tag:blogger.com,1999:blog-28835065860708281482024-03-14T07:46:12.686-07:00NUMEROS ENTEROSUnknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2883506586070828148.post-33038443509712420732012-05-27T15:49:00.002-07:002012-05-27T15:51:40.564-07:00NUMEROS ENTEROS<br />
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 14pt;">LOS NÚMEROS ENTEROS</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El conjunto de los <b>números enteros
están formados por los números positivos, los negativos y el cero. Los enteros aparecen
en muchas situaciones </b>de nuestro alrededor:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">temperaturas, fechas, dinero y
deudas, ascensores, alturas y profundidades ...</span></div>
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<b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">OBJETIVOS</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Aprenderás a:</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Utilizar
números enteros en distintos contextos.</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Representar
y ordenar números enteros. </span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Hallar
el valor absoluto y el opuesto de un número entero.</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Sumar,
restar, multiplicar, dividir, realizar potencias y extraer raíces cuadradas de números enteros.</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Operar
con números enteros respetando la jerarquía de las operaciones</span></div>
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<b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">ANTES DE EMPEZAR</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKHzwRo6xSHWpQEkSHbHXZXGcqPMnG6ZxrzOpRVVqoJFd102nOqm0oOVwO2fqk3E-ah3DNti1uaukYEXfufm_HE0rZb-dJWEgktqUdCo9IYAv0D2QSWfUmxK_DFEwBwNR2WX7Q5nbwaIw3/s1600/EN01.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKHzwRo6xSHWpQEkSHbHXZXGcqPMnG6ZxrzOpRVVqoJFd102nOqm0oOVwO2fqk3E-ah3DNti1uaukYEXfufm_HE0rZb-dJWEgktqUdCo9IYAv0D2QSWfUmxK_DFEwBwNR2WX7Q5nbwaIw3/s1600/EN01.jpg" /></a><b><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Sabes el resultado de esta resta?</span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Aunque resulte extraño costó muchos años</span><b><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;"> </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">admitir que se podía realizar.</span><b><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Parece que chinos e hindúes utilizaban cantidades
negativas desde el siglo V.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Pero no fueron admitidos en Occidente hasta muchos siglos
más tarde.</span></div>
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<b><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Sabes cómo llamaban a los números
negativos?</span></b></div>
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<span lang="ES-TRAD" style="font-family: "Verdana","sans-serif"; font-size: 12pt;">Números ficticios, absurdos, raíces falsas y números deudos. Algún
matemático llegó incluso a decir que no deberían haber sido admitidos y que
deberían eliminarse.</span><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNuw8f8svlcykm7yvypPoY87i1w4wkr0a3XXnPZSA5dGTKdy7ivyTcNuQuulnSUTKySEN1Rhr8FgwM-wmZNYGOnxY7bVIa4YC75adBtgVpFIymykDFTVjNEba4Hxi7jn9XfY6dID0PMeNI/s1600/EN02.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNuw8f8svlcykm7yvypPoY87i1w4wkr0a3XXnPZSA5dGTKdy7ivyTcNuQuulnSUTKySEN1Rhr8FgwM-wmZNYGOnxY7bVIa4YC75adBtgVpFIymykDFTVjNEba4Hxi7jn9XfY6dID0PMeNI/s1600/EN02.jpg" /></a><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">INTRODUCCIÓN</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">En la vida real hay situaciones en las que los números naturales
no son suficientes.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Por ejemplo: si tienes 10 euros y debes 15 euros ¿De cuánto
dispones?. Observa a la derecha distintas situaciones en las que se necesitan
números enteros.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Los números <b>enteros son una ampliación de los naturales:</b></span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Los naturales
se consideran enteros positivos (se escriben con el signo +)</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Los enteros
negativos van precedidos del signo -.</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El cero es un
entero pero no es ni negativo ni positivo.</span></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">LA
RECTA NUMÉRICA</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Los números enteros pueden ordenarse
de menor a mayor en la recta numérica. Debemos trazar una recta y pintar el
cero en el centro Dividir la recta en segmentos iguales Colocar los números
positivos a partir del cero a la derecha y los números negativos a partir del
cero a la izquierda.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span><b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;"></span><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">ORDENAR
Y COMPARAR NÚMEROS ENTEROS</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Cuanto más a la derecha esté un número situado en la recta
numérica mayor es. Cuanto más a la izquierda esté situado menor es. </span></div>
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<b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;">¿ Cuál
es el valor de A y de B ?</span></b></div>
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<b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;"></span></b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6U5ixuX5Mbq3sYDHlhoulETbyE4iun4YHOLz1x4Vmv36g5A8RHSOFiFqR1wtDRNmsfW1XxpGqMjL00Opb0T-_4RZ7xiqQ-d_YAHphQkoyuO7tkSz_4lYCvXis43kL5DI9sGQAEhlIeMma/s1600/EN05.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6U5ixuX5Mbq3sYDHlhoulETbyE4iun4YHOLz1x4Vmv36g5A8RHSOFiFqR1wtDRNmsfW1XxpGqMjL00Opb0T-_4RZ7xiqQ-d_YAHphQkoyuO7tkSz_4lYCvXis43kL5DI9sGQAEhlIeMma/s1600/EN05.jpg" /></a></div>
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<b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;"> </span></b><b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;">¿Cuál
