{"id":32,"date":"2023-04-26T12:09:26","date_gmt":"2023-04-26T10:09:26","guid":{"rendered":"https:\/\/www.jankafialka.sk\/?page_id=32"},"modified":"2024-10-21T17:23:46","modified_gmt":"2024-10-21T15:23:46","slug":"zaporne-cisla-inak","status":"publish","type":"page","link":"https:\/\/www.jankafialka.sk\/?page_id=32","title":{"rendered":"Z\u00e1porn\u00e9 \u010d\u00edsla inak"},"content":{"rendered":"\n<p>Z\u00e1porn\u00e9 \u010d\u00edsla nepatria k \u00faplne najob\u013e\u00fabenej\u0161\u00edm t\u00e9mam na hodin\u00e1ch matematiky na z\u00e1kladnej \u0161kole. Je to dan\u00e9 tak trochu historicky. Z\u00e1porn\u00e9 \u010d\u00edsla sa v Eur\u00f3pe ve\u013emi dlho nepova\u017eovali za rovnocenn\u00e9 t\u00fdm kladn\u00fdm. \u013dudia si toti\u017e \u010d\u00edslo predstavovali ako po\u010det alebo d\u013a\u017eku. Po\u010det minc\u00ed alebo d\u013a\u017eka cesty nem\u00f4\u017ee by\u0165 predsa z\u00e1porn\u00e1. Na \u010falekom v\u00fdchode ale z\u00e1porn\u00e9 \u010d\u00edsla existuj\u00fa u\u017e odnepam\u00e4ti. Z\u00e1porn\u00e9 a kladn\u00e9 \u010d\u00edsla vn\u00edmaj\u00fa ako vz\u00e1jomne opa\u010dn\u00e9. Ako teplo a chlad.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Zozn\u00e1menie<\/h3>\n\n\n\n<p>Pozrite si t\u00fato anim\u00e1ciu:<\/p>\n\n\n\n<button onclick=\"spusti();\"><b><i>Spusti znova!<\/i><\/b><\/button>\n<br><br>\n<canvas id=\"platno\" width=\"280\" height=\"280\">\n<\/canvas>\n\n\n\n<p>V\u0161imli ste si, \u010do sa tam deje? \u010cerven\u00e9 a modr\u00e9 gu\u013e\u00f4\u010dky sa pri stretnut\u00ed vz\u00e1jomne zru\u0161ia.<\/p>\n\n\n\n<script>\n\nfunction kresli(cervenych,modrych,platno){\nconst canvas = document.getElementById(platno);\nconst ctx = canvas.getContext(\"2d\");\nconst w = canvas.width;\nconst h = canvas.height;\n\n\/\/pole gulocok [stred farba pohyb]\nlet Pole = [];\nlet farba;\n\nfor (var i=0; i<(1*cervenych+1*modrych);i++){\nif (i<cervenych){\nfarba=\"#ff6464\";}\nelse {farba=\"#3264ff\";}\n\nPole[i]= [Math.floor((w-10)*Math.random())+5, Math.floor((h-10)*Math.random())+5, farba, 2*Math.random()-1, 2*Math.random()-1];\n}\n\nfunction pohyb(){\nctx.fillStyle=\"rgb(250,250,250)\";\nctx.fillRect(0,0,w,h);\nctx.strokeStyle=\"black\";\nctx.strokeRect(0,0,w,h);\n\n\/\/kreslim gulocky\nfor (i=0;i<(1*cervenych+1*modrych);i++){\n\/\/odrazy od stien\nif (Pole[i][0]<=5||Pole[i][0]>=(w-5)){Pole[i][3]=-Pole[i][3];}\n\nif (Pole[i][1]<=5||Pole[i][1]>=(h-5)){Pole[i][4]=-Pole[i][4];}\n\n\/\/odraz od inych gulocok\nfor(j=(i+1);j<(1*cervenych+1*modrych);j++){\nlet xs= Pole[i][0]-Pole[j][0];\nlet ys= Pole[i][1]-Pole[j][1];\nif (!((Math.pow(xs,2)+ Math.pow(ys,2))>100 || (Math.pow(xs,2)+ Math.pow(ys,2))<64 || Pole[i][2] == \"rgba(0,0,0,0)\" || Pole[j][2] == \"rgba(0,0,0,0)\")){\nPole[i][3]=-Pole[i][3];\nPole[j][3]=-Pole[j][3];\nPole[i][4]=-Pole[i][4];\nPole[j][4]=-Pole[j][4];\n\/\/miznutie gulocok, ktore maju roznu farbu a stretli sa\n\nif (!(Pole[i][2]==Pole[j][2]))\n{if (!(Pole[i][2]==\"rgba(0,0,0,0)\" ||Pole[j][2]==\"rgba(0,0,0,0)\")){\nPole[i][2]=\"rgba(0,0,0,0)\";\nPole[j][2]=\"rgba(0,0,0,0)\";}}\n}\n}\nPole[i][0]+=Pole[i][3];\nPole[i][1]+=Pole[i][4];\nctx.fillStyle=Pole[i][2];\nctx.beginPath();\nctx.arc(Pole[i][0],Pole[i][1],5,0,2*Math.PI);\nctx.fill();\n}\n\nrequestAnimationFrame(pohyb);\n}\nrequestAnimationFrame(pohyb);\n}\nfunction spusti(){\nlet modrych = 10;\nlet cervenych = 10;\nlet platno=\"platno\";\nkresli(cervenych,modrych, platno);\n}\nspusti();\n<\/script>\n\n\n\n<h3 class=\"wp-block-heading\">2. Uh\u00e1dnite, \u010do zostane<\/h3>\n\n\n\n<p>Je \u010das na prv\u00fa \u00falohu. Vysk\u00fa\u0161ajte uh\u00e1dnu\u0165, ko\u013eko ak\u00fdch gu\u013e\u00f4\u010dok zostane pred t\u00fdm, ne\u017e anim\u00e1cia \u00falohu vyrie\u0161i sama.<\/p>\n\n\n\n<button onclick=\"spusti2();\"><b><i>Spusti nov\u00e9 zadanie<\/i><\/b><\/button>\n<br><br>\n<p>\nNa za\u010diatku bolo \n<label id=\"labRed\">?