{"id":6124,"date":"2013-07-09T05:30:54","date_gmt":"2013-07-09T05:30:54","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6124"},"modified":"2014-12-02T08:26:59","modified_gmt":"2014-12-02T08:26:59","slug":"math-basics-a-review-of-division","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-basics-a-review-of-division\/","title":{"rendered":"Math Basics: A Review of Division"},"content":{"rendered":"

Overview:\u00a0 What Is Division?<\/strong>
\nDivision is the inverse of multiplication.\u00a0 For example, 20\/5 =4, because 4 X 5 = 20.\u00a0 Expressed in terms of a mathematical definition, for any whole number s, when s does not equal zero, r\/s = z only if r = s X z.\u00a0 The number that is the answer is called the quotient, the number that is being divided by is the divisor, and the number that is being divided into is the dividend.\u00a0 In 20\/5 =4, 4 is the quotient, 5 is the divisor, and 20 is the dividend.\u00a0 Solving a division problem involves multiplication and subtraction, whether it is short division (the divisor is a one-digit number), or long division (the divisor is two digits or above).<\/p>\n

Division as Repeated Subtraction<\/strong>
\nThere are two separate models of division.\u00a0 Divide 20 by measuring off sets of 5, and there are 4 groups of 5.\u00a0 Division on the abacus uses the measurement method of division, measuring the sets of the divisor and then subtracting them until the smallest possible remainder is left.\u00a0 (If the number is 20\/5 , the answer will be 4 with no remainder.)\u00a0 This method can also be demonstrated using a calculator.\u00a0 For example 300-24=276-24=252-24=228-24=204-24=180-24=156-24=132-24=108-24=84-24=60-24=36-24=12, or 300\/24 = 12 remainder 12, or 12 12\/24 or 12.5.<\/p>\n

The Division Algorithm<\/strong>
\nWhether division is long or short, the algorithm is the same.\u00a0 It involves multiplying the divisor by a number that is close to the dividend and subtracting the product from the dividend until the remainder is smaller than the divisor, or until there’s nothing left to subtract.\u00a0 For example, in 300\/24, 300-240 (10 X 24) =60-48 (2 X 24) =12, so the quotient is 12 remainder 12 or 12.5.\u00a0 To check, multiply 12.5 X 24 =300.\u00a0 Alternatively, multiply 12 X 24= 288, and add 12 to equal 300.<\/p>\n

Another Method for Long Division<\/strong>
\nAnother method for long division multiplies each digit of the divisor separately, subtracts, and then adds like products, using place value.\u00a0 In this method 300\/24 = 12.5 , because the divisor 24 equals 20 +4.\u00a0 Multiplying 20 X 4 by 10 gives 200 (10 X 20) + 40 (10 X 4).\u00a0 300-240 = 60.\u00a0 The largest multiple of 20 + 4 that will divide into 60 is 48 or 40 (2 X 20) + 8 (2 X 4).\u00a0 The same remainder of 12\/24 is still there in this problem.\u00a0 This method has the advantage of dividing by one digit at a time, but it is way more cumbersome than the modern method.<\/p>\n

Why Not Divide by Zero?<\/strong>
\nAll numbers multiplied by zero equal zero.\u00a0 Therefore, there isn’t any unique number that will give a meaningful answer.\u00a0 If 24 X 0 = 0 and 3 X 0 =0, 24 does not equal 3.\u00a0 Using the definition of division as the inverse of multiplication, dividing by zero is completely meaningless.<\/p>\n

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Overview:\u00a0 What Is Division? Division is the inverse of multiplication.\u00a0 For example, 20\/5 =4, because 4 X 5 = 20.\u00a0 Expressed in terms of a mathematical definition, for any whole number s, when s does not equal zero, r\/s = z only if r = s X z.\u00a0 The number that is the answer is […]<\/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":[11],"tags":[82,529,530,969,1529],"class_list":["post-6124","post","type-post","status-publish","format-standard","hentry","category-math-fundamentals","tag-algorithms","tag-division","tag-division-by-zero","tag-inverse","tag-repeated-subtraction"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6124","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=6124"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6124\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}