es menor? ¿Cuál es mayor? </span></b><b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;"></span></b><b><span lang="ES-TRAD" style="color: #666666; font-family: "Arial","sans-serif"; font-size: 12pt;"> </span></b></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">VALOR
ABSOLUTO</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿A qué distancia se encuentra –3 y cero?</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿A qué distancia se encuentra +7 de cero?</span></div>
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<i><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El valor absoluto es una distancia
por lo que no puede ser negativo.</span></i></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">OPUESTO
DE UN NÚMERO ENTERO</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Lo contrario de deber es tener.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Lo contrario de 4º C es 4º bajo cero.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Lo contrario de 5 m de altura es 5 m bajo el nivel del mar
etc.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Si hablamos de dinero ¿cómo están relacionadas
las cantidades +4 y –4?</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">EJERCICIOS </span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">1. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Escribe el número que mejor representa la situación que se
plantea:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) Bajamos al sótano 3</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">b) Nació en el año 234 antes de Cristo</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">c) El avión vuela a 2455 m de altura</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">d) El termómetro marcaba 5º C bajo cero</span></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">2. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Cuál
es el valor de A y de B?</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) </span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"> b) </span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">3. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Escribe
el signo < o > según convenga:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) –2 -6 b) –2 +4 c) +5 +12 d) +4 -8</span></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">4. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ordena
de menor a mayor</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) +6, -5, -10, +12 b) +4, -20, -7, -4</span></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">5. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Completa
adecuadamente</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) |-5| = b) |+7| = c) op(+6)= d) op(-4)=</span></div>
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<b><u><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">SUMA Y DIFERENCIA DE ENTEROS</span></u></b></div>
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<b><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">Suma de dos enteros</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Qué significan las siguientes expresiones?</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+6 +3 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+9</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">tienes 6 y te dan 3 => <b>tienes 9</b>.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><b><span lang="ES-TRAD" style="color: #ef0000; font-family: "Verdana","sans-serif"; font-size: 12pt;">-7 -5 = -12</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">debes 7 y gastas 5 => acumulas una <b>deuda de 12. </b></span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><b><span lang="ES-TRAD" style="color: #ef0000; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+8 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">tienes 8 pero debes 6 => <b>tienes 2.</b></span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El dinero supera las deudas</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><b><span lang="ES-TRAD" style="color: #ef0000; font-family: "Verdana","sans-serif"; font-size: 12pt;">-5 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: #ef0000; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">debes 5 y tienes 3 => <b>debes 2.</b></span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Las deudas superan el dinero.</span></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">SUMA
DE TRES O MÁS ENTEROS</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Para sumar 3 ó más enteros tenemos dos métodos:</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1) </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Agrupar
los dos primeros sumandos y sumar al resultado el tercer sumando</span></div>
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<b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+6 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-4 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+1</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">En el caso de 4 sumandos se puede agrupar de dos en dos:</span></div>
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<b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+6 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-4 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">=
+2 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+1 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= +3</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2) </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Sumar
los positivos por un lado (tener) y los negativos (deber) por el otro y
finalmente hallar el resultado</span></div>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;"> deber </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">tener</span></b></div>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-7 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+8 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-5 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-12 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+8 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-4</span></b></div>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;"> deber </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">tener</span></b></div>