<\/label> \u010derven\u00fdch a\n<label id=\"labBlue\">?<\/label> modr\u00fdch gu\u013e\u00f4\u010dok.\n<\/p>\n<p>\nV\u00fdsledok: <input type=\"number\" id=\"vysledok\" style=\"width: 3em;\">\n<select id=\"vyberFarby\">\n<option value=\"0\">akej farby?<\/option>\n<option value=\"1\">\u010derven\u00fdch<\/option>\n<option value=\"-1\">modr\u00fdch<\/option>\n<\/select>\n<button onclick=\"potvrd();\">Potvr\u010f\n<\/button>\n<\/p>\n\n<canvas id=\"platno2\" width=\"280\" height=\"280\">\n<\/canvas>\n\n\n\n<script>\nlet cervenych,modrych;\nfunction spusti2(){\ncervenych= Math.floor(12*Math.random());\nmodrych = Math.floor(12*Math.random());\nlet platno=\"platno2\";\nkresli(cervenych, modrych, platno);\nlet get= document.getElementById(\"labRed\");\nget.innerHTML=\"\"+cervenych;\nlet get2= document.getElementById(\"labBlue\");\nget2.innerHTML=\"\"+modrych;\n}\n\nfunction potvrd(){\nlet vysledok = document.getElementById(\"vysledok\");\nlet vys=vysledok.value;\n\nlet farba=document.querySelector(\"#vyberFarby\");\nlet f=farba.value;\nif ((cervenych-modrych)==f*vys){alert(\"spr\u00e1vne\");}\nelse alert(\"nespr\u00e1vne\");\n}\nspusti2();\n<\/script>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u010co mohlo by\u0165 na za\u010diatku?<\/h3>\n\n\n\n<p>\nTeraz opa\u010dn\u00e1 \u00faloha - ak chceme, aby nakoniec zostalo <b><label id=\"zadanie\"><\/label> <\/b>gu\u013e\u00f4\u010dok, ko\u013eko mohlo by\u0165 na za\u010diatku \u010derven\u00fdch a ko\u013eko modr\u00fdch?\n<button onclick=\"zadanie();\"> Zme\u0148 zadanie<\/button>\n<\/p>\n<p>\nNa za\u010diatku mohlo by\u0165: \n<input type=\"number\" style =\"width: 2em; border:solid 1px #ff6464;\" id=\"red3\">\n\n<input type=\"number\" style =\"width: 2em; border:solid 1px #3264ff;\" id=\"funguj\">\n<label id=\"anonie\"><\/label>\n<\/p>\n<button onclick=\"spusti3();\"><b><i>Potvr\u010f a spusti anim\u00e1ciu<\/i><\/b><\/button>\n<br><br>\n<canvas id=\"platno3\" width=\"280\" height=\"280\">\n<\/canvas>\n\n\n\n<script>\nlet zadan, f;\nfunction zadanie(){\nf=Math.random();\nif (f<0.5) f=\"\u010derven\u00fdch\";\nelse f=\"modr\u00fdch\";\nlet zad = document.getElementById(\"zadanie\");\nzadan=Math.floor(10*Math.random());\nzad.innerHTML=zadan+\" \"+f;\n}\nzadanie();\nfunction spusti3(){\n\nlet platno =\"platno3\";\nlet re= document.getElementById(\"red3\");\nlet cerv= re.value;\nlet blu= document.getElementById(\"funguj\");\nlet modr= blu.value;\nif(isNaN(cerv) || isNaN(modr)){alert(\"Je nutn\u00e9 zada\u0165 \u010d\u00edsla!\");\nre.value=\"\";\nblu.value=\"\";\nkresli(0,0,platno);}\nelse kresli(cerv, modr, platno);\n\nlet an=document.getElementById(\"anonie\");\nlet anif;\nif (f==\"\u010derven\u00fdch\"){if(zadan==(1*cerv-1*modr)) anif=\"\u00c1no\"; else anif=\"Nie\";} \nelse {if (zadan==(1*modr-1*cerv)) anif=\"\u00c1no\"; else anif=\"Nie\";}\nan.innerHTML=anif;\n}\n<\/script>\n\n\n\n<p>Vysk\u00fa\u0161ajte viac mo\u017enost\u00ed, ako dosta\u0165 ten ist\u00fd v\u00fdsledok. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u010co \u010falej<\/h2>\n\n\n\n<p>Ak sa dohodneme, \u017ee \u010derven\u00e1 gu\u013e\u00f4\u010dka je kladn\u00e1 jednotka a modr\u00e1 gu\u013e\u00f4\u010dka z\u00e1porn\u00e1 jednotka, z\u00edskali sme pr\u00e1ve pekn\u00fd model cel\u00fdch \u010d\u00edsel. Presved\u010dili sme sa o tom, \u017ee jedno cel\u00e9 \u010d\u00edslo sa d\u00e1 zn\u00e1zorni\u0165 r\u00f4znymi dvojicami. Napr. -2 je 5 \u010derven\u00fdch a 7 modr\u00fdch alebo len dve modr\u00e9 alebo ... (nekone\u010dne ve\u013ea mo\u017enost\u00ed).<\/p>\n\n\n\n<p>Na tomto by sme mohli postavi\u0165 aj oper\u00e1cie - s\u010d\u00edtanie ako prid\u00e1vanie gu\u013e\u00f4\u010dok, od\u010d\u00edtanie ako odoberanie, n\u00e1sobenie a delenie tak, ako sme zvyknut\u00ed s jednou \u00fapravou.