{"id":1333,"date":"2026-03-06T12:13:46","date_gmt":"2026-03-06T10:13:46","guid":{"rendered":"https:\/\/blog.edu.turku.fi\/allu\/?page_id=1333"},"modified":"2026-03-27T08:52:14","modified_gmt":"2026-03-27T06:52:14","slug":"jaollisuus-ja-jakoyhtalo","status":"publish","type":"page","link":"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/jaollisuus-ja-jakoyhtalo\/","title":{"rendered":"Jaollisuus ja jakoyht\u00e4l\u00f6"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" href=\"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/\" style=\"background-color:#d6d6ff\">Palaa takaisin<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Jaollisuus ja jakoyht\u00e4l\u00f6<\/h2>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-left\">Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#e6f3b7\">Helppo<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" style=\"background-color:#d6d6ff\">Perus<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#fcd8c8\">Vaikea<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 1. <\/strong>Meneek\u00f6 jako tasan? Jos ei, kirjoita jakoj\u00e4\u00e4nn\u00f6s.<\/h3>\n\n\n\n<p><strong>a)<\/strong> <math data-latex=\"\\frac{87}{3}\"><semantics><mfrac><mn>87<\/mn><mn>3<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{87}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>b) <\/strong><math data-latex=\"\\frac{31}{7}\"><semantics><mfrac><mn>31<\/mn><mn>7<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{31}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c)<\/strong> <math data-latex=\"\\frac{78}{9}\"><semantics><mfrac><mn>78<\/mn><mn>9<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{78}{9}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>d)<\/strong> <math data-latex=\"\\frac{98}{7}\"><semantics><mfrac><mn>98<\/mn><mn>7<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{98}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>e)<\/strong> <math data-latex=\"\\frac{543}{3}\"><semantics><mfrac><mn>543<\/mn><mn>3<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{543}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-1&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-76f8bc8c1ad1ca46f0118695b9766ad1\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-1-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-1\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-1\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-1-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a)<\/strong> <math data-latex=\"\\frac{87}{3}=29\"><semantics><mrow><mfrac><mn>87<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>29<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{87}{3}=29<\/annotation><\/semantics><\/math>, menee tasan<br><br><strong>b) <\/strong> <math data-latex=\"\\frac{31}{7}\\approx4,429\"><semantics><mrow><mfrac><mn>31<\/mn><mn>7<\/mn><\/mfrac><mo>\u2248<\/mo><mn>4,429<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{31}{7}\\approx4,429<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 3, ei mene tasan<br><br><strong>c)<\/strong> <math data-latex=\"\\frac{78}{9}\\approx8,667\"><semantics><mrow><mfrac><mn>78<\/mn><mn>9<\/mn><\/mfrac><mo>\u2248<\/mo><mn>8,667<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{78}{9}\\approx8,667<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 6, ei mene tasan<br><br><strong>d) <\/strong><math data-latex=\"\\frac{98}{7}=14\"><semantics><mrow><mfrac><mn>98<\/mn><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{98}{7}=14<\/annotation><\/semantics><\/math>, menee tasan<br><br><strong>e)<\/strong> <math data-latex=\"\\frac{543}{3}=181\"><semantics><mrow><mfrac><mn>543<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>181<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{543}{3}=181<\/annotation><\/semantics><\/math>, menee tasan<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2. <\/strong>Kirjoita jakolaskua vastaava jakoyht\u00e4l\u00f6.<\/h3>\n\n\n\n<p><strong>a)<\/strong> <math data-latex=\"\\frac{123}{11}\"><semantics><mfrac><mn>123<\/mn><mn>11<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{123}{11}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>b)<\/strong> <math data-latex=\"\\frac{98}{7}\"><semantics><mfrac><mn>98<\/mn><mn>7<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{98}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c)<\/strong> <math data-latex=\"\\frac{571}{57}\"><semantics><mfrac><mn>571<\/mn><mn>57<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{571}{57}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>d)<\/strong> <math data-latex=\"\\frac{343}{13}\"><semantics><mfrac><mn>343<\/mn><mn>13<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{343}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-2&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-76f8bc8c1ad1ca46f0118695b9766ad1\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-2-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-2\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-2\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-2-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a) <\/strong><math