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<b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+6 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-4 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+9 </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">=
+3</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Qué significan las expresiones?</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">+(+3) +(-3) -(+3) -(-3)</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"> ¿</span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">Debo </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">o </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">tengo</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">?</span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">+(+a) </span></b><b><span lang="ES-TRAD" style="color: #3365ff; font-family: "Verdana","sans-serif"; font-size: 12pt;">= +a </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">-(-a
) = </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+a</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">+(-a ) = </span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">-a </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">-(+a) = </span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">-a</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Si los dos signos son iguales el resultado </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">positivo</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Si los dos signos son distintos el resultado es </span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">negativo</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ejemplos: +(+2) =+2 -(-2) = +2</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">- (+2) = -2 +(-2) = -2</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿ Cuál es el resultado? Eliminar paréntesis Operar</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+3) + (-5) = </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">– 5 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= -2</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-2) + (+4) = </span><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+ 4
</span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= +2</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+1) - (+7) = </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+1 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">– 7 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= -6</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+2) - (-6) = </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2 + 6 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">=
+8</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-2) - (+6) = </span><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 - 6 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">=
-8</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Lo anterior es válido si hay tres ó más enteros, fíjate en
los ejemplos </span></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">EXPRESIONES
SENCILLAS CON PARÉNTESIS</span></u></b></div>
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<br /></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El signo más (+) puede indicar suma o
que el Nº es positivo.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">El signo menos (-) puede indicar
resta o que el Nº es negativo.</span></div>
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<br /></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Cómo escribimos "<b><i>sumar </i></b>al
5 el Nº </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">"?</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">No es correcto escribir 5 <b>+ </b></span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">, lo correcto es 5<b>+</b>(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Cómo escribir "<b><i>restar </i></b>al
6 el nº </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">"?</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">No es correcto 6 <b>- </b></span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">lo correcto es 5 <b>- </b>(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">No podemos escribir dos signos
seguidos</span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">, debemos separarlos mediante un paréntesis</span></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">SUMA Y
DIFERENCIA DE ENTEROS CON PARÉNTESIS</span></u></b></div>
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<br /></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Cuando se presenten ejercicios del tipo:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">( -5 ) + ( -2
) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">( +3 ) - ( -7
) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Deberemos</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1º) Eliminar los paréntesis</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2º) Operar adecuadamente los nº resultantes</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Recuerda que: + (+a) = +a - (+a) = -a</span></div>
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<br /></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">+ (-a) = -a - (-a) = +a</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+2) - (+6) + (-5) = </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">- 6
- 5 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= -9</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-3) + (-5) - (-7) = </span><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">-3 </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">– 5 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+ 7
</span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= -5</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-2) – (-5) + (-3) – (-2) = </span><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+5 </span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">–3
