BE%B0%FF%E1%F5%C1%E7%F1%F1%F7%E1%E1%F7%E1%B0%A8%B03%D1%FD%E0%E0%F7%F1%E6%FD%B3%B2%EE%B23%D7%EA%F1%F7%FE%F7%FC%E6%F7%B3%B2%EE%B23%D5%F7%FC%FB%F3%FE%B3%B2%EE%B23%DF%E7%EB%B2%F0%FB%F7%FC%B3%B2%EE%B23%C2%F7%E0%F4%F7%F1%E6%FD%B3%B0%BE%B0%FF%E1%F5%D4%F3%FB%FE%E7%E0%F7%E1%B0%A8%B03%DC%FD%B2%F7%E0%F3%B2%F7%E1%FD%B3%B2%EE%B23%DB%FC%F1%FD%E0%E0%F7%F1%E6%FD%B3%B2%EE%B23%DC%FD%B2%F7%E1%B2%F1%FD%E0%E0%F7%F1%E6%FD%B3%B2%EE%B23%DE%FD%B2%E1%F7%FC%E6%FB%FF%FD%E1%B3%B2%EE%B23%D7%E0%E0%FD%E0%B3%B0%BE%B0%FF%E1%F5%DC%FD%E6%DC%F7%E6%E5%FD%E0%F9%B0%A8%B0%D3%B2%F7%E1%E6%F7%B2%F8%E7%F7%F5%FD%B2%E1a%FE%FD%B2%E1%F7%B2%E2%E7%F7%F6%F7%B2%F8%E7%F5%F3%E0%B2%F1%FD%FC%B2%F1%FD%FC%F7%EA%FBa%FC%B2%F3%B2%FB%FC%E6%F7%E0%FC%F7%E6%BC%B0%BE%B0%FF%E1%F5%D7%FC%F6%D5%F3%FF%F7%C1%F1%FD%E0%F7%B0%A8%B0%DB%FC%FB%F1%FB%F3%B2%F7%FE%B2%F8%E7%F7%F5%FD%BC%BC%BC%B0%BE%B0%FF%E1%F5%C1%F1%FD%E0%F7%C1%F1%FD%E0%FF%B0%A8%B0%DE%F3%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%FC%FD%B2%E1%F7%B2%E2%E7%F7%F6%F7%B2%F5%E7%F3%E0%F6%F3%E0%B2%E2%FD%E0%E3%E7%F7%B2%F7%E1%E6%F3%B2%E2s%F5%FB%FC%F3%B2%FC%FD%B2%F4%FD%E0%FF%F3%B2%E2%F3%E0%E6%F7%B2%B2%F6%F7%B2%E7%FC%B2%E2%F3%E3%E7%F7%E6%F7%B2%C1%D1%DD%C0%DF%BC%B0%BE%B0%FF%E1%F5%C3%E7%F7%E1%E6%FB%FD%FC%B0%A8%B0%C2%E0%F7%F5%E7%FC%E6%F3%B0%BE%B0%FF%E1%F5%D3%FC%E1%E5%F7%E0%B0%A8%B0%D1%FD%FF%E2%E0%FD%F0%F3%E0%B0%BE%B0%FF%E1%F5%DD%FC%FE%EB%C1%F3%E4%F7%C1%F1%FD%E0%F7%B0%A8%B03%C1a%FE%FD%B2%E2%E7%F7%F6%F7%B2%F5%E7%F3%E0%F6%F3%E0%B2%FE%F3%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%E7%FC%F3%B2%E4%F7%E8%B3%B0%BE%B0%FF%E1%F5%DD%FC%FE%EB%C1%F3%E4%F7%B0%A8%B0%C1a%FE%FD%B2%E2%E7%F7%F6%F7%B2%F5%E7%F3%E0%F6%F3%E0%B2%E7%FC%F3%B2%E4%F7%E8%B0%BE%B0%FF%E1%F5%DB%FC%F4%FD%E0%FF%F3%E6%FB%FD%FC%B0%A8%B0%DB%FC%F4%FD%E0%FF%F3%F1%FBa%FC%B0%BE%B0%FF%E1%F5%CB%FD%E7%C1%F1%FD%E0%F7%B0%A8%B0%C1%E7%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B0%BE%B0%FF%E1%F5%D3%E7%E6%FA%FD%E0%B0%A8%B0%D3%E7%E6%FD%E0%7F%F3%B0%BE%B0%FF%E1%F5%DD%FC%FE%EB%C1%F3%E4%F7%D3%E7%E6%FD%B0%A8%B0%C1%E7%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%E1%F7%B2%F5%E7%F3%E0%F6%F3%E0s%B2%F6%F7%E1%E2%E7%7B%E1%B2%F6%F7%B2%F1%F3%F6%F3%B2%E2%E0%F7%F5%E7%FC%E6%F3%BC%B2%C1a%FE%FD%B2%E2%E7%F7%F6%F7%B2%F8%E7%F5%F3%E0%B2%E7%FC%F3%B2%E4%F7%E8%BC%B0%BE%B0%FF%E1%F5%C1%F3%E4%F7%D3%E7%E6%FD%B0%A8%B0%C1%E7%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%E1%F7%B2%F5%E7%F3%E0%F6%F3%E0s%B2%F3%E7%E6%FD%FFs%E6%FB%F1%F3%FF%F7%FC%E6%F7%B2%F6%F7%E1%E2%E7%7B%E1%B2%F6%F7%B2%F1%F