data-latex=\"123=11\\cdot11+2\"><semantics><mrow><mn>123<\/mn><mo>=<\/mo><mn>11<\/mn><mo>\u22c5<\/mo><mn>11<\/mn><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">123=11\\cdot11+2<\/annotation><\/semantics><\/math><br><strong>b) <\/strong><math data-latex=\"98=7\\cdot14+0\"><semantics><mrow><mn>98<\/mn><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>14<\/mn><mo>+<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">98=7\\cdot14+0<\/annotation><\/semantics><\/math><br><strong>c)<\/strong> <math data-latex=\"571=57\\cdot10+1\"><semantics><mrow><mn>571<\/mn><mo>=<\/mo><mn>57<\/mn><mo>\u22c5<\/mo><mn>10<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">571=57\\cdot10+1<\/annotation><\/semantics><\/math><br><strong>d)<\/strong> <math data-latex=\"343=13\\cdot26+5\"><semantics><mrow><mn>343<\/mn><mo>=<\/mo><mn>13<\/mn><mo>\u22c5<\/mo><mn>26<\/mn><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">343=13\\cdot26+5<\/annotation><\/semantics><\/math><br><br><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-3870768e75c932eec3615d155d7cebda\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 <\/strong>3. Kirjoita luvut jakoyht\u00e4l\u00f6n muotoon <math data-latex=\"a = bq + r\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mi>b<\/mi><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a = bq + r<\/annotation><\/semantics><\/math>, kun 0 \u2264 r &lt; b<\/p>\n\n\n\n<p style=\"font-size:18px\"><strong>a)<\/strong> <math data-latex=\"\\frac{38}{5}\"><semantics><mfrac><mn>38<\/mn><mn>5<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{38}{5}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>b)<\/strong> <math data-latex=\"\\frac{83}{9}\"><semantics><mfrac><mn>83<\/mn><mn>9<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{83}{9}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c)<\/strong> <math data-latex=\"\\frac{141}{11}\"><semantics><mfrac><mn>141<\/mn><mn>11<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{141}{11}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-3&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-76f8bc8c1ad1ca46f0118695b9766ad1\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-3-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-3\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-3\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-3-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a)<\/strong> <math data-latex=\"38 = 5 \\cdot 7 + 3\"><semantics><mrow><mn>38<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>+<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">38 = 5 \\cdot 7 + 3<\/annotation><\/semantics><\/math><br><strong>b)<\/strong> <math data-latex=\"83 = 9 \\cdot 9 + 2\"><semantics><mrow><mn>83<\/mn><mo>=<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">83 = 9 \\cdot 9 + 2<\/annotation><\/semantics><\/math><br><strong>c) <\/strong><math data-latex=\"141 = 11 \\cdot 12 + 9\"><semantics><mrow><mn>141<\/mn><mo>=<\/mo><mn>11<\/mn><mo>\u22c5<\/mo><mn>12<\/mn><mo>+<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">141 = 11 \\cdot 12 + 9<\/annotation><\/semantics><\/math><br><br><br><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 4.<\/strong> Luokassa on 25 opiskelijaa. Heid\u00e4t jaetaan 4 hengen ryhmiin ryhm\u00e4ty\u00f6t\u00e4 varten.<\/h3>\n\n\n\n<p><strong>a)<\/strong> Kuinka monta t\u00e4ytt\u00e4 ryhm\u00e4\u00e4 muodostuu?<\/p>\n\n\n\n<p><strong>b)<\/strong> Kuinka monta opiskelijaa j\u00e4\u00e4 yli?<\/p>\n\n\n\n<p><strong>c) <\/strong>Kirjoita jakoyht\u00e4l\u00f6 tilanteesta.<br><\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-4&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-76f8bc8c1ad1ca46f0118695b9766ad1\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-4-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-4\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-4\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-4-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><math data-latex=\"\\frac{25}4 = 6\"><semantics><mrow><mfrac><mn>25<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{25}4 = 6<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 1<\/p>\n\n\n\n<p><strong>a)<\/strong> 6 ryhm\u00e4\u00e4<\/p>\n\n\n\n<p><strong>b)<\/strong> 1 opiskelija j\u00e4\u00e4 yli. H\u00e4nelle tosin l\u00f6ytyy varmaankin paikka jostakin ryhm\u00e4st\u00e4.<\/p>\n\n\n\n<p><strong>c)<\/strong> <math data-latex=\"25 = 4 \\cdot 6 + 1\"><semantics><mrow><mn>25<\/mn><mo>=<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mn>6<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">25 = 4 \\cdot 6 + 1<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 5. <\/strong>Tiedet\u00e4\u00e4n, ett\u00e4 luku n on jaollinen luvulla 9.