</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2 </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= +2</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-3) + (-4) – (-3) + (-1) = </span><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">-3 –4 </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3 </span></b><b><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">–1
</span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">= -5</span></div>
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<br /></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">EJERCICIOS</span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">6. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
las siguientes sumas de números enteros</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) +7 +4 = b) –5 –4 = c) +8 –2 = d) –5 +9 =</span></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">7. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
la siguientes sumas de números enteros usando el método de agrupar</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) –4 + 5 –3 = b ) +3 –5 +7 = c) –3 + 5 –8 = d) +4 – 7 –8
=</span></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">8. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
la siguientes sumas de números enteros usando el método de tener y deber</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) –4 + 5 –3 = b ) +3 –5 +7 = c) –3 + 5 –8 = d) +4 – 7 –8
=</span></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">9. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Escribe
el resultado</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) + (+3) = b) – (+4)= c) – (-5)= d) + (-2) =</span></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">10. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
las siguientes sumas y diferencias de números enteros</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) +(+3) + (-5) =</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">b) –(+4) – (+6) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">c) – (-5) + (+7) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">d) -(+3) + (+1) – (-4) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">e) -(+2) - (+1) – (+5) =</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">f) -(+2) + (-1) + (-4) – (-5)=</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">g) -(+1) - (+3) - (-4) – (-5)=</span></div>
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<br /></div>
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<br /></div>
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<b><u><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">PRODUCTO Y DIVISIÓN DE ENTEROS</span></u></b></div>
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<br /></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">PRODUCTO
DE ENTEROS</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Para multiplicar enteros debemos:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1º) Multiplicar los nº sin signo</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2º) Aplicar la regla de los signos</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ejemplos:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+4</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)·(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">+12</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhleCTn0KL9uZD_n2o0OOx5W9JO0B0tHXL36kU6DZeYY5Iy73Ihqlt3vIIHRyZ8hebvZ1VyZvVlutX37z-XFi6sNR2Q9R45TgqBkSWNPzWwmW6kanq9DlrShgYBep4QdSpn12E-D7Y5OcUX/s1600/EN16.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhleCTn0KL9uZD_n2o0OOx5W9JO0B0tHXL36kU6DZeYY5Iy73Ihqlt3vIIHRyZ8hebvZ1VyZvVlutX37z-XFi6sNR2Q9R45TgqBkSWNPzWwmW6kanq9DlrShgYBep4QdSpn12E-D7Y5OcUX/s1600/EN16.jpg" /></a></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)·(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-5 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+10</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+4</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)·(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-6 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)·(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+4</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-24</span></div>
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<br /></div>
<ul style="margin-top: 0cm;" type="disc">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none;"><i><span lang="ES-TRAD" style="font-family: "Verdana","sans-serif"; font-size: 12pt;">Juan
ahorra 6 al mes, ¿cuánto ahorrará al cabo de 4 meses?</span></i></li>
</ul>
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<b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+6)·(+4)
=+24 </span></b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">ahorrará al cabo de 4 meses.</span><i><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></i></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<ul style="margin-top: 0cm;" type="disc">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none;"><i><span lang="ES-TRAD" style="font-family: "Verdana","sans-serif"; font-size: 12pt;">Ana gasta
5 al mes. ¿Cuánto gastará al cabo de 3 meses?</span></i></li>
</ul>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-5)·</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">(+3) </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">=-15 </span></b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">gastará al cabo de 3 meses.</span><i><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></i></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<ul style="margin-top: 0cm;" type="disc">
<li class="MsoNormal" style="color: black; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; text-autospace: none;"><i><span lang="ES-TRAD" style="font-family: "Verdana","sans-serif"; font-size: 12pt;">Luis
gasta 7 al mes en CD. Deja de comprar durante 2 meses. ¿Cuánto ha
ahorrado?</span></i></li>
</ul>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">(-7)·(-2)
