{"id":4528,"date":"2013-06-29T06:38:38","date_gmt":"2013-06-29T06:38:38","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4528"},"modified":"2025-12-08T13:37:07","modified_gmt":"2025-12-08T19:37:07","slug":"proportions-in-the-real-world","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/proportions-in-the-real-world\/","title":{"rendered":"Proportions in the Real World"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_5aq7a7EUyPE\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_5aq7a7EUyPE\" data-source-videoID=\"5aq7a7EUyPE\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Proportions in the Real World Video\" height=\"720\" width=\"1280\" class=\"size-full\" data-matomo-title = \"Proportions in the Real World\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_5aq7a7EUyPE:hover {cursor:pointer;} img#videoThumbnailImage_5aq7a7EUyPE {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/04\/proportions-in-the-real-world-thumb.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_5aq7a7EUyPE\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_5aq7a7EUyPE\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Proportions in the Real World\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5aq7a7EUyPE\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5aq7a7EUyPE\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_5aq7a7EUyPE\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Proportions can be very helpful in solving many real-world problems. Just be sure that when you set up your proportion, you&#8217;re consistent in both your ratios. <\/p>\n<p>Let&#8217;s look at this problem:<\/p>\n<h3>Solving Proportions Example<\/h3>\n<p>\nSuppose Hannah makes $10 per hour pulling weeds for a neighbor. How much money would she make if she were to work for 12 hours? <\/p>\n<p>So what we&#8217;re trying to determine is how much money she would make if she worked in 12 hours. And the information we already have is that she&#8217;s going to make $10 just by working one hour ($10 per hour).<\/p>\n<p>So we can set up a proportion with the amount of money she makes divided by the time, or the hours, spent working. <\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(\\frac{\\text{money}}{\\text{time}}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>So again, we know that she makes $10 in one hour. So as we set up our proportion, again, it&#8217;s very important to be consistent!<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(\\frac{\\text{money}}{\\text{time}}=\\frac{10}{1}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>So if in our first ratio, we&#8217;re going to put &#8220;dollars per hour,&#8221; then our other ratio needs to also be set up as &#8220;dollars per hour,&#8221; And since the money is what we don&#8217;t know, how much money would she earn, we don&#8217;t know the dollars so there we can put a variable, divided by, and then in 12 hours, so that&#8217;s our time.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(\\frac{\\text{money}}{\\text{time}}=\\frac{10}{1}=\\frac{x}{12}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>So with both ratios, we&#8217;ve put our money divided by the time. Now that we&#8217;ve set up our proportion, we can solve it by using cross products, or just by cross multiplying.<\/p>\n<p>We&#8217;re going to multiply \\(1\\times x\\), which is just \\(x\\), equals \\(10\\times 12=120\\). <\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x=120\\)<\/div>\n<\/blockquote>\n<p><\/center><\/p>\n<p>Therefore, she would make $120 by working 12 hours.<\/p>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4528","1":"page","2":"type-page","3":"status-publish","5":"page_category-math-advertising-group","6":"page_category-ratios-and-proportions","7":"page_type-video"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4528"}],"version-history":[{"count":4,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4528\/revisions"}],"predecessor-version":[{"id":254905,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4528\/revisions\/254905"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}