{"id":6498,"date":"2013-12-12T19:30:26","date_gmt":"2013-12-12T19:30:26","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6498"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"math-review-of-absolute-value","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/12\/12\/math-review-of-absolute-value\/","title":{"rendered":"Math Review of Absolute Value"},"content":{"rendered":"

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

Number sentences involving absolute value refer to a number’s distance from zero.\u00a0 Absolute value has a number of applications, including measurements and tolerances.\u00a0 It is important to read problems carefully that involve absolute value.<\/p>\n

What is Absolute Value?<\/strong><\/p>\n

The mathematical definition of absolute value is a number’s distance\u00a0 from zero on the number line.\u00a0 It is always a positive number, as the distance from 0 for the number 4 and the number -4 is the same.\u00a0 Multiplying the absolute value of |ab| is the same as |a| \u2219 |b|.<\/p>\n

How To Solve Problems Using the Number Line<\/strong><\/p>\n

A sentence such as |x-3| = 6 can be solved by graphing it on the number line.\u00a0 What the problem means in that the distance between x and 3 is 6 units in either direction.\u00a0 Therefore, one can go forward 6 units from 3 to 9, or backward 6 units, past 0 to -3.\u00a0 The solution set is {-3, 9}, because there are always two values that solve the number sentence, a positive one and a negative one.<\/p>\n

How to Solve Problems Using a Compound Sentence<\/strong><\/p>\n

The sentence |x-3| = 6 actually means two different things, either x -3 = 6 or x-3 = -6.\u00a0 This is also a way to check to make sure the solution set is correct.\u00a0 The sentence x-3 = 6 is solved by the positive 9 and the sentence x -3 = -6 is solved by the negative 3.<\/p>\n

Some Applications of Absolute Value<\/strong><\/p>\n

Absolute value can be applied when the direction of a difference does not matter, just that there is a difference.\u00a0 For example, many parts are manufactured with a tolerance of measurement.\u00a0 For example, a shaft might be measured with a diameter of 10 mm\u00a0 \u00b1 .04 mm.\u00a0 That tolerance could be measured by the sentence |x-10| = .04.\u00a0 As in the above example, there are two sentences within the compound sentence, either x – 10 = .04 or x – 10 = -.04.\u00a0 The shaft could measure as small as 9.96 mm (because 9.96 – 10 = -.04 mm) or as large as 10.04 mm (because 10.04 – 10 = .04 mm).<\/p>\n

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Overview: Number sentences involving absolute value refer to a number’s distance from zero.\u00a0 Absolute value has a number of applications, including measurements and tolerances.\u00a0 It is important to read problems carefully that involve absolute value. What is Absolute Value? The mathematical definition of absolute value is a number’s distance\u00a0 from zero on the number line.\u00a0 […]<\/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":[31,352,1219],"class_list":["post-6498","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-absolute-zero","tag-compound-sentences-in-math","tag-number-line"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6498","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6498"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6498\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}