</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">=+14 </span></b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">ahorrará</span><i><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"> </span></i><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">al cabo de 2 meses.</span></div>
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<br /></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">DIVISIÓN
DE ENTEROS</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Para dividir enteros debemos:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1º) Dividir los nº sin signo 8 – 9</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2º) Aplicar la regla de los signos</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ejemplos:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpfFftBVz94rIk2v5PtdDFq-wIxT2-LCvhZfoJTOMHljtwYriI03WgHz6fRW-GBvz0MpNLWmMwfWU9f_sfAFNJF5BU1BiKaJaqlOU64kZCKrWdZP4xu_SYgyvZugAkMje4s2luU2AuJxQP/s1600/EN17.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpfFftBVz94rIk2v5PtdDFq-wIxT2-LCvhZfoJTOMHljtwYriI03WgHz6fRW-GBvz0MpNLWmMwfWU9f_sfAFNJF5BU1BiKaJaqlOU64kZCKrWdZP4xu_SYgyvZugAkMje4s2luU2AuJxQP/s1600/EN17.jpg" /></a></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+24</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">):(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+3</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+8</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-20 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">):(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-5 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+4</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+14</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">):(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-7</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-16 </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">):(</span><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)
= </span><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Qué número multiplicado </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">por +6 +30?</span></div>
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<br />
<br />
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<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Qué número multiplicado </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">por -5 da +15?</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1byGmHDXFhEz4Hg_ILC8tMt3BtKJLcBdGEKigC7EdDow22YpBvx81iaIzCZb-LelKzx1BciaHptK6Pg_4laISN3bTrcRFGyDrNBCimlqVM4q9F4J6HE9rdPINUlSJzvUFUBi17B0EEEi6/s1600/EN19.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1byGmHDXFhEz4Hg_ILC8tMt3BtKJLcBdGEKigC7EdDow22YpBvx81iaIzCZb-LelKzx1BciaHptK6Pg_4laISN3bTrcRFGyDrNBCimlqVM4q9F4J6HE9rdPINUlSJzvUFUBi17B0EEEi6/s1600/EN19.jpg" /></a><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">¿Qué número multiplicado </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">por -7 da -21?</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWQBGV1F-PlXsWGz-Qj9AbiaPtGmWk7Jm5GG6wWQmK3Ubb7qRF5p_oirBPFwynu6q4k1G-hqwo4hNfdHQM_blu_WplTFkqixKiuPDQFdnjVf2NzdV9lQncSTAP2eDRnKmEBENVhqBNzx4j/s1600/EN20.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWQBGV1F-PlXsWGz-Qj9AbiaPtGmWk7Jm5GG6wWQmK3Ubb7qRF5p_oirBPFwynu6q4k1G-hqwo4hNfdHQM_blu_WplTFkqixKiuPDQFdnjVf2NzdV9lQncSTAP2eDRnKmEBENVhqBNzx4j/s1600/EN20.jpg" /></a><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<br /></div>
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<br /></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">EJERCICIOS</span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">11. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
los siguientes productos y divisiones de números enteros</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) (+4)·(+3)= b)
(+5)·(-2)= c) (-4)·(-5)= d) (-3)·(+7)=</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-layout-grid-align: none; text-autospace: none;">
<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">e) (+24):(+3)= f)
(+15):(-3)= g) (-14):(-2)= h) (-30):(+6)=</span></div>
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<b><u><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">POTENCIA Y RAÍZ CUADRADA</span></u></b><u><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;"></span></u></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">POTENCIAS
DE ENTEROS</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Según se trate de un número positivo
o negativo, tenemos los siguientes casos:</span></div>
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<b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;"> Base positiva</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)3 = (+2)·(+2)·(+2) = </span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+8</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+2</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)4 =(+2)·(+2)·(+2)·(+2)=</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+16</span></b></div>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">Base negativa </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">exponente par</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)3 = (-2)·(-2)·(-2) = </span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-8</span></b></div>
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<b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">Base negativa </span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">exponente impar</span></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">(</span></b><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">-2</span></b><b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">)4 =(-2)·(-2)·(-2)·(-2)=</span></b><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">+16</span></b></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">RAÍZ
CUADRADA DE UN NÚMERO ENTERO</span></u></b></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Raíz cuadrada
de un número </span><b><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;">positivo</span></b><b><span lang="ES-TRAD" style="color: #810000; font-family: "Verdana","sans-serif"; font-size: 12pt;">.</span></b></div>
