{"id":6495,"date":"2013-12-12T19:30:11","date_gmt":"2013-12-12T19:30:11","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6495"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"ratios-and-proportions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/ratios-and-proportions\/","title":{"rendered":"Ratios and Proportions"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Ratios and proportions are common ways to compare numbers.\u00a0 They have many mathematical applications, such as scale models, percentages, and interest.\u00a0 Ratios and proportions can be set up with variables, and solved for those variables.<\/p>\n

What Is a Ratio?<\/strong><\/p>\n

A ratio is a comparison of two numbers by division, and can be expressed in three different ways.\u00a0 Suppose there are 2 blue marbles in a jar to every 3 red marbles.\u00a0 That ratio of blue marbles to red marbles could be expressed as 2 to 3, 2:3, or the fraction 2\/3. The fractional form is the one most often used in equations.<\/p>\n

What Is a Rate?<\/strong><\/p>\n

In a ratio, the units must be the same, as the ratio of 6 grams to 11 grams.\u00a0 In a rate, the units are different, such as 40 miles per gallon, or 13 feet per second.\u00a0 Many problems that involve rates can be set up comparing proportions.<\/p>\n

What Is a Proportion?<\/strong><\/p>\n

A proportion states that two ratios are equal, such as 2\/3 = 4\/6.\u00a0 Proportions have a useful property that can be used to solve equations when one of the values is unknown, called the means-extremes property of proportions.\u00a0 In algebraic terms, if a\/b equals c\/d, then ad = bc.\u00a0 That can be tested in the above example, as 2(6) = 4(3).<\/p>\n

Solving Proportions with Algebra<\/strong><\/p>\n

If a set of proportions contains a variable, it can be turned into an equation and solved using the means-extremes property and cross multiplying.\u00a0 Suppose the problem were 3\/15 = b\/45.\u00a0 Then it could be turned into an equation by cross multiplying, so that 3(45) =15b, or 135 = 15b, or 135\/15 = b =9.\u00a0 If the problem were x\/5 = (x + 3)\/10, then 10x = 5(x + 3), or 10x = 5x + 15.\u00a0 Subtracting 5x from both sides, 10x-5x = 5x-5x +15, or 5x = 15, or 5x\/5 =15\/5, or x =3.<\/p>\n

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Overview: Ratios and proportions are common ways to compare numbers.\u00a0 They have many mathematical applications, such as scale models, percentages, and interest.\u00a0 Ratios and proportions can be set up with variables, and solved for those variables. What Is a Ratio? A ratio is a comparison of two numbers by division, and can be expressed in […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[13],"tags":[1432,1494],"class_list":["post-6495","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-proportions","tag-ratios"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6495"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6495\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}