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">S\u010d\u00edtanie a od\u010d\u00edtanie<\/h3>\n\n\n\n<p>Za\u010dnime jednoduch\u00fdm pr\u00edkladom, ko\u013eko je <span style=\"color:blue\">-2<\/span> + <span style=\"color:red\">5<\/span>? M\u00e1me tu dve \u010d\u00edsla <span style=\"color:blue\">-2<\/span> a <span style=\"color:red\">5<\/span> a oper\u00e1ciu +. Za\u010dneme prv\u00fdm \u010d\u00edslom. <span style=\"color:blue\">-2<\/span> znamen\u00e1, \u017ee m\u00e1me dve modr\u00e9 gu\u013e\u00f4\u010dky. Oper\u00e1cia + znamen\u00e1, \u017ee budeme prid\u00e1va\u0165. Druh\u00e9 \u010d\u00edslo je kladn\u00e9, tak\u017ee prid\u00e1me 5 \u010derven\u00fdch gu\u013e\u00f4\u010dok. \u010co bude v\u00fdsledkom? Dve modr\u00e9 a dve \u010derven\u00e9 sa zru\u0161ia navz\u00e1jom, tak\u017ee zostan\u00fa tri \u010derven\u00e9. <span style=\"color:blue\">-2<\/span> + <span style=\"color:red\">5<\/span> = <span style=\"color:red\">3<\/span>. \u017diadna ve\u013ek\u00e1 veda. Sta\u010d\u00ed si da\u0165 pozor na to, \u017ee modr\u00e1 gu\u013e\u00f4\u010dka sa ozna\u010duje tak, \u017ee pred \u010d\u00edslo sa d\u00e1 m\u00ednus.<\/p>\n\n\n\n<p>Od\u010d\u00edtanie m\u00f4\u017ee by\u0165 ve\u013emi jednoduch\u00e9, napr. <span style=\"color:blue\">-5<\/span> \u2012 (<span style=\"color:blue\">-3<\/span>). Tu m\u00e1me p\u00e4\u0165 modr\u00fdch gu\u013e\u00f4\u010dok a odober\u00e1me z nich tri modr\u00e9. Zostan\u00fa n\u00e1m teda dve modr\u00e9 <span style=\"color:blue\">-5<\/span> \u2012 (<span style=\"color:blue\">-3<\/span>) = <span style=\"color:blue\">-2<\/span>.<\/p>\n\n\n\n<p>M\u00f4\u017ee ale nasta\u0165 drobn\u00e1 komplik\u00e1cia - nem\u00e1me \u010do odobera\u0165. Napr. <span style=\"color: red\">1<\/span> \u2012 <span style=\"color: red\">4<\/span> znamen\u00e1, \u017ee m\u00e1me na za\u010diatku jednu \u010derven\u00fa gu\u013e\u00f4\u010dku. Ale mohla to by\u0165 aj skupina desiatich \u010derven\u00fdch a deviatich modr\u00fdch alebo \u0161tyroch \u010derven\u00fdch a troch modr\u00fdch. Odobra\u0165 \u0161tyri \u010derven\u00e9 tak nemus\u00ed by\u0165 probl\u00e9m. Ke\u010f m\u00e1me \u0161tyri \u010derven\u00e9 a tri modr\u00e9, \u0161tyri \u010derven\u00e9 m\u00f4\u017eeme odstr\u00e1ni\u0165 a zostan\u00fa n\u00e1m iba tie tri modr\u00e9. Preto  <span style=\"color: red\">1<\/span> \u2012 <span style=\"color: red\">4<\/span> = <span style=\"color: blue\">-3<\/span>. <\/p>\n\n\n\n<p>Alebo <span style=\"color:red\">3<\/span> \u2012 (<span style=\"color:blue\">-2<\/span>) znamen\u00e1, \u017ee m\u00e1me tri \u010derven\u00e9 gu\u013e\u00f4\u010dky a chceme odobra\u0165 dve modr\u00e9. Vyzer\u00e1 to na prv\u00fd poh\u013ead nerie\u0161ite\u013ene, ale my si vieme poradi\u0165. Ke\u010f m\u00e1me tri \u010derven\u00e9 gu\u013e\u00f4\u010dky, tak oni mohli by\u0165 pokojne zn\u00e1zornen\u00e9 aj napr\u00edklad piatimi \u010derven\u00fdmi a dvoma modr\u00fdmi predt\u00fdm, ne\u017e sa navz\u00e1jom zru\u0161ili. V tomto stave by sme dve modr\u00e9 odobra\u0165 mohli. Tak\u017ee <span style=\"color:red\">3<\/span> \u2012 (<span style=\"color:blue\">-2<\/span>) = <span style=\"color:red\">5<\/span>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">N\u00e1sobenie a delenie<\/h3>\n\n\n\n<p>Na rozdiel od s\u010d\u00edtania a od\u010d\u00edtania, v \u00faloh\u00e1ch na n\u00e1sobenie a delenie, iba prv\u00e9 \u010d\u00edslo znamen\u00e1 po\u010det a farbu gu\u013e\u00f4\u010dok. Druh\u00e9 \u010d\u00edslo spolu s oper\u00e1ciou ur\u010duje, \u010do sa bude robi\u0165. (<span style=\"color:blue\">-3<\/span>) \u2219 4 znamen\u00e1, \u017ee m\u00e1me tri modr\u00e9 gu\u013e\u00f4\u010dky a ich po\u010det potrebujeme zo\u0161tvorn\u00e1sobi\u0165. Preto (<span style=\"color:blue\">-3<\/span>) \u2219 4 = <span style=\"color:blue\">-12<\/span>. Podobne <span style=\"color:red\">20<\/span> : 4 = <span style=\"color:red\">5<\/span>, preto\u017ee 20 \u010derven\u00fdch gu\u013e\u00f4\u010dok sme rozdelili na \u0161tyri rovnak\u00e9 skupiny. V ka\u017edej skupinke bolo potom 5 \u010derven\u00fdch gu\u013e\u00f4\u010dok.