{"id":115292,"date":"2020-01-29T18:20:42","date_gmt":"2020-01-29T17:20:42","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/aritmetica\/operaciones-naturales.html"},"modified":"2024-05-27T17:41:35","modified_gmt":"2024-05-27T15:41:35","slug":"operaciones-naturales","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\/operaciones-naturales.html","title":{"rendered":"Operaciones con n\u00fameros naturales"},"content":{"rendered":"

\n

Suma o adici\u00f3n de n\u00fameros naturales<\/h2>\n

a + b = c<\/strong><\/h3>\n
Los términos de la suma<\/strong>, a<\/strong> y b<\/strong>, se llaman sumandos<\/strong><\/span> y el resultado, c<\/strong>, suma<\/strong><\/span>.<\/p>\n
Propiedades de la suma<\/h3>\n
1.<\/h2>\n
Interna<\/strong>: a + b $\"Explicaciones$ $\"Explicaciones$ <\/strong><\/p>\n
<\/p>\n
2. <\/h2>\n
Asociativa<\/strong>: (a + b) + c = a + (b + c)<\/strong><\/p>\n
(2 + 3) + 5 = 2 + (3 + 5)<\/p>\n
5 + 5 = 2 + 8 <\/p>\n
10 = 10 <\/p>\n
<\/p>\n
3.<\/h2>\n
Conmutativa<\/strong>: a + b = b + a <\/strong><\/p>\n
2 + 5 = 5 + 2<\/p>\n
7 = 7<\/p>\n
<\/p>\n
4. <\/h2>\n
Elemento neutro<\/strong>: a + 0 = a <\/strong>\n <\/p>\n
3 + 0 = 3<\/p>\n
a - b<\/span> = c<\/span><\/strong><\/h3>\n
Los términos que intervienen en una resta<\/strong> se llaman: a<\/strong>, minuendo<\/span><\/strong> y b<\/strong>, sustraendo<\/span><\/strong>. Al resultado, c<\/strong>, lo llamamos diferencia<\/span><\/strong>.<\/p>\n
Propiedades de la resta<\/h3>\n
<\/p>\n
1. <\/h2>\n
No es una operación interna<\/strong><\/p>\n
2 \u2212 5 $\"Explicaciones$ $\"Explicaciones$ <\/p>\n
<\/p>\n
2. <\/h2>\n
No es Conmutativa<\/strong><\/p>\n
5 \u2212\t2 ≠ 2 \u2212 5<\/p>\n
a · b = c<\/span><\/strong><\/h3>\n
Los términos a<\/strong> y b<\/strong> se llaman factores<\/span><\/strong> y el resultado, c<\/strong>, producto<\/span>.<\/strong><\/p>\n
Propiedades de la multiplicaci\u00f3n<\/h3>\n
<\/p>\n
1. <\/h2>\n
Interna<\/strong>: a · b <\/strong> $\"Explicaciones$ $\"Explicaciones$ <\/p>\n
<\/p>\n
2. <\/h2>\n
Asociativa<\/strong>: (a · b) · c = a · (b · c)<\/strong><\/p>\n
(2 · 3) · 5 = 2· (3 · 5)<\/p>\n
6 · 5 = 2 · 15<\/p>\n
30 = 30<\/p>\n
<\/p>\n
3. <\/h2>\n
Conmutativa<\/strong>: a · b = b · a <\/strong><\/p>\n
2 · 5 = 5 · 2 <\/p>\n
10 = 10 <\/p>\n
<\/p>\n
4. <\/h2>\n
Elemento neutro<\/strong>: a · 1 = a <\/strong><\/p>\n
3 · 1 = 3<\/p>\n
<\/p>\n
5. <\/h2>\n
Distributiva<\/strong>: a · (b + c) = a · b + a · c<\/strong><\/p>\n
2 · (3 + 5) = 2 · 3 + 2 · 5<\/p>\n
2 · 8 = 6 + 10<\/p>\n
16 = 16<\/p>\n
<\/p>\n
6. <\/h2>\n
Sacar factor común<\/strong>: a · b + a · c = a · (b + c)<\/strong><\/p>\n
2 · 3 + 2 · 5 = 2 · (3 + 5)<\/p>\n
6 + 10 = 2 · 8<\/p>\n
16 = 16<\/p>\n
D : d<\/span> = c<\/span><\/strong><\/h3>\n
Los términos que intervienen en un divisi\u00f3n<\/strong> se llaman, D<\/strong>, dividendo<\/span><\/strong> y d<\/strong> divisor<\/span><\/strong>. Al resultado, c<\/strong>, lo llamamos cociente<\/span><\/strong>.<\/p>\n
Propiedades de la divisi\u00f3n <\/h3>\n
<\/p>\n
1.<\/h2>\n
División exacta<\/span><\/strong> <\/p>\n
$\"Explicaciones$ 15 = 5 \u00b7 3 <\/strong><\/p>\n
<\/p>\n
2. <\/h2>\n
División entera<\/span><\/strong><\/p>\n
$\"Explicaciones$ 17 = 5 \u00b7 3 + 2 <\/strong><\/p>\n
<\/p>\n
3. <\/h2>\n
No es una operación interna<\/strong><\/p>\n
2 : 6 $\"Explicaciones$ $\"Explicaciones$ <\/p>\n
<\/p>\n
4. <\/h2>\n
No es Conmutativo<\/strong>.<\/p>\n
6 : 2 ≠ 2 : 6<\/p>\n
