| TemplateBot (Diskussion | bidrag) |
(7 mellanliggande versioner av 4 användare visas inte)
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| Rad 4: |
Rad 4: |
| | Distributiva lagen används när man '''multiplicerar in''' ett tal eller [[Algebraiskt uttryck *Wordlist*|uttryck]], t.ex. 7 eller $5x$, i en parentes. Det multipliceras då med '''alla''' termer inuti parentesen.</translate> | | Distributiva lagen används när man '''multiplicerar in''' ett tal eller [[Algebraiskt uttryck *Wordlist*|uttryck]], t.ex. 7 eller $5x$, i en parentes. Det multipliceras då med '''alla''' termer inuti parentesen.</translate> |
| | <PGFTikz> | | <PGFTikz> |
| − | [[File:law_of_distr_1.svg|center|link=]] | + | [[File:law_of_distr_1a.svg|center|link=]] |
| | TAGS: | | TAGS: |
| | <PGFTikZPreamble> | | <PGFTikZPreamble> |
| | | | |
| | </PGFTikZPreamble> | | </PGFTikZPreamble> |
| − | \begin{tikzpicture}[font=\footnotesize,scale=0.9] | + | \begin{tikzpicture}[font=\footnotesize] |
| | \draw[gray!50,rounded corners=2pt,fill=cyan!7] (-1.5,-0.45) rectangle (1.5,0.45); | | \draw[gray!50,rounded corners=2pt,fill=cyan!7] (-1.5,-0.45) rectangle (1.5,0.45); |
| − | \node[scale=0.9] (eq) at (0,0) {$a(b+c) = a \g b + a \g c $}; | + | \node[scale=1] (eq) at (0,0) {$a(b+c) = a \t b + a \t c $}; |
| | \draw [->] ($(eq.north west) + (0.18,-0.15)$) to [in=125, out=65,looseness=1.1] ++(0.28,0.05); | | \draw [->] ($(eq.north west) + (0.18,-0.15)$) to [in=125, out=65,looseness=1.1] ++(0.28,0.05); |
| | \draw [->] ($(eq.north west) + (0.18,-0.15)$) to [in=130, out=55,looseness=1] ++(0.74,0); | | \draw [->] ($(eq.north west) + (0.18,-0.15)$) to [in=130, out=55,looseness=1] ++(0.74,0); |
| | \end{tikzpicture} | | \end{tikzpicture} |
| | </PGFTikz> | | </PGFTikz> |
| − | | + | <t1>Om två parenteser multipliceras ihop använder man den s.k. [[utvidgade distributiva lagen *Rules*|utvidgade distributiva lagen]].</t1> |
| − | <translate><!--T:3--> | |
| − | Distributiva lagen kan visas geometriskt. I rektangeln är höjden 4 och basen $(2+3).$ Den totala arean är '''lika stor''' oavsett om rektangeln är uppdelad eller ej.</translate>
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| − | | |
| − | <jsxgpre id="distributiva435">
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| − | var b = mlg.board([-1,5,7.1,-1],{grid:false});
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| − | var p1,p2,p3,p4,p5,p6,p7,p8,pol1,pol2,t,t2,t3,t4,t5,t6,s1,s2,s3,s4,s5,s7,s8,plus;
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| − | var sT = [];
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| − | mlg.af("distributiva435.start", function(){
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| − | for (var i = 0;i < sT.length; i++){
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| − | clearTimeout(sT[i]);
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| − | }
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| − | | |
| − | ready=true;
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| − | b.remove();
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| − | p1 = b.node(0,0);
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| − | p2 = b.node(0,4);
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| − | p3 = b.node(2,4);
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| − | p4 = b.node(2,0);
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| − | p5 = b.node(2,0);
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| − | p6 = b.node(2,4);
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| − | p7 = b.node(5,4);
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| − | p8 = b.node(5,0);
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| − | b.segment([0,1],[2,1],{strokeWidth:0.5,opacity:0.2});
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| − | b.segment([0,2],[2,2],{strokeWidth:0.5,opacity:0.2});
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| − | b.segment([0,3],[2,3],{strokeWidth:0.5,opacity:0.2});
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| − | b.segment([0,4],[2,4],{strokeWidth:0.5,opacity:0.2});
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| − | b.segment([1,4],[1,0],{strokeWidth:0.5,opacity:0.2});
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| − | b.segment([2,4],[2,0],{strokeWidth:0.5,opacity:0.2});
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| − | s1 = b.segment([2,1],[5,1],{strokeWidth:0.5,opacity:0.2});
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| − | s2 = b.segment([2,2],[5,2],{strokeWidth:0.5,opacity:0.2});
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| − | s3 = b.segment([2,3],[5,3],{strokeWidth:0.5,opacity:0.2});
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| − | s4 = b.segment([3,0],[3,4],{strokeWidth:0.5,opacity:0.2});
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| − | s5 = b.segment([4,0],[4,4],{strokeWidth:0.5,opacity:0.2});
