Cultura y noticias hispanas del Valle del Hudson
Les presento este mes algo de aritmética inteligente: problemas que puedes resolver sin lápiz ni papel ¡si le buscas la vuelta!
Inteligente quiere decir saber qué operaciones tienen prioridad, y usar las importantes propiedades aritméticas que menciono abajo.
Ejemplo 1: computa 4×7 + 6×7.
Explicación: las multiplicaciones se calculan primero, y luego la adición, así que piensa en esto como 4 sietes y 6 sietes. En total, hay 10 sietes, así que la respuesta es 70. Este método se aprovecha de la propiedad distributiva de la multiplicación sobre la suma. Si primero multiplicas 4×7, luego 6×7, y finalmente sumas los productos, entonces te habrás hecho la vida muy difícil.
Ejemplo 2: computa 42,5×73,9 + 73,9×57,5
Explicación: Observa que ambos productos tienen a 73,9. Ya que no importa el orden en que multiplicamos los factores, el segundo producto es lo mismo que 57,7×73,9. Igual que en el primer ejemplo, sumamos 42,5 y 57,5 para conseguir 100 y la respuesta final es 100×7,39 = 739. ¡Para nada difícil!
Ahora que viste estos dos ejemplos, estás preparada para el Juego A, un problema de aritmética mental.
Juego A: Desafío de aritmética mental
Encuentra la respuesta usando solamente tu mente. ¡Sin lápices ni calculadoras!
Computa 73×14 + 73×31 + 45×27
Juego B: ¡El KenKen te hace inteligente!
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)
Juego C: Los anillos
Instrucciones: en este juego de anillos, completa las perlas con los números 1, 2, 3, 4, 5 y 6, de tal manera que cada anillo sume el número mágico, que este mes es el 14 (el del mes pasado era el 13).
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ArkiQJgmCz2SyXywrp1AFZCU9JcRyPx2OB403OOodxHHueJ7ZEyXQ6Fd0MsgAaokySJIfDoXq+g43rupvNpv45JiGTIFQZQ6HzDUhJQgq22bYN06IMNESRMAzX6zUL+5yzXC53u12SJGUPw38SZNv2dDpVfVAJqWQC0yLQEAWCICBfeeGx2WzOZbTf77mtNdDcR7+D5shH3OZHw+FQvzasD2iICIECKpPRfD7nM3Icx5Ew6EMdz/NGoxGH9rQsS6GVLF1AQ5gcj0fP80T75zt83//hhx9YjxZUhFDj/JeLhGHI59TLeDwW/a4CAA01Jk1T3/dFO+cyn5+f/X6f0QgxvLAOgkMZJtu2TbM8aKgZx+NRhlVYNS8vL51Oh+LAcBxH9dgzXbbbLdNkdMuyjGpw0FADdrudaMPU5ePj4+HhgXw8OI5jcui0GtYyMuFMLAI0VIs0TbltxtNiNpsNBgPsMTAajUBAdWAqI0NCRaCh6yRJwigdkQNPT09NP30TjoNTh12m6Gg00j5UhC8OVIIaUbwu9rWABhHNKIpc1xUtEyLqX63R6/U06DKBMCrhpH3QGl9DZUVgi7y+vtJ9XM5o4CBEHRMZVbeUHYzy1/U+9gEaKkUbByEqTGR4Ci8Lttst9X19jbfP9IzmkKOZgxDnJjI5c5cD1As86Woi0NAF0jRVNyZdzePjY/5NmxD7FA71831amgg0dAFdHYSwbducSyMkge60SD8TgYZOkfagBi1+85vfHA4H0c1sHPv9nuKOvmYmAg19RxiGoi3Bg9VqJbqlTSSOY4qH9XUyEWjoT6Rpql9YuoyLd/gCHKBYiUUbE4GG/oRyxzUIoVVvH2jKfr+nleVoWZYGyRagoT9gyHKsyHK5FN3q5hLHMa0dNA1yrEFDWZZlaZrKX76DBbvdTnTbG039czZ6mwg0lGVKVfCgi+u6aZqKbn6jobWX7ziO6FfBBzRkVmT6nM1mI7oHTGexWFAxkbpVQUBD5k6FciouGgL44HkelaC1olmppmvI8KkQAjbvZYDK9pmiW/imawimQt8gQiQNtEykXLjadA2ZuUF2DhzvkAQqJhoOh6LfoxlGa8jAXKEy4HiHPFAxkVoXUhutoc1mI3r4S0QURaI7BPgDVEykUEFxczWUpqnogS8XEKiWCnITKRQkMldDsCI7Ac52yAZ5PpEqQSJzNQQrsnMggUg2yE00n89Fv8R1zNUQ7JGdA/tlEkJ4z4cSR/AN1VCSJKKHvIys12vRPQNcgPAErPxLM0M1FASB6CEvIxAekhPyqiCSL80M1ZD2BaexgXRqOYnjmGTjTPKlmaEa8jxP9HiXFCjJKC3b7ZZkQiTz0sxQDcFx1jKgEJrMENaxlvZqTEM1JHqwywtoSHJI7vaQNqHRRA1FUSR6sMuLtD+YACKOY5L7zuQ8a2aiho7Ho+jBLi+gIfkhDBJJGKsGDQHfAUftlYAkp1HCWLWJGoKkoWpE9w9QC5JMItkO35uoIai4WI3o/gFqsd/vtZkQgYaAU0T3D1AXksuFpCqeb5yG4jj+6aefRI90qZFtxg6UQbJr1uv1RD/+nzBIQ2EYoiOCj4+Poke61KBvdLFYyJljAhQh2TWTZ0JkhIa22+1wOMxbv9/vix7p8vLx8ZE3lGVZ0+kUZCQ52AmN8kyINNfQiYBAQ1eZTCYnzQUykpwwDLFPvUoyIdJWQxcFBBq6yrmGQEbygx2rlmRCpKGGKgSUI3qwy8vLy0tFu4GM5IQkVi3DjoRWGgrD8KqAQEPVPD09XW09y7IkL6NlINhVq2XIIdJEQ3EcN0pvn0wmose7pPT7/Zpt2Ov1ZPghBXKwJ0TCr73XQUOLxaJpiM5xHNHjXVLu7+8bteRwOJTwqKSZYE+IHMcR++Rqa2i/39dchZ0AqUMXmc1meN8x0/IRaZoeLwH1as/BnhCJjfepqqE4jkky2R8eHkQPeRkp2yarA6012vF4PBwOm83G87w6RTKXy6Xneb7vHw4HqGCLPSESG+xTUkPb7Zak8hNiNptxGNhqUSc+Xc14PMb4XY2iaLfbrVYrKm/hed7hcIiiiMW3Jz94Q0Pszr1iGmoaiq7g7e2NykevEw8PD+QNW39aFEWR7/vs7q1cLpe+75t2FS32hEjghoNKGtrv94S3NRUZDAaMvn5FwQ4MXWQ8Hpf1Y5qmQRDQmvvUwfO8IAh4fqtiwZsQCQxUK6MhwjsJzul0OtyGgRIQXg16jm3bJzvBaZrudjtR16Isl0tDZIQXNhVYMF8BDcVxjLcddhVYlxWhONPMsSwrP7UkUEBFTJBRHMd4/SXqiJnsGtputySXVVYD67Kcz89PRo3cbrd//PHH//iP/xD9it/heZ7eMWy8ue1oNBLytFJriPpC7IS//du//e1vfyt6REjBjz/+yKKFO52OzFNO3/d1TT7CLhErZF0mqYbiOKYeqiiCynplcJn9H0mSJC8LRwvbtuXPilitVrpOi/BW2ULWZTJqKI5jFnEKRC4gRJIkogeCeDabTd4gtGT08vIi+rUacDgcRHzpbMFbTAhZl0mnof1+zygYVAyXFtlsNqJHgWDOM2tIZNTpdFQ8OVx0sR5gB6r5r8vk0pDneSwcVF0lx/AJUcXwq1O56YSHh4ePjw/R74TJarXSLFSEVx+W/7pMIg1hZ39W4zjO1SPgJk+IriYZe55XMx3u4eFB/mBQNZqZCG9M8c9jlEVDJOdUy7Btu2Z+epqmMqS08Mf3/TrtU+cgsQYOQmhmIozlhWVZnB9SCg1R3xTDKA9o4B2Krus2Gm8VxS21cRBCJxPhrcs4F0ITryHqDsIuxMXzlJMM4LXSfD4/+YHVzEEIbUyEty5jWkDqHMEaousgwhrJURSJ/vj5sV6vsRuqOC3qdDrqxqSrWa1W2E0kD3j7ZZwLVIvUEPVkOfJqpIfDQfTHz4Omy7GLoGmRinvz9dFjFx/vSCbPJxSmIboOojiHXK/Xoj9+5tCqUuh5nuhXYY4G52Dx8hh5lh8SoyGKDrIsi257pWnKrhCXDNDKGA7DUPSr8MB1XdVPe+CdL+MZHhKgIYoOGg6HLDI+oyjSdf+e1irDqBQHDYJEGNv2PE918NYQxfygivp+5GgZrqY4nExYuhbZ7Xa0mk4IGNv2PLOHuGqIYp40h3zzIAhEf/w0obgDfTweRb+NAJSuaY0XHuJ2Ax0/DXmeR0VAlmVxy63SxkR0s2D0jp2V4XkerQbkD154iNsrc9IQrXPzVHblG6GBieg6yMB08xyl70HDGG7cotQ8NBTHMS0HCSkNp3TEerPZUHSQUZHpc5SOVWNkD3GLUjPXEK0aZo7jCLzfNooiFY961Dy5Wh+Tp0IIddOIMHaHuN2hyFxDVLbnBd6glJOmqULbQ67rsli9mjwVQqgbIcILzvJ5NrYaolLTXgYH5RwOB/mH4mq1YrGto0GYjAqKRojwotR8toMYagj7bgBpHYRIkkTmQwzsMlxUXJayQN2DZhgDkM/sj5WGqISlJXRQjoTTIs/z2OW2aJnPiY2iNUAworR8NstYaYj8nlWZHYRI0/THH38UPSK+ffv2bblcsl4pwE1KRRQNVGPkUjM9q5DDREPkISH5HYSwLOv+/t5xHFF1v7hdhWxmymIZJNWaBIKxWcan8BB9DZGHhETlB2GQP3On03l6evr8/OQ5ErjFSmFFdo6K6zKM+YFt2xwejLKGyLOEFHLQxbp2tm0znRytVqvD4cD5fBOkC52j4rpsu91iDEkOD0ZZQ+PxmMRBlmVxPqtBQnWn2rb98vJCq0Dqer3mb58c2CM7R8X9MryVCocHo6khPNcW4XwfACE137fT6fT7/aenp7e3t3/5l3+p84kvl0vP83zfPxwOMtTcYj2kVWS5XIruFhwwRiWHmQE1DcVxXPNSvTL43xVJCEbdkjzgF0XR8RISRhzMLOtRBwk76yoYA5NDNVhqGiKsZ8ZnX5Au0u470AUCQ2WomE6NEbpVRkOEu2MqDs4MS0Mq2tbkm7WrUbEkI0ZCH4dEajoaIklWtCxLla2xEzA0xPkWOirIfHJFLCpGqTGGKoePloKGCEu78ryHhC4YOakqaki2MyvyoOJpez01RHh2TMVhmSNnj1JH9GCXFxWroMk5hSfVEEmiEJ8ETXZgaIjkbmshpGkqerBLjej+aYyGGgrDsOkr5aiVqXgRDA0ptwKF3fpqRPdPYzTUEEZwJEe5ecE5oCFAdP80RjcNkeRMK7pDfwJoCBDdP43RTUPYm/QaLMcQoCFAdP80RisNkUyFVNwtuoj2GgrDsOYhOGOZTqdq/aZqpSHsqZDqu2NFNNbQdrtFb9fv90WPdKlB3eo4jiqnsvXREMlUSJVxWActNbRYLIrHjkBD1RQ7dzgcyt+/+mgIeyqkSmnXmmiWvrhYLM5rJHQ6HdEjXWrOu1hyGWmiIeypkDaR6RxtNHRRQDmiR7q8fHx8lDWatDLCyDeWUUPYUyE5RyAJGBfSytYInuddrRIlqtq//Ewmk+qmk1BGcv52NtMQdtq0usfoK5BzfluTPAh9lclkInq8S8rLy0udBhyNRvKsA3TQEPaF9BrkTJ+DoSEZomNhGDbqx5eXF9HjXVIeHx/rN+N4PJbhl1jOfZUGGsI+TN/r9Zi+gyhUrL44nU6bduLj46Po8S4p/X6/UUtaliW80jFGpWa5NIR9CaLwpmcEXi3qJElQ2ekgCHbfk1ekZvG02+0Wr1g47NmX0el0MNpzOBwySjJCH08YhiffVRiGeaVzjAeWS0N4H7GuU6Gs9qZhfi1Ho8uCXNdFl3MEQUB4L1Acx4QXN7EbyepSsU1WB/KASxRFh8Nhs9k0LY85mUwcx3l8fHx4eKjzqBLdzIG9T6/rVCirbJP7+/vHx0eKwd3lcrnZbDA+CM/zSOrSISBKfU7N+HQFtm03nRalaRoEwWazoVUSczabvb29DQaD+/v7suds+slhUFdDeMFpLTfIcs5vbe10Oo+Pj7SuSLyI67o1fRTHMUklliIQHjqH8HbinJrToiAI1us10zeaTCaDweB8pUk6TmpQS0MXb0mm2MTqkr9pv993HIfpV3LCcrk8HA5lV2VhR4Iu8vDwwPPVlAAvMHSRimlRkiS73Y5nOfDZbOY4Tj454rOpUktD2EXvNZ4KIXq9Xr/fF7hmcV13t9udyIjwzriLfH5+inpHCXl7e6PbvJZlnSS1JEki9momJCOJNIQ3/5QhR4YpSZL867/+q8APJQfJKMuyMAxpLRZOgOyhIoPBgEUjj0ajOI7TNJXnisqvry/CHZI6XNcQdua0KqUPMEjT1Pd90V/IKa7r/t3f/R3dgZFzf38v+v1kYTabUVyRnfD09PTv//7vol/xO/IfOXZc1xBeupBOdYVOOB6Py+VS9LdRytvbG4tB0uv1/u3f/k30y0nBbDajGHfLub+/l3lHcrVaRVHEaExd1xDeJF/LfXo5J0HnfH5+Nk3wrWA4HKLeDIJA9JtJAVqkVJclaMpgMFDiCDGjadEVDWGvyPQLTidJslqtRH8GDXh6eiIcG+cHxGWeBvLh5KZWKjLivMdKiOd5Zfuz2FzREN6KTL/g9PF4VPEOZewFWq/XuzifhQnRxaM2i8UCL0e00+kwzTJjxHK5pLtAu6IhvPw3Fe/2rkDpsffx8dHIRFePX5o8Iar4sOM4bnps+OHhQYmF2EVc16V4+LFKQ3hZi5Zl0Xo4GVDaQYiPj4+ap4fqFKPQoEGwuTrw6hdRUdpBOUEQUBllVRryPA9DQzqtyLQZcrPZrNpEw+Gw/oG1pmcp9WCz2dRsn6sp7Ho4CEHFRFUawjuWrc2KTBsHIcqyXTCK4ERRJPpteOO6btO4bFkuu04OQpCbqEpDGFsA2qzINHMQ4jxOhNJ2MdpHicQFihwOB4xWCsPwpNqhfg5CEEasSzWEt1U/Go1InkYSNL4xOa+SY1kWybw1TVNzYtWEE/x8u1nRfbE6uK5LYqJSDeEdZ9UgazFJEhX35uvjOM5wOLIp8CIAABuISURBVCRP7DJkaYaxHDtnv9/bti1zkjQ5q9UKu6FKNYRXYEiDrEW1chTxoLXBcTgcRL8Kc2htS5uwjF2v13iNU6ohjDMcGpwjM+Fb+fbtm+u6tI5Niy1GwRpaZxc0XuafgBdEu6whvIyh8XhM3F8iMedb+fbt22q1otJoaZrqOn+sv0N/tYn0XuYXwfuFu6whvMrTSm/VGxVzRdD6qdfSRLQ0nek+YTwHwwOXNYRXvk/pwJAhy7EiFJdmmkmcJNp6glFT7JymwcfLGsI4SqZ0YChJEtEdJwbsmOI5URTpYSKKDsrM2PE4p+n24mUNYSQuKh0YMvN0AoLiAUUNVmd0HaRlEmxNGi35L2uoqYPaKmcMmTltzqEb0VPaRLRi0jl6TA+xqb/kv6AhvPi0upWnTZ4KIahfV61iUJZ6XUGTp0KI+lq/oCG8/Gm6XcgNQ1KBq2GxxRkEgSq71HRL5+QYPhX61iRCdEFDGNtk6sanVfzdZgGLS2CiKJJ/gcaipGmWZWEYin4zKag5x7ygIYxtMkVrDKVpKrqbZMH3fUaNLM+VWye4rouX8lsHWOkjlstlnea6oKGT0gR1UPSSaBOORNXEdV127ZwkiWzDcrPZsJgE5e8r+v0kok45vQsaauqgtrL50/IvGXhSv/oiHpLc7zaZTD4/P5m+Kfy8FakTqKajoZNrZJQAfrJOoL5dfZEgCETZfzKZoOvbWOe4wc9bkToT7VMN4e3WM+tQhsBP1glM12UnHI9HbpsDs9nMcZz7+/v8cx0Oh+xeDX7ezrk60TZXQ+v1WnTvSAeLfesK0jQ9HA7s5g5vb2+DweC8AjdTDcHP2zlXN0BONYSRNMS0U9khumtkhNHVwFdJ0zQIgs1mQx48+vj4eHl5sW27+nY2du8CP2/nXC1XcKohjKQhFTVk+AGOMmTYakjT9Hg87na7zWbjeV61mFar1e9+97uXl5enp6d+v1//Ykh2z69K0iZnqvclKWhIxUOtMHMuQ3TP4ND0i2WnIQgMlVG93j/VEEYJahWThiB5ugy6d5PzAUNDjPZ2IXm6jOr1/qmGDMldlC2bTh5YZw+xQB4NSZsyLpzqylYUNKRiiQ/RnSIvoqLUJGB8tIw0BPHpMqrDjhQ0pFzuIhwlq4BPEiNd5PloYZZdQUW7magh2CarQIbNsqZgfLSMXlOG0yrSUtFupxrCuJ4MNKQThmiIUUBTdO9JTUUxmVMNNe1O0JBm1KzMIBWgISWo2LM3UUOQNFSN6P5pDGhICUBD3wG7qtWI7p/GYBTqAw3xBzT0HaChakT3T2NAQ0oAGvoO0FA1ovunMbAoUwLQ0HdAxn01ovunMaAhJWigIcuytNcQ7JRVABv2JIjuPalpoCFIXzQcQzQ0n89ZPIno3pOainYzUUNwRWIFhmgIDnPwp6LdTNRQBr9a5cDRVhJAQ2VUp8UaWugDzv6Uwe4GQXb0ej1JNOT7vugOlBTmJ+xV1BD8apXBuSo+FZp+sew0BAn6ZVRXxadQBFZFDUHqUBns7jJlB4aGGFV3g92PMoIgqGg3ChoajUYsepQpkDp0EanOtSZJcjwegyDYlROG4W63K95BVhN2jy26DyWluriwoTdzQOnyi4iteZYkCbomCG/JPJlM0NVAdazE7i3gytZzrt7ESeG6xF6vx65T2QFR6nOqZ86MCMPQ93263YFuK3t4eOD/xUKU+pzqQtSZybe2wudyTkVhKuokSeL7PutbvT4/P5+enk7mR0zn7xAeOufq9uuphsIwxNCQitc5QHjohKtXa1Jsef47lW9vb/1+H32urKOZcGPiCVd/3k41lMm0/cka+FyKcMgYCoJA7Fp4Mpn0+33We7twC16ROj9vFzSEkQzG6IQOa+BzKcJ0RXY8HuXJ1frtb3/L9GVhol2kzs/bBQ0ZksGYweGyAuyOkqVpKqfud7sduyQp2ADJqdPIFzQ0Ho+bakjFPXsEfC4IRntkYRjKvPJdLpeMssYhPxZRMwXkgoYwUocsy2LQlTwIgkB0T4nnaloHBtJOgs5hcZoXEtMQNS1/QUN4e/ZxHFPvSz7I/HPNB+rjMIoitbL4VqsV9QWaKhZmR/2V/gUN4e3ZK7pZlhk/f3Zdl+4IlHwhVobrutUHDpoCE6L6C94LGsqw9uwVjVJnWZamqYrDhhZ0p0JKL3Jd16WbAWfyhKjRpsdlDWFslqkbpc4UHzwk0J0K6VHmgmK03uQJUaPY/2UNYWyWqRulRqgVy6AFxSGn0y8/xWYxc8l/9RDZCZc1tFgsmmqo3W7v93tKfScAA48CUcwV0m86SctEaZqalhTium7T7NDLGtrv9xgaUjSXOseow64Y30oZ+jkIQStibdovHMapoMsayrAuLFOx/lkRo364aJ0g03iMUdw7M+cXDm+KXaohjCi16uGhzJjjHbSWY0mS6L3JSCufKE1TE4KP2FPsUg1h5FK3FQ8PIfTY7qlgPp/TqrJowtBqGm0t4z//8z/n87not2ELdrpDqYbwcqnH4zFBT8mCTps+J8xmM1STkDzPy5yFBmG4Oo7j0WjUbrcHg4HoV2EISQJaqYYyrCRG27axH0UqdP2dHwwGxc7Cnr1qHBI6hyScv91ui5Vznp6eRL8NEwjn11UaQgpvioqVGM/RcjFfdFAO3rTInFg+AiOaFsex4zjnDe44jui3oQx5qLFKQ/P5HENDqm/b52hmosfHx7Iu6/V6jY4EmpmS1+j3dbFYVOw162QiKlH8Kg3hZQ9psy7LNDJRhYNyRqNRnZGm/e5YGcvlss542+/3dXaZ9TARrZ3EKg1lWAVh27qsyxAamOjiWuwilmVNp9Pqmi0ax++vUh2FjeO40Sko1U20Xq9pHUi8oiGMw2VtjdZliDRN1+u16E7HYTab1XdQTq/XWywWF5vC5LOa38pPAsdxPJ1OMTJ+Hx8fRb8TJnRv1ryiIc/zmrZsW9kLFKtRbn/68/Oz7L7Amp14Hno0eSqEOJ8QLRYLvEUDwrbt2Wwm+rWaQb1k8BUNZVinOtpa5DGeo1BBr8lk0ul0sMdGznA4zGVk+FQIUSyYSyignIeHh4+PD9FvVovlckm3OBziuoYubjpexXEc6s8qA0mSyHPRzUVms1mdgHQj0DJNufkgI/73f/93Pp9TEVCRl5cX0W92BYrBoBOuawhvXWZZlrrVqa9yOBzknBZNJpOTi5Ipov1ZhJr8+te/ZtTC/X5fzmnRcrlkuu90XUMZ7rqsLMypB7LdPLFcLoMgwNtSqIPeBxGaQhJ0q2axWOx2O6l+5Jhe6IaopSG8dZmWgeoT/uEf/mEymYj9SlzXLX4o2+0W72ejmre3N7GvKRUvLy/UW7h4tiZNUxlyRB3H+cd//EcO46iWhvDyGNvtNru7QCUBvWa/3xeSA7JcLi/+UsVxjFGnpYJOp8P/7WTm8/OTYvO2223Hcc6DGEmSiJoZOY6DVvd8aszX0lCGm8eodJ38OhRf9v7+/uXl5fPzk8NX4nne1U3T+XxOa1pk2zaHl1ILWusyy7Kqf63TNA2CgE8O7efn5+PjY3GPlc+apq6G8M6XtVW+v+wqZZNE27Ydx2GRDLJarQ6HQ/3T3vv93rZtvI4ronq+LwuobEeORqP6OzlRFPm+z8JHn5+fLy8vZWLFHR8NqKuhOI7xGlrXnfusRkmmh4eHp6enyWRCoqTVarXZbIIgwA4T4iX4FuEzxVOLt7c3kia9OgmqIEmSIAg2mw1JnYPZbPb29vb4+Hh1Wof3kI2oq6EMN1Dd1uuIWZFGleHu7+/7/f4//dM/+b7v/ZHisn+1WqH/uF6vd7tdEASNbnqqJgxD7GjR/f09jWGrG7PZDK892yWRIDzSND0ej4fDYbfbrddr9AkV9eS6bv697Xa7p6enfr/fKKuDw4KmgYbw6jG29Z0QYdTJFRssq64+UQYEhsrACA81ralCnaYP3JZNQ1mWYQcatJwQKaehrPkp8La+BQPJaTQcUPUCsb2fYV11IZ2G8K5RbEsw/FiAoSEZPsSs4RoNMobKeHp6qtmGFFdhhGBoiEMecjMNZbg7920dt8zU1RBiu93W+T0Xnp8pLXWi1MPhUKpj3hga4vDRNtYQ3sVBbR0nRHL2aFOuHhMXPdjlZTKZVH/wEv70Ymw0yaihOI6xd381O2Wmh4YQFTISPdjlpWyzTE4BIeScwjfWUEYwIer1epKskKkg5zKbhHMZPTw8iB7sUnPSvzILCKGPhkgmRNJOBzCQc9OBHM/z8lfr9/uiR7rU5D07Go2U6Fx9NJQRTIjaGhVm1FVDiP1+7zgOaKgay7LG47FC+ShaaYhkQqRNrFpvDSH+7//+T/RIlxrlggxaaSgjmxDpcXWHCRoy6pJoDET3T2N00xDJhMiyLIXmsWWAhgDR/dMY3TSUESRVt7VYmoGGANH90xgNNZQRJFW31V+aYWhIuXKUURSJHulSI7p/GqOnhrCP3SOU3jXTKX2xAtEjXV6Kd5apgp4ayrJsNBo1fbEc27aV22vIAQ0ZjnJz20ybwxznhGFIUtxP3WpEcv6wUIdPFWQVUVFDcv52UtBQRrZ535b+iEMZhmhI8ltqBXJ+n738YGiIQwyXjoYygopo7XbbsiwVg0QYGhqNRqKfujEyXJglJ1cvR5EQObd3qWmIMFat4qlXFasvYhCGoejxLilRFInunMZgxE9U0lCWZYQ3F9u2TetJ+NDUvA8PDy8vL7vdrli9/ATf9/N6+Kxv7K1JkiSix7ukiO4ZHDAGpmIaiuOYJI2orVq4+qqGOp3OYDB4eXn5+PjA+9Bd10UXdYj94ZXqSnVJUDE+jXfNF4cHo6mhjHhp1lYqp7HsusT7+/vHx0ds9ZThuu5msxFyCGaz2dB9Fw1QMT6NNzw5PBhlDWXEu2ZtpTbOio+N5j7U7XMO8hHP+VEQBKxfSjlUDAx5ntd0MFqWxeHB6GsoI9s1Q6gy40VPe39///T0xOK26Grq3GRPhTRNOb+a5CyXSw7NTh1pN1WYaIgwobGtzhb+r371K+H3uy+XSw4yWq/XYl9TKnzfZ93gLMDYROKTYsJEQxnZ4XslTJSm6W63+81vfiN6RPwBz/MoXjZ9DqzLiqi4IstkTaHO2GkoI7jzXn4THY/H4jXh8rDZbBht86dpCvtlCEVXZBlW0hCfLSOGGspoBIlkM1Gapr7vix4IVbiuy2g3DfbLEIfDgUXzsgZvt55PhSy2GiIPEklloiiK5JwEncMieAF5jN++fXNdV5K00qbg7dbzOdvAVkMZjUwiSUykXHBktVolSUK3EeCYq6LB6Qw3k4bPszHXUEYjXI0QmE+k6HrEdV26wVSoCUvd7NzAiNVyOwLJQ0MZjXC1KBOlaar0XrXrunS3802eEKmYOZ2DcdBqPB7zeTZOGsrIijQKaZosy9I01aPoF0UTGVudWt2oUIYbn+Z2soqfhuI4Jt84Q4xGIw6RM20chKBoIsn3Chmh6AYZAuMYR5vjRTL8NJRRNZFt20wPeWrmIAQtExmYQ7Rarag0nSjwivBwezyuGsqybL/fk2/hIyzLYmdrRWPSV6EVsTatFpqiadM5GD//POt/8dZQRtVEbTbJ5hovOlzXpbXXo3TkvhFKR6Yz3MAQzyCsAA1ltE00HA4phoqUyw9qymq1ohJqTdNUlWROElQp9lABXmCI5660GA1ltE1kWRaVzyVJEhOiHpvNhryt4jh+e3vjX96EJ0rvjuXgpcvwLLAnTEMZbRO12+3xeEw4LdIvLF0G4Ue23W5RHspgMBD9KgxRPSSEwMgY6vV6PJ9QpIYyBibq9XrYcWujbsLB/p2P4/hk2+Xp6Un02zBBxft/zikrVVwN56rwgjWUMTBRG2taZGBW3nq9btpZ+STo/KsV/TaU0cNBGe5WPefjCuI1lLExUdNokZlnFOpXSovjuDrEoJOJtHFQhrUia/M6WJ8jhYYyqpmNRYbDYZ0giGlZMDk1K3jN5/M6vxN6mEgnB+GtyPjfGCiLhjJmJmrXWKOZsPFcRvWo2263jTpFdRPp5KAMd0XGp/BrEYk0hKB1Fv8Ey7LKGlf7RKFqyiZEYRhilC5uK7t3xq5qpUDwVmT8a3tJp6GMxk1nZfR6vfPYm8lTIcTJFCAMQ8Ifg36/r1Y+0XK51GNvvghexUHOW/UIGTWUZdlisaAetC42dC4jw6dCiHxCRC6gnPv7+8lkIvrNarFerzXIUTwHryt5nuHIkVRDWZbt93u8KWVNer3edDr9r//6L9GjQAr++7//m8VyWPKUIuo14eQhjmO8H3Ih1Zbl1VCWZXEc0yqWdpGHhwfRA0EW3t7e2DXy+/u76Pe7wHq9Vrei61XwKi8LWZFlkmsIwS5U9PLyInosSMT9/T2LRrZte7/fB0EgTwxuuVwyvVpSBvBWEkJWZJkSGsrKk3cJ+fz8FD0iJOLx8ZF6CzuOk6dKoHtuxZ4c5nPRtnCwr8MRdf+NGhrKGCzQYEV2wsfHB8XmLctiT9P0cDjwnxmtVisTBITAGyn8sxZzlNEQguIOGqzIzul0OlTatk7yehiGHAqnua672Wy0X4IVCcMQr9e4FcA/RzENZQRpdSd8fHywHgPKMRgMCFvVsqxGX3OapkEQUPeR67rr9ToIAi134qvB3vHkfI6siHoaQtQ85VRGp9Oh+93rAeGefc0TfGUcj8fdbud5Hl78CKlnt9sZNfc5AXsqxLmyxwmqaigjixbZtk17COsAdnjIsiy6pSGSJDkej4fDYbfb+b7vXWK32+12uyAIjsejgbOei2D/kHC7C+giCmsIgbeJJnlanUAwvuDidhggEOypkKh0oRzlNYSYTqeN1miqnDPgT7/fr9+Mw+FQ7K8oUAR7KsT/TvYTNNFQ1vA8FGQMlVEzSn3xkDAgEOypkGVZwiez+mgIsd/v6+yjiR7s8vL09HT1q51Op8I/XOAE7KkQ/+pC5+imIcR2u62Q0f39vejBLi8Vh8tAQNKCnTbdFrpPn6OnhhBlMur3+6IHu7xMJhMQkHJgZ9KJ3afP0VlDiHMZgYYqONEQCEh+8A7TIyQpOKm/hhDb7TZfPEPSUAWz2Qy1Uq/Xm8/nICDJwa4r1JZmKpSZoyFEGIbj8fiHH34QPdilZjgcwi6YKuAVvZdqKpSZpiGEUbezYiC6f4C6kESm5ZkKZaAh4BzR/QPUBftCLcuy5JkKZaAh4BzR/QPUgqQqqQy5QkVM1NDxeBQ90uXFdV3R/QNcB+861nwqJNvOA2gI+I6LJRMBqYjjmKQmsoT7D6Ah4DtAQ/JDUhZKYKXXCkzUUJqmoge7vGw2G9H9A1TheR62g9qi6wqVYaKGsiwTPdjlZbfbie4coJQwDEmKjkq1SV/EUA2tVivR411SzLm+QjniOMbeoW9LGZnOMVRDHO6EUJQoikR3DnAZwkrhAi/euIqhGoLUoTJE9wxwmfl8TuKg4XAo+g2qMFRDsFl2EdgmkxOSQxtt+XKmzzFUQxlEqS/h+77obgFO2e/3hFeEyrwcQ5irIc/zRI966ZD8N9NACDMV29IvxxDmauhwOIge9dIhuk+A7yDcGmursBxDmKuhKIpEj3q5WK/XovsE+A5CB7XbbVWCfeZqKMuy5XIpeuxLBGQMSQXh9nxb4mTFc4zWEKzLclzXhfuX5YHcQbZtS5useI7RGkqSRPTwlwU4SiYP5A6yLGu/34t+jwYYraEM0qn/yPF4FN0VQJbRcFBbylIe1ZiuIchj/AZZi9JAxUHj8Vj0ezTGdA1lkEAEwWkJiOOYioOUyBI6BzRk+oRouVyK7gHTIc8PQqgVli4CGsoysydESqS3aQwtBykXli4CGsoygydEEBUSC/l5sRw5yyrWBDT0BzabjWgnCACqCwlksVjQcpByW2MngIb+QJqmruuK1gJX4Dy9QEhuGdPMQRloqEgYhqLNwI/lcglp00KI43g0GtFykEInNioADX2HOdmMsBwTwn6/JyzcoZ+DMtDQCWmamnDeFa7fEAJhIVddHZSBhs7RvgDI29vbeDxWNMFEUeguxDRzUAYaukgQBKJdwYqPj49Op9Nut3u9nrppJmrheR6tHTEtHZSBhsrQ8uqO2Wx2f39f/KCn06noltYZ6pMgLR2UgYYq0CyTaDabPTw8nH/WvV5P6cw3aaE+CdLVQRloqBptTFTmoOL3DdEiWoRhOBwO6QqorebR+ZqAhq6ggYmuOghhWZb8N8lIThzHFPMSi2iQo1gBaOg6vu+LNgk+NR2UA2s0bBaLBcWcoBzLsvR2UAYaqomie2f5vlhThsMhyKg+2+2Wyin5c5Q+N18f0FBdoihS69CZ4zh4DspxHAfKgFSz3W5ZhIEQtm0b0v6goQakaapEZaLZbDYYDGgNBsdxTPhBbgpTAbXb7dFoZM6mAWioMYfDQeZp0WQyOUkOogIs03IWiwVTAbXNy+cCDeGQJImc06LHx0emw8O2be3DpWXEcTyfz1kEoYtYlmWg7kFD+ByPR3nOwW42mzRN6R7grhgq4/HYkLBFlmX7/Z5KvfqrmBMMOgE0REoQBGJltNlskiTJn4fFAYKKYbNYLHQNYYRhyGH6k6NxduJVQEN0CIJgtVrxtI/ruicCKkKxwGgdRqORNj6K43ixWHBTeRtytUBDdImiaLPZsA5gr1arIAiu1k5kdKSgGuQjFVcWaO4jpMX00DcJoCEmhGG42WzoLtY8zzscDmXTnzLm8znPaVGObdvj8VjyH/k4jj3PG4/H3FZeRSzLgptREKAhtiRJEgTBZrPB2FlbLpee5+12O8IL5oVMi4oMh8PpdOp5ngw/+2EYIvUwynuuCUyCioCGuJIkyfF4DMNwV8LhcDgej4TeuQjnaFEZvV4vtxKfrMjtdrtYLKbT6XA4lKQFJJ8k8gc0ZBC0LkqnCxKT4zjT6XQ+n2+32+122zS6tN/v0f84n8+n06njOJJI54TpdAqToHNAQ8bB+hQCC5CqigiJ5pAwGo1UjNzzATRkKIyqUgDn2LYNq7BqQENGM51OJVy5aEOv1zP27EsjQEOmgwoGgozoAgJqBGgIyDKQET2QgCAO3QjQEPAnQEYkwAwIG9AQcAEIYDdiOByCgEgADQGlbLdbnic8VQRKU1IBNARcIQzD6XQKk6MivV5vPp9DAIgWoCGgLp7nSZiEzRPLsmD6wwLQENAM/uV4ZGA0GsFpeHaAhgBMtPcRmvtIUhhAb0BDAAUEVu2hjhKVkjQDNATQJAzDxWLhOI5aSur1eo7jQNqhKEBDACvyAmMSHui3LEuqYmyGAxoCOLHf7z3Pm06no9GIf+XD4XA4Go2Qd6DghmyAhgBhhGGYl0ZEkybCQkK2baO/ZDqdIuNst1uY7MgPaAiQlziOt9cQ/YwABUBDAAAIBjQEAIBgQEMAAAgGNAQAgGBardb/A3I2ixr2pgZZAAAAAElFTkSuQmCC)
Juego D:
Hay varias maneras de resolver el juego de los anillos. ¿Cuántas soluciones existen exaxtamente?