<\/p>\n\n\n\n<p>Ak del\u00edme alebo n\u00e1sob\u00edme z\u00e1porn\u00fdm \u010d\u00edslom, stane sa jedna vec navy\u0161e. P\u00f4vodn\u00e9 gu\u013e\u00f4\u010dky, charakterizuj\u00face prv\u00e9 \u010d\u00edslo pr\u00edkladu, sa prefarbia na opa\u010dn\u00fa farbu, z modr\u00fdch bud\u00fa \u010derven\u00e9 a z \u010derven\u00fdch modr\u00e9. Tak\u017ee, napr. <span style=\"color:red\">10<\/span> : (-2) znamen\u00e1, \u017ee m\u00e1me desa\u0165 \u010derven\u00fdch gu\u013e\u00f4\u010dok, budeme ich deli\u0165 na dve \u010dasti a e\u0161te ich nezabudmene v\u0161etky prefarbi\u0165 na modro. Dalo by sa to zap\u00edsa\u0165 aj ako <span style=\"color:red\">10<\/span> : (-2) = (<span style=\"color:blue\">-10<\/span>) : 2 = <span style=\"color:blue\">-5<\/span>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Vysk\u00fa\u0161ajte sa<\/h2>\n\n\n\n<p>Te\u00f3ria je jedna vec. Po\u010fme si overi\u0165, \u010di ju budete vedie\u0165 pou\u017ei\u0165 v konkr\u00e9tnych \u00faloh\u00e1ch. <\/p>\n\n\n\n<script src=\"https:\/\/unpkg.com\/vue@3.2.47\"><\/script>\n<script src=\"https:\/\/unpkg.com\/jspdf@latest\/dist\/jspdf.umd.min.js\"><\/script>\n\n    <div id=\"app\">\n<ul class=\"ram\" style=\"column-count:2;\">\n      <li>{{ number1a }} + {{ zp1}}{{number1b}}{{zz1 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer1\" :style=\"{ 'text-decoration': (spravne1) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n     <li>{{ number2a }} + \n{{ zp2}}{{number2b}}{{zz2 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer2\" :style=\"{ 'text-decoration': (spravne2) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n     <li>{{ number3a }} + \n{{ zp3}}{{number3b}}{{zz3 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer3\" :style=\"{ 'text-decoration': (spravne3) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number4a }} + \n{{ zp4}}{{number4b}}{{zz4 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer4\" :style=\"{ 'text-decoration': (spravne4) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number5a }} + \n{{ zp5}}{{number5b}}{{zz5 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer5\" :style=\"{ 'text-decoration': (spravne5) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n\n    <li>{{ number6a }} \u2012 \n{{ zp6}}{{number6b}}{{zz6 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\"  v-model=\"answer6\" :style=\"{ 'text-decoration': (spravne6) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number7a }} \u2012 \n{{ zp7}}{{number7b}}{{zz7 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer7\" :style=\"{ 'text-decoration': (spravne7) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number8a }} \u2012 \n{{ zp8}}{{number8b}}{{zz8 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer8\" :style=\"{ 'text-decoration': (spravne8) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number9a }} \u2012 \n{{ zp9}}{{number9b}}{{zz9 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer9\" :style=\"{ 'text-decoration': (spravne9) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number10a }} \u2012 \n{{ zp10}}{{number10b}}{{zz10 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer10\" :style=\"{ 'text-decoration': (spravne10) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n\n<li>{{ number11a }} \u22c5 {{ zp11}}{{number11b}}{{zz11 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer11\" :style=\"{ 'text-decoration': (spravne11) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n     <li>{{ number12a }} \u22c5 \n{{ zp12}}{{number12b}}{{zz12 