<\/h3>\n\n\n\n<p><strong>a)<\/strong> Onko n jaollinen luvulla 3? Perustele.<\/p>\n\n\n\n<p><strong>b)<\/strong> Voiko n olla parillinen? Perustele.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-5&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-c7d583cf8aac7a233a09db686a9912d8\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-5-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-5\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-5\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-5-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Tiedet\u00e4\u00e4n, ett\u00e4 n on jaollinen luvulla 9, eli <math data-latex=\"n = 9k\"><semantics><mrow><mi>n<\/mi><mo>=<\/mo><mn>9<\/mn><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">n = 9k<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>a) Koska <math data-latex=\"9 = 3 \\cdot 3\"><semantics><mrow><mn>9<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">9 = 3 \\cdot 3<\/annotation><\/semantics><\/math>, saadaan<br><math data-latex=\"n = 3 \\cdot (3k)\"><semantics><mrow><mi>n<\/mi><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>k<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">n = 3 \\cdot (3k)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>On siis jaollinen luvulla 3.<\/p>\n\n\n\n<p>b) Jos k on parillinen, my\u00f6s n on parillinen.<br>Esim. <math data-latex=\"n = 18\"><semantics><mrow><mi>n<\/mi><mo>=<\/mo><mn>18<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n = 18<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Voi olla parillinen.<br><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 6.<\/strong> T\u00e4ydenn\u00e4 jakoyht\u00e4l\u00f6, eli ratkaise q ja r.<\/h3>\n\n\n\n<p>a) <math data-latex=\"75 = 8q + r\"><semantics><mrow><mn>75<\/mn><mo>=<\/mo><mn>8<\/mn><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">75 = 8q + r<\/annotation><\/semantics><\/math>, miss\u00e4 0 \u2264 r &lt; 8<\/p>\n\n\n\n<p>b) <math data-latex=\"5q + r = 143\"><semantics><mrow><mn>5<\/mn><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><mo>=<\/mo><mn>143<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5q + r = 143<\/annotation><\/semantics><\/math>, miss\u00e4 0 \u2264 r &lt; 5<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-6&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-c7d583cf8aac7a233a09db686a9912d8\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-6-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-6\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-6\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-6-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) <math data-latex=\"75 = 8q + r\"><semantics><mrow><mn>75<\/mn><mo>=<\/mo><mn>8<\/mn><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">75 = 8q + r<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\frac{75}8 = 9\"><semantics><mrow><mfrac><mn>75<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{75}8 = 9<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 3<\/p>\n\n\n\n<p><math data-latex=\"q = 9\"><semantics><mrow><mi>q<\/mi><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">q = 9<\/annotation><\/semantics><\/math>, <math data-latex=\"r = 3\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r = 3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>b) <math data-latex=\"5q + r = 143\"><semantics><mrow><mn>5<\/mn><mi>q<\/mi><mo>+<\/mo><mi>r<\/mi><mo>=<\/mo><mn>143<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5q + r = 143<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\frac{143}5 = 28\"><semantics><mrow><mfrac><mn>143<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{143}5 = 28<\/annotation><\/semantics><\/math>, jakoj\u00e4\u00e4nn\u00f6s 3<\/p>\n\n\n\n<p><math data-latex=\"q = 28\"><semantics><mrow><mi>q<\/mi><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">q = 28<\/annotation><\/semantics><\/math>, <math data-latex=\"r = 3\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r = 3<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 7.<\/strong> Keksi luku, joka antaa jakoj\u00e4\u00e4nn\u00f6ksen 3, kun se jaetaan luvulla 5.<\/h3>\n\n\n\n<p>a) Anna yksi esimerkki.<\/p>\n\n\n\n<p>b) Anna kolme erilaista esimerkki\u00e4.<\/p>\n\n\n\n<p>c) Selit\u00e4, millaisia n\u00e4m\u00e4 luvut ovat. Miss\u00e4 muodossa ne kaikki voidaan kirjoittaa?