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Contacta al Círculo de Matemática por email: [email protected]
Si te gustó resolver estos problemas, envíanos por favor tus soluciones o comentarios.
Correo:
La Voz / Bard College
PO Box 5000
Annandale-on-Hudson, NY 12504
[email protected]
*Japheth Wood es profesor de matemáticas en Bard College
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La Voz, Cultura y noticias hispanas del Valle de Hudson
Inteligente quiere decir saber qué operaciones tienen prioridad, y usar las importantes propiedades aritméticas que menciono abajo.
Ejemplo 1: computa 4×7 + 6×7.
Explicación: las multiplicaciones se calculan primero, y luego la adición, así que piensa en esto como 4 sietes y 6 sietes. En total, hay 10 sietes, así que la respuesta es 70. Este método se aprovecha de la propiedad distributiva de la multiplicación sobre la suma. Si primero multiplicas 4×7, luego 6×7, y finalmente sumas los productos, entonces te habrás hecho la vida muy difícil.
Ejemplo 2: computa 42,5×73,9 + 73,9×57,5
Explicación: Observa que ambos productos tienen a 73,9. Ya que no importa el orden en que multiplicamos los factores, el segundo producto es lo mismo que 57,7×73,9. Igual que en el primer ejemplo, sumamos 42,5 y 57,5 para conseguir 100 y la respuesta final es 100×7,39 = 739. ¡Para nada difícil!
Ahora que viste estos dos ejemplos, estás preparada para el Juego A, un problema de aritmética mental.
Juego A: Desafío de aritmética mental
Encuentra la respuesta usando solamente tu mente. ¡Sin lápices ni calculadoras!
Computa 73×14 + 73×31 + 45×27
Juego B: ¡El KenKen te hace inteligente!
Juego C: Los anillos
Instrucciones: en este juego de anillos, completa las perlas con los números 1, 2, 3, 4, 5 y 6, de tal manera que cada anillo sume el número mágico, que este mes es el 14 (el del mes pasado era el 13).
Juego D:
Hay varias maneras de resolver el juego de los anillos. ¿Cuántas soluciones existen exaxtamente?
Visítanos en nuestro sitio Web: http://bardmathcircle.blogspot.com/
Contacta al Círculo de Matemática por email: [email protected]
Si te gustó resolver estos problemas, envíanos por favor tus soluciones o comentarios.
Correo:
La Voz / Bard College
PO Box 5000
Annandale-on-Hudson, NY 12504
[email protected]
*Japheth Wood es profesor de matemáticas en Bard College
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La Voz, Cultura y noticias hispanas del Valle de Hudson
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