50 lines
11 KiB
HTML
50 lines
11 KiB
HTML
|
<!DOCTYPE html><html><head><meta content="text/html; charset=utf-8" http-equiv="Content-Type" /><meta content="width=device-width, initial-scale=1" name="viewport" /><!--replace-start-0--><!--replace-start-5--><!--replace-start-8--><title>The Associative Property of Addition and Multiplication - My Zettelkasten</title><!--replace-end-8--><!--replace-end-5--><!--replace-end-0--><link href="https://cdn.jsdelivr.net/npm/fomantic-ui@2.8.7/dist/semantic.min.css" rel="stylesheet" /><link href="https://fonts.googleapis.com/css?family=Merriweather|Libre+Franklin|Roboto+Mono&display=swap" rel="stylesheet" /><!--replace-start-1--><!--replace-start-4--><!--replace-start-7--><link href="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" rel="icon" /><meta content="Let a, b , c represent members of \mathbb{W} or \mathbb{Z} then:" name="description" /><meta content="The Associative Property of Addition and Multiplication" property="og:title" /><meta content="My Zettelkasten" property="og:site_name" /><meta content="article" property="og:type" /><meta content="Associativity" property="neuron:zettel-id" /><meta content="Associativity" property="neuron:zettel-slug" /><meta content="prealgebra" property="neuron:zettel-tag" /><meta content="theorems" property="neuron:zettel-tag" /><script type="application/ld+json">[]</script><style type="text/css">body{background-color:#eeeeee !important;font-family:"Libre Franklin", serif !important}body .ui.container{font-family:"Libre Franklin", serif !important}body h1, h2, h3, h4, h5, h6, .ui.header, .headerFont{font-family:"Merriweather", sans-serif !important}body code, pre, tt, .monoFont{font-family:"Roboto Mono","SFMono-Regular","Menlo","Monaco","Consolas","Liberation Mono","Courier New", monospace !important}body div.z-index p.info{color:#808080}body div.z-index ul{list-style-type:square;padding-left:1.5em}body div.z-index .uplinks{margin-left:0.29999em}body .zettel-content h1#title-h1{background-color:rgba(33,133,208,0.1)}body nav.bottomPane{background-color:rgba(33,133,208,2.0e-2)}body div#footnotes{border-top-color:#2185d0}body p{line-height:150%}body img{max-width:100%}body .deemphasized{font-size:0.94999em}body .deemphasized:hover{opacity:1}body .deemphasized:not(:hover){opacity:0.69999}body .deemphasized:not(:hover) a{color:#808080 !important}body div.container.universe{padding-top:1em}body div.zettel-view ul{padding-left:1.5em;list-style-type:square}body div.zettel-view .pandoc .highlight{background-color:#ffff00}body div.zettel-view .pandoc .ui.disabled.fitted.checkbox{margin-right:0.29999em;vertical-align:middle}body div.zettel-view .zettel-content .metadata{margin-top:1em}body div.zettel-view .zettel-content .metadata div.date{text-align:center;color:#808080}body div.zettel-view .zettel-content h1{padding-top:0.2em;padding-bottom:0.2em;text-align:center}body div.zettel-view .zettel-content h2{border-bottom:solid 1px #4682b4;margin-bottom:0.5em}body div.zettel-view .zettel-content h3{margin:0px 0px 0.4em 0px}body div.zettel-view .zettel-content h4{opacity:0.8}body div.zettel-view .zettel-content div#footnotes{margin-top:4em;border-top-style:groove;border-top-width:2px;font-size:0.9em}body div.zettel-view .zettel-content div#footnotes ol > li > p:only-of-type{display:inline;margin-right:0.5em}body div.zettel-view .zettel-content aside.footnote-inline{width:30%;padding-left:15px;margin-left:15px;float:right;background-color:#d3d3d3}body div.zettel-view .zettel-content .overflows{overflow:auto}body div.zettel-view .zettel-content code{margin:auto auto auto auto;font-size:100%}body div.zettel-view .zettel-content p code, li code, ol code{padding:0.2em 0.2em 0.2em 0.2em;background-color:#f5f2f0}body div.zettel-view .zettel-content pre{overflow:auto}body div.zettel-view .zettel-content dl dt{font-weight:bold}body div.zettel-view .zettel-content blockquote{background-color:#f9f9f9;border-left:solid 10px #cccccc;margin:1.5em 0px 1.5em 0px;padding:0.5em 10px 0.5em 10px}body div.zettel-view .zettel-content.raw{background-color:#dddddd}body .ui.label.zettel-tag{color:#000
|
||
|
|
async=""
|
||
|
|
id="MathJax-script"
|
||
|
|
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
|
||
|
|
></script>
|
||
|
|
<link
|
||
|
|
href="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/themes/prism.min.css"
|
||
|
|
rel="stylesheet"
|
||
|
|
/><link rel="preconnect" href="https://fonts.googleapis.com" /><link
|
||
|
|
rel="preconnect"
|
||
|
|
href="https://fonts.gstatic.com"
|
||
|
|
crossorigin
|
||
|
|
/><link
|
||
|
|
href="https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans+Condensed:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Serif:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&display=swap"
|
||
|
|
rel="stylesheet"
|
||
|
|
/>
|
||
|
|
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/components/prism-core.min.js"></script>
|
||
|
|
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/plugins/autoloader/prism-autoloader.min.js"></script>
|
||
|
|
<style>
|
||
|
|
body .ui.container,
|
||
|
|
body ul {
|
||
|
|
font-family: "IBM Plex Sans" !important;
|
||
|
|
}
|
||
|
|
body blockquote {
|
||
|
|
border-left-width: 3px !important;
|
||
|
|
font-style: italic;
|
||
|
|
}
|
||
|
|
.headerFont,
|
||
|
|
.ui.header,
|
||
|
|
body h1,
|
||
|
|
h2,
|
||
|
|
h3,
|
||
|
|
h4,
|
||
|
|
h5,
|
||
|
|
h6 {
|
||
|
|
font-family: "IBM Plex Sans Condensed" !important;
|
||
|
|
}
|
||
|
|
body p {
|
||
|
|
line-height: 1.4;
|
||
|
|
}
|
||
|
|
.monoFont,
|
||
|
|
body code,
|
||
|
|
pre,
|
||
|
|
tt {
|
||
|
|
font-family: "IBM Plex Mono" !important;
|
||
|
|
font-size: 12px !important;
|
||
|
|
line-height: 1.4 !important;
|
||
|
|
}
|
||
|
|
</style>
|
||
|
|
<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">The Associative Property of Addition and Multiplication</h1><p><strong>Let <span class="math inline">\(a\)</span>, <span class="math inline">\(b\)</span> , <span class="math inline">\(c\)</span> represent members of <span class="math inline">\(\mathbb{W}\)</span> or <span class="math inline">\(\mathbb{Z}\)</span> then:</strong></p><p><span class="math display">$$ (a + b) + c = a + (b + c) $$</span></p><p><span class="math display">$$ a \cdot (b \cdot c) = (a \cdot b) \cdot c $$</span></p><p>When grouping symbols (parentheses, brackets, braces) are used with the multiplication and addition of whole numbers and integers, the particular placement of the grouping symbols relative to each of the addends or multiplicands does not change the sum/product.</p></div></article><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">prealgebra</span><span class="ui basic label zettel-tag" title="Tag">theorems</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html>
|