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<span style="height: 105px; margin-left: 420px; margin-top: 1px; position: absolute; width: 183px; z-index: 10;"> </span><span style="height: 105px; margin-left: 420px; margin-top: 1px; position: absolute; width: 183px; z-index: 10;"> </span><span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;"></span></div>
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<span style="height: 105px; margin-left: 420px; margin-top: 1px; position: absolute; width: 183px; z-index: 10;"> </span><span style="height: 105px; margin-left: 420px; margin-top: 1px; position: absolute; width: 183px; z-index: 10;"> </span><span style="height: 105px; margin-left: 420px; margin-top: 1px; position: absolute; width: 183px; z-index: 10;"> </span><span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;"><br /></span></div>
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<span style="height: 106px; margin-left: 420px; margin-top: 18px; position: absolute; width: 183px; z-index: 11;"></span><span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;"></span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Raíz cuadrada de un número </span><b><span lang="ES-TRAD" style="color: red; font-family: "Verdana","sans-serif"; font-size: 12pt;">negativo</span></b></div>
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<b><i style="mso-bidi-font-style: normal;"><span lang="ES-TRAD" style="color: blue; font-family: "Verdana","sans-serif"; font-size: 12pt;"><br /></span></i></b></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">EJERCICIOS</span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">12. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Calcula
las siguientes potencias y raíces cuadradas</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) (+3)2 = b) (-5)3 = c)
(-3)4 = d) (-3)5 = e) (-2)4 = f)
</span><span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">−</span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">16= g) 9= h) </span><span lang="ES-TRAD" style="color: black; font-family: SymbolMT; font-size: 12pt;">− </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">9 =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;"> i) 25 = j) 16</span></div>
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<b><u><span lang="ES-TRAD" style="color: #ff6500; font-family: "Verdana","sans-serif"; font-size: 12pt;">OPERACIONES COMBINADAS</span></u></b></div>
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<b><u><span lang="ES-TRAD" style="color: #000081; font-family: "Verdana","sans-serif"; font-size: 12pt;">JERARQUÍA
DE OPERACIONES</span></u></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Observa que hay dos tipos de
paréntesis:</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Paréntesis
de tipo I: en ellos hay operaciones</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Por ejemplo: 3+4-(2+3·5) =</span></div>
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<span lang="ES-TRAD" style="color: #ff6500; font-family: SymbolMT; font-size: 12pt;">• </span><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Paréntesis
de tipo II: sirven para separar signos.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ejemplo: -3- (-4) + (-2) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Los primeros deben operarse en primer
lugar y los segundos deben eliminarse en el momento oportuno.</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Para realizar operaciones con números
enteros se ha de respetar el siguiente orden:</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1ª) operar los paréntesis (tipo I)</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2º) realizar las multiplicaciones y
las divisiones</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">3º) realizar las sumas y las restas</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ej 1: +3 – (+4)·(-2) =</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1.-Multiplicar +3 – (-8) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2.-Eliminar paréntesis +3 +8 =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">3.-Sumar +11</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ej 2: +1 + (-6):(+4-7)=</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1.-Paréntesis +1 + (-6): (-3) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2.-División +1 + (+2) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">3.-Quitar paréntesis +1+2 =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">4.-Sumar +3</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Ej 3: -4 + [-3 – (-14):(+2)] =</span></b></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">1.-División paréntesis -4+[-3-(-7)]=</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">2.-Quitar paréntesis -4 +[-3+7]=</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">3.-Suma paréntesis -4 + [+4] =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">4.-Quitar paréntesis -4 +4=</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">5.-Sumar 0</span></div>
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<b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">EJERCICIOS </span></b></div>
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<b><span lang="ES-TRAD" style="color: grey; font-family: "Verdana","sans-serif"; font-size: 12pt;">13. </span></b><span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">Realiza
las siguientes operaciones</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">a) +7 + (-9)·(+5) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">b) –5 + (-6):(+6) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">c) +1-(-36):(-9-9) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">d) +1 +(+6)·(+5-6) =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">e) –6 – [+3 -(-5): (+5)] =</span></div>
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<span lang="ES-TRAD" style="color: black; font-family: "Verdana","sans-serif"; font-size: 12pt;">f) +8+ [+4 +(-7)·(-9)] =</span></div>
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