<\/p>\n
5. <\/h2>\n
Cero dividido entre cualquier número da cero.<\/strong><\/p>\n
0 : 5 = 0<\/p>\n
<\/p>\n
6. <\/h2>\n
No se puede dividir por 0.<\/strong><\/p>\n
Propiedades de las potencias<\/h3>\n
<\/p>\n
1.<\/h2>\n
<\/strong>a^{0<\/sup> = 1 <\/strong><\/p>\n}
<\/p>\n
2. <\/h2>\n
<\/strong>a^{1<\/sup> = a<\/strong><\/p>\n}
<\/p>\n
3. <\/h2>\n
<\/strong>Producto de potencias con la misma base<\/strong>: a^{m<\/sup> · a ^{n <\/sup> = a^{m+n<\/sup><\/strong><\/p>\n}}}
2^{5 <\/sup> · 2^{2 <\/sup> = 2^{5+2 <\/sup> = 2^{7<\/sup><\/p>\n}}}}
<\/p>\n
4. <\/h2>\n
<\/strong>Cocointe de potencias con la misma base<\/strong>: a^{m <\/sup> : a ^{n <\/sup> = a^{m - n<\/sup><\/strong><\/p>\n}}}
2^{5 <\/sup> : 2^{2 <\/sup> = 2^{5 - 2 <\/sup>= 2^{3<\/sup> <\/p>\n}}}}
<\/p>\n
5. <\/h2>\n
<\/strong>Potencia de una potencia<\/strong>: (a^{m<\/sup>)^{n<\/sup> = a^{m · n <\/sup><\/strong> <\/p>\n}}}
(2^{5<\/sup>)^{3<\/sup> = 2^{15<\/sup> <\/p>\n}}}
<\/p>\n
6. <\/h2>\n
Producto de potencias con el mismo exponente<\/strong>: a^{n <\/sup> · b ^{n <\/sup> = (a · b) ^{n<\/sup><\/strong><\/p>\n}}}
2^{3 <\/sup> · 4^{3 <\/sup> = 8^{3<\/sup><\/p>\n}}}
<\/p>\n
7. <\/h2>\n
Cociente de potencias con el mismo exponente<\/strong>: a^{n <\/sup> : b^{n <\/sup> = (a : b)^{n<\/sup><\/strong><\/p>\n}}}
6^{3 <\/sup> : 3^{3 <\/sup> = 2^{3<\/sup><\/p>\n}}}
Propiedades de las ra\u00edces <\/h3>\n
<\/p>\n
1.<\/h2>\n
Ra\u00edz exacta<\/span><\/strong>: Radicando= (Raíz)^{2<\/sup><\/strong><\/span> <\/p>\n}
$\"Explicaciones$ <\/p>\n
<\/p>\n
2. <\/h2>\n
Ra\u00edz entera<\/span><\/strong>: Radicando= (Raíz)^{2<\/sup> + Resto <\/strong><\/span><\/p>\n}
$\"Explicaciones$ <\/p>\n
Prioridades en las operaciones<\/h3>\n
1\u00ba.<\/h2>\n
Efectuar las operaciones entre par\u00e9ntesis, corchetes y llaves..<\/strong> <\/p>\n
2\u00ba.<\/h2>\n
Calcular las potencias y ra\u00edces<\/strong>.<\/p>\n
3\u00ba.<\/h2>\n
Efectuar los productos<\/strong> y cocientes<\/strong>.<\/p>\n
4\u00ba.<\/h2>\n
Realizar las sumas<\/strong> y restas<\/strong>. <\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"
Suma o adici\u00f3n de n\u00fameros naturales a + b = c Los términos de la suma, a y b, se llaman sumandos y el resultado, c, suma. Propiedades de la suma 1. Interna: a + b 2. Asociativa: (a + b) + c = a + (b + c) (2 + 3) + 5 = […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[377],"tags":[371],"class_list":["post-115292","post","type-post","status-publish","format-standard","hentry","category-aritmetica","tag-o"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["Aritm\u00e9tica<\/a>"],"unlinked":["Aritm\u00e9tica<\/span>"]},"tags":{"linked":["o<\/a>"],"unlinked":["o<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 2 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 27 mayo 2024"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 20 min","modified":"Actualizado el 27 mayo 2024 17 h 41 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=115292"}],"version-history":[{"count":1,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115292\/revisions"}],"predecessor-version":[{"id":136029,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/115292\/revisions\/136029"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=115292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=115292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=115292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}