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer12\" :style=\"{ 'text-decoration': (spravne12) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n     <li>{{ number13a }} \u22c5 \n{{ zp13}}{{number13b}}{{zz13 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer13\" :style=\"{ 'text-decoration': (spravne13) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number14a }} \u22c5 \n{{ zp14}}{{number14b}}{{zz14 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer14\" :style=\"{ 'text-decoration': (spravne14) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number15a }} \u22c5 \n{{ zp15}}{{number15b}}{{zz15 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer15\" :style=\"{ 'text-decoration': (spravne15) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n\n    <li>{{ number16a }} : \n{{ zp16}}{{number16b}}{{zz16 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer16\" :style=\"{ 'text-decoration': (spravne16) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number17a }} : \n{{ zp17}}{{number17b}}{{zz17 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer17\" :style=\"{ 'text-decoration': (spravne17) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number18a }} : \n{{ zp18}}{{number18b}}{{zz18 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer18\" :style=\"{ 'text-decoration': (spravne18) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number19a }} : \n{{ zp19}}{{number19b}}{{zz19 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer19\" :style=\"{ 'text-decoration': (spravne19) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n    <li>{{ number20a }} : \n{{ zp20}}{{number20b}}{{zz20 }} = <textarea maxlength=\"3\" cols=\"3\" rows=\"1\" v-model=\"answer20\" :style=\"{ 'text-decoration': (spravne20) ? 'none' : 'line-through'}\"><\/textarea><\/li>\n<\/ul>\n<button @click=\"kontrola\"><b><i>Potvr\u010f !<\/i><\/b><\/button>&nbsp;&nbsp;\n<button @click=\"reset\"><b><i>Nov\u00e9 zadanie<\/i><\/b><\/button>\n    <\/div>\n\n    <script>\nlet klik=0;\n      const app = Vue.createApp({\n        data() {\n          return {\n            number1a: 0,\n            number1b: 0,\n            answer1: '',\nzp1:'',\nzz1:'',\nspravne1: true,\nnumber2a: 0,          number2b: 0,            answer2: '',\nzp2:'',\nzz2:'',\nspravne2: true,\nnumber3a: 0,\n            number3b: 0,\n            answer3: '',\nzp3:'',\nzz3:'',\nspravne3: true,\nnumber4a: 0,\n            number4b: 0,\n            answer4: '',\nzp4:'',\nzz4:'',\nspravne4: true,\nnumber5a: 0,\n            number5b: 0,\n            answer5: '',\nzp5:'',\nzz5:'',\nspravne5: true,\nnumber6a: 0,\n            number6b: 0,\n            answer6: '',\nzp6:'',\nzz6:'',\nspravne6: true,\nnumber7a: 0,\n            number7b: 0,\n            answer7: '',\nzp7:'',\nzz7:'',\nspravne7: true,\nnumber8a: 0,\n            number8b: 0,\n            answer8: '',\nzp8:'',\nzz8:'',\nspravne8: true,\nnumber9a: 0,\n            number9b: 0,\n            answer9: '',\nzp9:'',\nzz9:'',\nspravne9: true,\nnumber10a: 0,\n            number10b: 0,\n            answer10: '',\nzp10:'',\nzz10:'',\nspravne10: true,\nnumber11a: 0,\n            number11b: 0,\n            answer11: '',\nzp11:'',\nzz11:'',\nspravne11: true,\nnumber12a: 0,          number12b: 0,            answer12: '',\nzp12:'',\nzz12:'',\nspravne12: true,\nnumber13a: 0,\n            number13b: 0,\n            answer13: '',\nzp13:'',\nzz13:'',\nspravne13: true,\nnumber14a: 0,\n            number14b: 0,\n            answer14: '',\nzp14:'',\nzz14:'',\nspravne14: true,\nnumber15a: 0,\n            number15b: 0,\n            answer15: '',\nzp15:'',\nzz15:'',\nspravne15: true,\nnumber16a: 0,\n            number16b: 0,\n            answer16: '',\nzp16:'',\nzz16:'',\nspravne16: true,\nnumber17a: 0,\n            number17b: 0,\n            answer17: '',\nzp17:'',\nzz17:'',\nspravne17: true,\nnumber18a: 0,\n            number18b: 0,\n            answer18: '',\nzp18:'',\nzz18:'',\nspravne18: true,\nnumber19a: 0,\n            number19b: 0,\n            answer19: '',\nzp19:'',\nzz19:'',\nspravne19: true,\nnumber20a: 0,\n            number20b: 0,\n            answer20: '',\nzp20:'',\nzz20:'',\nspravne20: true,\n          }\n        },\n        methods: {\nkontrola(){\nlet skore=0;\n  if (this.answer1==(this.number1a+ this.number1b)){skore++; this.spravne1=true;}\nelse {this.spravne1=false;}\n  if (this.answer2==(this.number2a+ this.number2b)){skore++; this.spravne2=true;}\nelse {this.spravne2=false;}\n  if (this.answer3==(this.number3a+ this.number3b)){skore++; this.spravne3=true;}\nelse {this.spravne3=false;}\n  if (this.answer4==(this.number4a+ this.number4b)){skore++; this.spravne4=true;}\nelse {this.spravne4=false;}\n  if (this.answer5==(this.number5a+ this.number5b)){skore++; this.spravne5=true;}\nelse {this.spravne5=false;}\n\n  if (this.answer6==(this.number6a- this.number6b)){skore++; this.spravne6=true;}\nelse {this.spravne6=false;}\n  if (this.answer7==(this.number7a- this.number7b)){skore++; this.spravne7=true;}\nelse {this.spravne7=false;}\n  if (this.answer8==(this.number8a- this.number8b)){skore++; this.spravne8=true;}\nelse {this.spravne8=false;}\n  if (this.answer9==(this.number9a- this.number9b)){skore++; this.spravne9=true;}\nelse {this.spravne9=false;}\n  if (this.answer10==(this.number10a- this.number10b)){skore++; this.spravne10=true;}\nelse {this.spravne10=false;}\n\n if (this.answer11==(this.number11a* this.number11b)){skore++; this.spravne11=true;}\nelse {this.spravne11=false;}\n  if (this.answer12==(this.number12a* this.number12b)){skore++; this.spravne12=true;}\nelse {this.spravne12=false;}\n  if (this.answer13==(this.number13a* this.number13b)){skore++; this.spravne13=true;}\nelse {this.spravne13=false;}\n  if (this.answer14==(this.number14a* this.number14b)){skore++; this.spravne14=true;}\nelse {this.spravne14=false;}\n  if (this.answer15==(this.number15a* this.number15b)){skore++; this.spravne15=true;}\nelse {this.spravne15=false;}\n\n  if (this.answer16==(this.number16a\/ this.number16b)){skore++; this.spravne16=true;}\nelse {this.spravne16=false;}\n  if (this.answer17==(this.number17a\/ this.number17b)){skore++; this.spravne17=true;}\nelse {this.spravne17=false;}\n  if (this.answer18==(this.number18a\/ this.number18b)){skore++; this.spravne18=true;}\nelse {this.spravne18=false;}\n  if (this.answer19==(this.number19a\/ this.number19b)){skore++; this.spravne19=true;}\nelse {this.spravne19=false;}\n  if (this.answer20==(this.number20a\/ this.number20b)){skore++; this.spravne20=true;}\nelse {this.spravne20=false;}\n\nif (klik==0){\nif (skore>=18){alert(`Par\u00e1da! Dosiahol si ${skore} bodov z 20. Z\u00e1porn\u00e9 \u010d\u00edsla zvl\u00e1da\u0161 na v\u00fdborn\u00fa!`);}\n\nelse if (skore>=15){alert(`Tvoje sk\u00f3re je ${skore} bodov z 20. Pozri si svoje chyby - ozna\u010den\u00e9 pre\u010diarknut\u00edm a vysk\u00fa\u0161aj sa e\u0161te raz s nov\u00fdm zadan\u00edm.`);}\n\nelse {alert(`M\u00e1\u0161 ${skore} spr\u00e1vnych odpoved\u00ed z 20. Pozri si svoje chyby ozna\u010den\u00e9 pre\u010diarknut\u00edm. Potom si znovu prejdi cel\u00fa t\u00fato str\u00e1nku a vysk\u00fa\u0161aj sa znova s nov\u00fdm zadan\u00edm.`);}\n}\n\/\/ ak je klik vacsi ako nula, znamena to, ze uzivatel prepisal uz vyhodnotene vysledky - nedostane alert, iba sa zrusi preciarknutie.