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| − | s7 = b.segment([2,0],[2,4]);
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| − | s8 = b.segment([3,0],[3,4]);
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| − | b.opacity([s7,s8],0);
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| − | b.fadeOut([s7,s8]);
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| − | pol1 = b.polygon([p1,p2,p3,p4],{fillcolor:mlg.tiny,opacity:0.5});
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| − | pol2 = b.polygon([p5,p6,p7,p8],{opacity:0.5});
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| − | pol1.borders[2].visProp.visible = false;
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| − | pol2.borders[0].visProp.visible = false;
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| − | b.board.update();
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| − | t = b.text(2.5,4.5,'\\text{Area}=4(2+3)=20',{fontsize:1.3});
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| − | t2 = b.text(2.5,2,'4(2+3)',{fontsize:1.3});
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| − | t3 = b.text(5.5,2,'4',{fontsize:1.3});
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| − | t4 = b.text(2.5,-0.5,'(2+3)',{fontsize:1.3});
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| − | t5 = b.text(2,-0.5,'2',{fontsize:1.3,opacity:0});
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| − | t6 = b.text(3,-0.5,'3',{fontsize:1.3,opacity:0});
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| − | plus = b.text(2.5,2,'+',{fontsize:1.3,opacity:0});
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| − | });
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| − | mlg.af("distributiva435.animate", function(){
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| − | if(ready===true){
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| − | ready=false;
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| − | sT[0] = setTimeout(function(){b.remove(t2);
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| − | b.fadeOut(t4);
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| − | b.fadeIn(t5);
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| − | b.fadeIn(t6);
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| − | b.translate([pol2,s1,s2,s3,s4,s5,t3],1,0,1000);
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| − | b.translate(t6,1.5,null,1000);
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| − | b.translate(t5,-1,null,1000);
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| − | b.fadeOut(t,100);
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| − | },100);
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| − | sT[1] = setTimeout(function(){
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| − | b.text(4.5,2,'4\\cdot3',{fontsize:1.3});
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| − | var t3= b.text(1,2,'4\\cdot2',{fontsize:1.3});
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| − | b.fadeIn(t,700);
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| − | t.moveTo([3,4.5]);
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| − | b.changeText(t,'\\text{Area}=4\\cdot2+4\\cdot3=20');
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| − | b.opacity([s7,s8],1);b.fadeIn([s7,s8]);
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| − | b.fadeIn(plus);
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| − | b.fadeIn(t5);
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| − | b.fadeIn(t6);
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| − | },1100);
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| − | }
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| − | });
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| − | mlg.cf("distributiva435.start");
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| − | b.node(0,5);
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| − | b.node(6,-1);
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| − | b.cropB(0.1);
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| − | </jsxgpre>
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| − | | |
| − | <div class='jsx-btn-container'>
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| − | <jsxbtn onclick='mlg.cf("distributiva435.animate")'><translate><!--T:4-->
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| − | Multiplicera in 4</translate></jsxbtn>
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| − | <jsxbtn onclick='mlg.cf("distributiva435.start")'><translate><!--T:5-->
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| − | Återställ</translate></jsxbtn>
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| − | </div> | |
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| | [[Kategori:Algebra]] | | [[Kategori:Algebra]] |
