{"id":3151,"date":"2012-12-03T10:45:55","date_gmt":"2012-12-03T18:45:55","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=3151"},"modified":"2020-01-15T10:50:16","modified_gmt":"2020-01-15T18:50:16","slug":"doubling-and-halving-trick-for-gmat-math","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/doubling-and-halving-trick-for-gmat-math\/","title":{"rendered":"Doubling and Halving Trick for GMAT Math"},"content":{"rendered":"

\"Doubling<\/p>\n

Learn one of the handiest tricks for math without a calculator! \u00a0<\/strong><\/p>\n

Without a calculator, what is<\/p>\n

1. 35 x 12?<\/p>\n

2. 150 x 36?<\/p>\n

3. 125 x 84?<\/p>\n

On the GMAT, you don\u2019t get a calculator<\/a>. With the doubling and halving<\/strong> trick, all of these become much easier.<\/p>\n

 <\/p>\n

Thinking about multiplication<\/h2>\n

Every positive integer has a unique prime factorization<\/a> — that is to say, there is a unique way to express each whole number as a product of prime factors.\u00a0\u00a0 Therefore, whenever we multiply to positive integers, we can think of this the product of the prime factors of one times the product of the prime factors of the other — two big collections of factors being multiplied together.\u00a0\u00a0 Furthermore, the associative law the commutative law tell us we can multiply in any order — we could even swap around factors from one number to the other, and the overall result of the multiplication would not change.<\/p>\n

Doubling and halving<\/h2>\n

Suppose one factor ends in 5, and suppose the other factor is even.\u00a0 In this case, we know the even factor must be divisible by 2, so we can easily remove a factor of 2 from that one (thereby “halving” it) and multiply the multiple of 5 by 2 (thereby “doubling” it), which will make that one a multiple of ten.\u00a0 In this process, both numbers become simpler, and the multiplication often becomes something you could easily do in your head.<\/p>\n

For example, consider the multiplication 15 x 16.\u00a0 At first glance, that looks not-fun without a calculator.\u00a0 Now, we will perform “doubling and halving.”\u00a0 Remove a factor of 2 from 16, so 16 becomes 8 — it “halves.”\u00a0 Give that spare factor of 2 to 15 — multiply 15 by 2 to get 30.\u00a0 Therefore, 15 x 16 = 30 x 8 = 240.\u00a0\u00a0 After using the doubling-and-halving trick, the problem just becomes one-digit multiplication, with an extra zero along for the ride.<\/p>\n

In the case of 25 x 44, we can do doubling-and-halving once —- 44 becomes 22 and 25 becomes 50 —- to get\u00a0 25 x 44 = 50 x 22.\u00a0 That’s better, but we can do doubling-and-halving again<\/em> —- 22 becomes 11 and 50 becomes 100 —- so that\u00a0 25 x 44 = 50 x 22 = 100 x 11 = 1100.<\/p>\n

Take another look at the problems at the top, and see if you can simplify them with the doubling-and-halving trick before reading the solutions below.<\/p>\n

 <\/p>\n

Practice question<\/h2>\n

Here’s a free GMAT practice question on which you can use this trick.<\/p>\n

4) http:\/\/gmat.magoosh.com\/questions\/331<\/a><\/p>\n

 <\/p>\n

Solutions<\/h2>\n

1) Halve 12, so it becomes 6.\u00a0 Double 35, so it becomes 70.\u00a0 12 x 35 = 6 x 70 = 420<\/strong>.<\/p>\n

2) Halve 36, so it becomes 18.\u00a0 Double 150, so it becomes 300.\u00a0 150 x 36 = 300 x 18 = 5400<\/strong>.<\/p>\n

3) Halve 84, so it comes 42.\u00a0 Double 125, so it becomes 250.\u00a0 125 x 84 = 250 x 42.\u00a0 Now, perform the trick again.\u00a0 Halve 42, so it becomes 21.\u00a0\u00a0 Double 250, so it becomes 500.\u00a0 125 x 84 = 250 x 42 = 500 x 21.<\/p>\n

Now, notice that 21 = 20 + 1, so 500*21 = 500*(20 + 1) = 500*20 + 500<\/p>\n

Apply doubling & halving one more time, 500 to 1000, and 20 to 10:<\/p>\n

500*21 = 500*20 + 500 = 1000*10 + 500 = 10000 + 500\u00a0= 10500<\/strong>.<\/p>\n

No calculator, no problem!<\/p>\n","protected":false},"excerpt":{"rendered":"

Learn one of the handiest tricks for math without a calculator! \u00a0 Without a calculator, what is 1. 35 x 12? 2. 150 x 36? 3. 125 x 84? On the GMAT, you don\u2019t get a calculator. With the doubling and halving trick, all of these become much easier.   Thinking about multiplication Every positive […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[150],"tags":[],"ppma_author":[13209],"class_list":["post-3151","post","type-post","status-publish","format-standard","hentry","category-basics"],"acf":[],"yoast_head":"\nDoubling and Halving Trick for GMAT Math - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"description\" content=\"Did you know that doubling and halving can help you solve GMAT problems quicker and more accurately? 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Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=3151"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/3151\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=3151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=3151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=3151"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=3151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}