\n\nklik++;\n},\/\/tu konci kontrola\n          generateNumbers() {\n            this.number1a = Math.floor(Math.random() * 40) -20;\n            this.number1b = Math.floor(Math.random() * 40) -20;\nif (this.number1b<0) {this.zp1=\"(\"; this.zz1=\")\";}\nthis.number2a = Math.floor(Math.random() * 40) -20;\nthis.number2b = Math.floor(Math.random() * 40) -20;\nif (this.number2b<0) {this.zp2=\"(\"; this.zz2=\")\";}\nthis.number3a = Math.floor(Math.random() * 40) -20;\nthis.number3b = Math.floor(Math.random() * 40) -20;\nif (this.number3b<0) {this.zp3=\"(\"; this.zz3=\")\";}\nthis.number4a = Math.floor(Math.random() * 40) -20;\nthis.number4b = Math.floor(Math.random() * 40) -20;\nif (this.number4b<0) {this.zp4=\"(\"; this.zz4=\")\";}\nthis.number5a = Math.floor(Math.random() * 40) -20;\nthis.number5b = Math.floor(Math.random() * 40) -20;\nif (this.number5b<0) {this.zp5=\"(\"; this.zz5=\")\";}\n\nthis.number6a = Math.floor(Math.random() * 40) -20;\nthis.number6b = Math.floor(Math.random() * 40) -20;\nif (this.number6b<0) {this.zp6=\"(\"; this.zz6=\")\";}\nthis.number7a = Math.floor(Math.random() * 40) -20;\nthis.number7b = Math.floor(Math.random() * 40) -20;\nif (this.number7b<0) {this.zp7=\"(\"; this.zz7=\")\";}\nthis.number8a = Math.floor(Math.random() * 40) -20;\nthis.number8b = Math.floor(Math.random() * 40) -20;\nif (this.number8b<0) {this.zp8=\"(\"; this.zz8=\")\";}\nthis.number9a = Math.floor(Math.random() * 40) -20;\nthis.number9b = Math.floor(Math.random() * 40) -20;\nif (this.number9b<0) {this.zp9=\"(\"; this.zz9=\")\";}\nthis.number10a = Math.floor(Math.random() * 40) -20;\nthis.number10b = Math.floor(Math.random() * 40) -20;\nif (this.number10b<0) {this.zp10=\"(\"; this.zz10=\")\";}\n\nthis.number11a = Math.floor(Math.random() * 20) -10;\n            this.number11b = Math.floor(Math.random() * 20) -10;\nif (this.number11b<0) {this.zp11=\"(\"; this.zz11=\")\";}\nthis.number12a = Math.floor(Math.random() * 20) -10;\nthis.number12b = Math.floor(Math.random() * 20) -10;\nif (this.number12b<0) {this.zp12=\"(\"; this.zz12=\")\";}\nthis.number13a = Math.floor(Math.random() * 20) -10;\nthis.number13b = Math.floor(Math.random() * 20) -10;\nif (this.number13b<0) {this.zp13=\"(\"; this.zz13=\")\";}\nthis.number14a = Math.floor(Math.random() * 20) -10;\nthis.number14b = Math.floor(Math.random() * 20) -10;\nif (this.number14b<0) {this.zp14=\"(\"; this.zz14=\")\";}\nthis.number15a = Math.floor(Math.random() * 20) -10;\nthis.number15b = Math.floor(Math.random() * 20) -10;\nif (this.number15b<0) {this.zp15=\"(\"; this.zz15=\")\";}\n\nthis.number16b = Math.floor(Math.random() * 20) -10;\nif(this.number16b==0)this.number16b++;\nthis.number16a = this.number16b*(Math.floor(Math.random() * 20) -10);\nif (this.number16b<0) {this.zp16=\"(\"; this.zz16=\")\";}\nthis.number17b = Math.floor(Math.random() * 20) -10;\nif(this.number17b==0)this.number17b++;\nthis.number17a = this.number17b*(Math.floor(Math.random() * 20) -10);\nif (this.number17b<0) {this.zp17=\"(\"; this.zz17=\")\";}\nthis.number18b = Math.floor(Math.random() * 20) -10;\nif(this.number18b==0)this.number18b++;\nthis.number18a = this.number18b*(Math.floor(Math.random() * 20) -10);\nif (this.number18b<0) {this.zp18=\"(\"; this.zz18=\")\";}\nthis.number19b = Math.floor(Math.random() * 20) -10;\nif(this.number19b==0)this.number19b++;\nthis.number19a = this.number19b*(Math.floor(Math.random() * 20) -10);\nif (this.number19b<0) {this.zp19=\"(\"; this.zz19=\")\";}\nthis.number20b = Math.floor(Math.random() * 20) -10;\nif(this.number20b==0)this.number20b++;\nthis.number20a = this.number20b*(Math.floor(Math.random() * 20) -10);\nif (this.number20b<0) {this.zp20=\"(\"; this.zz20=\")\";}\n          },\nreset(){\nklik=0;\nthis.zp1=\"\";this.zz1=\"\"; this.zp2=\"\";this.zz2=\"\";\nthis.zp3=\"\";this.zz3=\"\"; this.zp4=\"\";this.zz4=\"\"; this.zp5=\"\";this.zz5=\"\"; this.zp6=\"\";this.zz6=\"\"; this.zp7=\"\";this.zz7=\"\"; this.zp8=\"\";this.zz8=\"\"; this.zp9=\"\";this.zz9=\"\"; this.zp10=\"\";this.zz10=\"\"; this.zp11=\"\";this.zz11=\"\"; this.zp12=\"\";this.zz12=\"\";\nthis.zp13=\"\";this.zz13=\"\"; this.zp14=\"\";this.zz14=\"\";\nthis.zp15=\"\";this.zz15=\"\";\nthis.zp16=\"\";this.zz16=\"\";\nthis.zp17=\"\";this.zz17=\"\";\nthis.zp18=\"\";this.zz18=\"\";\nthis.zp19=\"\";this.zz19=\"\";\nthis.zp20=\"\";this.zz20=\"\";\nthis.generateNumbers();\nthis.answer1='';\nthis.spravne1=true;\/\/nepreciarknute\nthis.answer2='';\nthis.spravne2=true;\nthis.answer3='';\nthis.spravne3=true;\nthis.answer4='';\nthis.spravne4=true;\nthis.answer5='';\nthis.spravne5=true;\nthis.answer6='';\nthis.spravne6=true;\nthis.answer7='';\nthis.spravne7=true;\nthis.answer8='';\nthis.spravne8=true;\nthis.answer9='';\nthis.spravne9=true;\nthis.answer10='';\nthis.spravne10=true;\nthis.answer11='';\nthis.spravne11=true;\nthis.answer12='';\nthis.spravne12=true;\nthis.answer13='';\nthis.spravne13=true;\nthis.answer14='';\nthis.spravne14=true;\nthis.answer15='';\nthis.spravne15=true;\nthis.answer16='';\nthis.spravne16=true;\nthis.answer17='';\nthis.spravne17=true;\nthis.answer18='';\nthis.spravne18=true;\nthis.answer19='';\nthis.spravne19=true;\nthis.answer20='';\nthis.spravne20=true;\n},\n        },\n        mounted() {     this.generateNumbers();\n        },\n      });\n      app.mount('#app');\n    <\/script>\n\n\n\n<p>Na z\u00e1ver sa m\u00f4\u017eete trochu <a href=\"https:\/\/www.jankafialka.sk\/?page_id=36\" target=\"_blank\" rel=\"noreferrer noopener\">zahra\u0165<\/a>.<\/p>\n\n\n\n<form method=\"post\" class=\"ram\">\nAko sa v\u00e1m darilo? M\u00e1te nejak\u00e9 pripomienky? Pode\u013ete sa.<br>\n<input type=\"hidden\" name=\"stranka\" value=\"zaporneCisla\">\nMeno: <textarea rows=\"1\" name=\"meno\"><\/textarea><br>\nKoment\u00e1r: <br><textarea rows=\"6\" style=\"width : 100%\" name=\"obsah\"><\/textarea><br>\n<input type=\"submit\" name=\"odosli\" value=\"Odo\u0161li\">\n<\/form>\n\n\n\n\n<h3 class=\"wp-block-heading\">Koment\u00e1re<\/h3>\n\n\n<table><tr><td>J<\/td><td>Krist\u00edna, vy\u0161\u0161ie m\u00e1m pr\u00edklad 3-(-2). Tak\u017ee 16-(-4) sa sprav\u00ed analogicky, len nie v tejto appke. Sk\u00faste kreslen\u00edm na tabu\u013eu. Nakresl\u00edte 16 \u010derven\u00fdch, p\u00fdtate sa, ko\u013eko to je, prihadzujete dvojice jedna \u010derven\u00e1 a jedna modr\u00e1 a p\u00fdtate sa, ak\u00e9 \u010d\u00edslo to je. \u017diaci by u\u017e mali vedie\u0165, \u017ee st\u00e1le 16. A p\u00fdtate sa, \u010di u\u017e m\u00f4\u017eeme 4 modr\u00e9 \u0161krtn\u00fa\u0165...<\/td><\/tr><tr><td>Krist\u00edna<\/td><td>Dobr\u00fd de\u0148, ako \u017eiakom vysvetli\u0165 pr\u00edklad typu 16-(-4)=? \u010eakujem:)<\/td><\/tr><tr><td>J<\/td><td>Je to par\u00e1dne.<\/td><\/tr><\/table>\n","protected":false},"excerpt":{"rendered":"<p>Z\u00e1porn\u00e9 \u010d\u00edsla nepatria k \u00faplne najob\u013e\u00fabenej\u0161\u00edm t\u00e9mam na hodin\u00e1ch matematiky na z\u00e1kladnej \u0161kole. Je to dan\u00e9 tak trochu historicky. Z\u00e1porn\u00e9 \u010d\u00edsla sa v Eur\u00f3pe ve\u013emi dlho nepova\u017eovali za rovnocenn\u00e9 t\u00fdm kladn\u00fdm. \u013dudia si toti\u017e \u010d\u00edslo predstavovali ako po\u010det alebo d\u013a\u017eku. Po\u010det minc\u00ed alebo d\u013a\u017eka cesty nem\u00f4\u017ee by\u0165 predsa z\u00e1porn\u00e1. Na \u010falekom v\u00fdchode ale z\u00e1porn\u00e9 \u010d\u00edsla [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1446,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-32","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Z\u00e1porn\u00e9 \u010d\u00edsla inak - jankafialka<\/title>\n<meta name=\"description\" content=\"Z\u00e1porn\u00e9 \u010d\u00edsla s\u00fa predstaven\u00e9 pomocou pohybuj\u00facich sa \u010derven\u00fdch a modr\u00fdch gu\u013e\u00f4\u010dok, ktor\u00e9 sa navz\u00e1jom ru\u0161ia.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.jankafialka.sk\/?page_id=32\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Z\u00e1porn\u00e9 \u010d\u00edsla inak - 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