<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-7&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-e5628343b5753705907f2a5b13351c11\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-7-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-7\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vinkki<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-7\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-7-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Mieti yleist\u00e4 muotoa: <math data-latex=\"a = bk + r\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mi>b<\/mi><mi>k<\/mi><mo>+<\/mo><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a = bk + r<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-8&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-c7d583cf8aac7a233a09db686a9912d8\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-8-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-8\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-8\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-8-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>a) Esim. 8<\/p>\n\n\n\n<p>b) Esim. 13, 18 ja 23<\/p>\n\n\n\n<p>c) Luvut ovat muotoa <math data-latex=\"5k + 3\"><semantics><mrow><mn>5<\/mn><mi>k<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5k + 3<\/annotation><\/semantics><\/math>, kun <math data-latex=\"k \u2208 Z\"><semantics><mrow><mi>k<\/mi><mo>\u2208<\/mo><mi>Z<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k \u2208 Z<\/annotation><\/semantics><\/math>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 8.<\/strong> Osoita, ett\u00e4 jos kokonaisluku a on jaollinen luvulla 5, niin a<strong>\u00b2<\/strong> on jaollinen luvulla 25.<\/h3>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-9&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-1bd547cfdd926e05cae3c903806636e4\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-9-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-9\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-9\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-9-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Oletetaan, ett\u00e4 a on jaollinen luvulla 5.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"a = 5k\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>5<\/mn><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a = 5k<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<p>T\u00e4ll\u00f6in <math data-latex=\"a\u00b2 = (5k)\u00b2 = 25k\u00b2\"><semantics><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>5<\/mn><mi>k<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>25<\/mn><msup><mi>k<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a\u00b2 = (5k)\u00b2 = 25k\u00b2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<strong>\u00b2<\/strong> on jaollinen luvulla 25.<\/li>\n<\/ul>\n\n\n\n<p>V\u00e4ite on tosi.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 9.<\/strong> V\u00e4ite:<\/h3>\n\n\n\n<p>\u201dKoska luku 42 on jaollinen luvuilla 6 ja 7, se on jaollinen luvulla 42.\u201d<\/p>\n\n\n\n<p>Onko v\u00e4ite oikein? Perustele.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-10&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-1bd547cfdd926e05cae3c903806636e4\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-10-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-10\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-10\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-10-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Tarkastetaan ensin:<\/p>\n\n\n\n<p><math data-latex=\"\\frac{42}{42} = 1\"><semantics><mrow><mfrac><mn>42<\/mn><mn>42<\/mn><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{42}{42} = 1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>jako menee tasan<\/li>\n<\/ul>\n\n\n\n<p>Koska <math data-latex=\"6 \\cdot 7 = 42\"><semantics><mrow><mn>6<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><mn>42<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6 \\cdot 7 = 42<\/annotation><\/semantics><\/math>, ja luvut 6 ja 7 ovat kesken\u00e4\u00e4n jaottomia (ei yhteisi\u00e4 tekij\u00f6it\u00e4), niiden tulo jakaa luvun.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jaollisuus ja jakoyht\u00e4l\u00f6 Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin. Teht\u00e4v\u00e4 1. Meneek\u00f6 jako tasan? Jos ei, kirjoita jakoj\u00e4\u00e4nn\u00f6s. a) 873\\frac{87}{3} b) 317\\frac{31}{7} c) 789\\frac{78}{9} d) 987\\frac{98}{7} e) 5433\\frac{543}{3} Teht\u00e4v\u00e4 2. Kirjoita jakolaskua vastaava jakoyht\u00e4l\u00f6. a) 12311\\frac{123}{11}<\/p>\n","protected":false},"author":3745,"featured_media":0,"parent":95,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1333","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1333","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/users\/3745"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/comments?post=1333"}],"version-history":[{"count":20,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1333\/revisions"}],"predecessor-version":[{"id":2627,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1333\/revisions\/2627"}],"up":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/95"}],"wp:attachment":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/media?parent=1333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}