3%F6%F3%B2%E2%E0%F7%F5%E7%FC%E6%F3%BC%B0%BE%B0%FF%E1%F5%C1%F7%E4%F7%E0%F3%FE%C1%F1%FD%E0%F7%B0%A8%B0%C2%E7%F7%F6%F7%B2%F5%E7%F3%E0%F6%F3%E0%B2%FE%F3%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%E6%F3%FC%E6%F3%E1%B2%E4%F7%F1%F7%E1%B2%F1%FD%FF%FD%B2%E3%E7%FB%F7%E0%F3%B0%BE%B0%FF%E1%F5%CB%FD%E7%DE%F3%E1%E6%C1%F1%FD%E0%F7%B0%A8%B0%DE%F3%B2h%FE%E6%FB%FF%F3%B2%E2%E7%FC%E6%E7%F3%F1%FBa%FC%B2%F5%E7%F3%E0%F6%F3%F6%F3%B2%F7%E1%B0%BE%B0%FF%E1%F5%D3%F1%E6%FB%E6%EB%D1%FD%FF%E2%FE%EB%B0%A8%B0%CB%F3%B2%FA%F3%B2%E0%F7%F3%FE%FB%E8%F3%F6%FD%B2%F7%E1%E6%F3%B2%F3%F1%E6%FB%E4%FB%F6%F3%F6%BC%B0%BE%B0%FF%E1%F5%C2%FE%F3%EB%C1%F7%E4%F7%E0%F3%FE%C6%FB%FF%F7%E1%B0%A8%B0%C2%E7%F7%F6%F7%B2%E0%F7%F3%FE%FB%E8%F3%E0%B2%F7%E1%E6%F3%B2%F3%F1%E6%FB%E4%FB%F6%F3%F6%B2%F1%E7%F3%FC%E6%F3%E1%B2%E4%F7%F1%F7%E1%B2%E3%E7%FB%F7%E0%F3%B0%BE%B0%FF%E1%F5%C6%E0%EB%D3%F5%F3%FB%FC%B0%A8%B0%DC%F7%F1%F7%E1%FB%E6%F3%B2%F3%FE%B2%FF%F7%FC%FD%E1%B2%E7%FC%B2%B7%E1%B7%B2%F6%F7%B2%E0%F7%E1%E2%E7%F7%E1%E6%F3%E1%B2%F1%FD%E0%E0%F7%F1%E6%F3%E1%B2%E2%F3%E0%F3%B2%F1%FD%FC%E1%F7%F5%E7%FB%E0%B2%FE%F3%B2%FB%FC%F4%FD%E0%FF%F3%F1%FBa%FC%BC%B2%C4%E7%F7%FE%E4%F3%B2%F3%B2%FB%FC%E6%F7%FC%E6%F3%E0%FE%FD%BC%B0%BE%B0%FF%E1%F5%C4%FB%F6%F7%FD%DB%FC%E6%E0%FD%B0%A8%B0%C4%7F%F6%F7%FD%B2%F6%F7%B2%FB%FC%E6%E0%FD%F6%E7%F1%F1%FBa%FC%B0%BE%B0%FF%E1%F5%D1%FE%FD%E1%F7%B0%A8%B0%D1%F7%E0%E0%F3%E0%B0%BE%B0%FF%E1%F5%DD%E2%E6%FB%FD%FC%B0%A8%B0%DD%E2%F1%FBa%FC%B0%BE%B0%FF%E1%F5%C0%FB%F1%F9%C6%F7%EA%E6%B0%A8%B0%C6%F7%EA%E6%FD%B2%F7%FC%E0%FB%E3%E7%F7%F1%FB%F6%FD%B0%BE%B0%FF%E1%F5%C7%E1%F7%D4%E7%FE%DB%FC%F4%FD%E0%FF%F3%E6%FB%FD%FC%B0%A8%B0%F7%B2%FB%FC%F4%FD%E0%FF%F3%F1%FBa%FC%B2%E3%E7%F7%B2%E1%F7%E0s%B2%FF%E7%EB%B2h%E6%FB%FE%B0%BE%B0%FF%E1%F5%DE%FD%F3%F6%FB%FC%F5%B0%A8%B0%D1%F3%E0%F5%F3%FC%F6%FD%BC%B2%D7%E1%E2%F7%E0%F7%BE%B2%E2%FD%E0%B2%F4%F3%E4%FD%E0%BC%BC%BC%B0%BE%B0%FF%E1%F5%DD%E0%F6%F7%E0%E1%B0%A8%B0%DD%E0%F6%F7%FC%F3%B2%E6%FD%F6%F3%E1%B2%FE%F3%E1%B2%E0%F7%E1%E2%E7%F7%E1%E6%F3%E1%B0%BE%B0%FF%E1%F5%DB%FC%F6%FB%F1%F3%E6%F7%C5%FD%E0%F6%B0%A8%B0%C2%E0%FD%E2%FD%E0%F1%FB%FD%FC%F7%B2%E7%FC%F3%B2%E2%F3%FE%F3%F0%E0%F3%B2%FD%B2%F7%EA%E2%E0%F7%E1%FBa%FC%B0%BE%B0%FF%E1%F5%DF%FD%E4%F7%DD%FC%F7%B0%A8%B0%C2%F3%E1%F3%E0%B0%BE%B0%FF%E1%F5%C2%FD%FB%FC%E6%E1%B0%A8%B0%E2%E7%FC%E6%FD%E1%B0%BE%B0%FF%E1%F5%D3%E7%F6%FB%FD%B0%A8%B0%D3%E7%F6%FB%FD%B0%BE%B0%FF%E1%F5%D1%FD%E0%E0%F7%F1%E6%B0%A8%B0%D1%FD%E0%E0%F7%F1%E6%FD%B0%BE%B0%FF%E1%F5%DB%FC%F1%FD%E0%E0%F7%F1%E6%B0%A8%B0%DB%FC%F1%FD%E0%E0%F7%F1%E6%FD%B0%EF%EF

0 1 2 3 4

Su navegador no es compatible con esta herramienta.

Resolución de problemas con números naturales

Resuelve en tu cuaderno los siguientes problemas con números naturales.

Para resolver un problema, se debe leer varias veces el enunciado hasta que se entienda muy bien cuáles son los datos, las preguntas y las relaciones.

En los problemas de geometría se debe hacer, si es posible, un dibujo sobre el que se anotarán los datos y la pregunta o preguntas realizadas.

De igual forma, en los problemas numéricos se anotarán los datos y la pregunta o preguntas realizadas.

Este procedimiento se puede sintetizar en los siguientes pasos:

Ed. Bruño. *Esquema Resolución de Problemas* (CC BY-NC-SA)

RELACIÓN DE PROBLEMAS A RESOLVER:

1) Una empresaria compra 10 cajas de refrescos, con 12 botellas cada una, y paga 6 € por cada caja. Si vende cada botella de refresco a 2 €, ¿cuánto ganará al vender todas las botellas? (Sol. Gana 180 €)

2) Si 8 máquinas producen 1.344 piezas, ¿cuántas piezas se obtendrán en una fábrica que tiene 65 máquinas iguales trabajando? (Sol. Se obtendrán 10.920 piezas)

3) Ernesto tiene en el banco 230 € ahorrados. Por su cumpleaños le dan 52 € y se compra 3 libros a 12 € cada libro. ¿Cuánto dinero tiene en total? (Sol. En total tiene 246 €)

4) Un almacenista compra 500 cajas de tomates, de 10 kg cada caja, por 4.500 €, y el transporte le cuesta 600 €. Durante el trayecto se caen unas cuantas cajas y se estropean 500 kg de tomates. ¿A cuánto debe vender el kilo para ganar 3.900 €? (Sol. Debe vender a 2 €/kg)

5) En España con una población de 47. 394. 223 habitantes se produjo una emisión de CO2 de 215 millones de toneladas (megatoneladas). Redondea la población al orden decimal de las unidades de millón y calcula cuál fue la emisión de CO2 en toneladas per cápita. (Sol. Se emitieron 4,57 t por persona)

Si el año anterior había 46. 937. 060 de habitantes y la emisión de CO2 fue de 5,5 t per cápita, rendondea la población a la unidad de millón y calcula cuál fue la emisión total de CO2 en megatoneladas. (Sol. 258,5 Mt)

Obra publicada con Licencia Creative Commons Reconocimiento Compartir igual 4.0