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Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n <\/i><\/b>Here\u2019s a phrase that might bring back some memories from middle school math class: Please Excuse My Dear Aunt Sally, or PEMDAS. (If you went to school outside of the U.S., you may have learned the acronym BEDMAS or BODMAS, instead.) You use this phrase to decide what order to do mathematical operations in: Parentheses first (from inside to outside), then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (also left to right). <\/span><\/p>\n PEMDAS isn\u2019t terribly fancy stuff. It\u2019s just a useful little tool that helps us communicate clearly\u2014it\u2019s what tells us, for instance, that \u201c2x(3+4)\u201d means something different from \u201c2×3 + 4.\u201d But if there\u2019s one thing the GMAT loves, it\u2019s making things look more complicated than they really are. <\/span><\/p>\n Here\u2019s an expression you could see on the GMAT: -24<\/sup><\/span>. It looks simple, but there\u2019s one small problem: there\u2019s no \u201cN,\u201d for \u201cnegative numbers,\u201d in PEMDAS. So, do you deal with the negative sign before or after you handle the exponent? If you handle it first, then you\u2019d raise -2 to the fourth power, which would give you an answer of 16. But if you hold off on it, you\u2019d raise 2 to the fourth power, then make the answer negative, which would give an answer of -16. <\/span><\/p>\n Here\u2019s how to decide: a negative sign is the same thing as <\/span>multiplying a number by -1<\/b>. When you\u2019re simplifying an expression, you handle the negative sign at the same time as you\u2019d handle multiplication. That means it comes <\/span>after<\/span><\/i> the exponent, since M comes after E in the acronym. The right thing to do here is to raise 2 to the 4<\/span>th<\/span> power, <\/span>then<\/span><\/i> make the answer negative. The correct answer is -16. <\/span><\/p>\n You might also see negative numbers in parentheses: (-2)4<\/sup><\/span>. Parentheses come <\/span>before<\/span><\/i> exponents, so you handle the \u201cmultiplication\u201d first. Then you raise -2 to the 4<\/span>th<\/span> power. The answer to this one is <\/span>positive<\/span><\/i> 16. <\/span><\/p>\n How do you simplify this fraction?<\/span><\/p>\n To simplify a complex fraction, you should <\/span>pretend that there are three sets of invisible parentheses<\/b>: a set around the top of the fraction, another set around the bottom of the fraction, and finally, a third set around the entire thing. (By the way, you identify the \u201ctop\u201d and \u201cbottom\u201d of a multi-decker fraction on the GMAT by finding the <\/span>longest, boldest line<\/b> in the fraction.)<\/span><\/p>\n Here\u2019s how this fraction <\/span>really<\/span><\/i> looks:<\/span><\/p>\n Now apply PEMDAS. Simplify everything inside each set of parentheses as much as you can. Note that it\u2019s fine to leave the numerator as an improper fraction. <\/span><\/p>\n Now, divide 3\/2 by 4, since that\u2019s inside the outer set of parentheses:<\/span><\/p>\n Let\u2019s put it all together. Here\u2019s an expression that contains fractions, exponents, and negative numbers. Try simplifying it using PEMDAS.<\/span><\/p>\n Don\u2019t get intimidated by the multi-decker fraction. Find the longest, boldest line first, and split the fraction there:<\/span><\/p>\n Then simplify what\u2019s in the parentheses as much as you can. Let\u2019s work on the numerator first. Be careful with the negatives:<\/span><\/p>\n Next, the denominator:<\/span><\/p>\n Here\u2019s what the original fraction really says:<\/span><\/p>\n The whole thing simplifies to -1. <\/span><\/p>\n Suppose you\u2019re solving an equation like this one:<\/span><\/p>\n 3x \u2014 7 = 20<\/span><\/p>\n What do you do first? You add 7 to both sides. Next, you divide both sides by 3. Addition first, <\/span>then<\/span><\/i> division. But PEMDAS tells you to always divide <\/span>before<\/span><\/i> you add, right? Here\u2019s why this happens. <\/span><\/p>\n E<\/strong>quations<\/b> and <\/span>expressions<\/b> aren\u2019t exactly the same thing. (-2)4<\/sup><\/span>\u00a0is an expression, and so is x\u00b3<\/span>\/x\u00b2<\/span>. On the other hand, 3x-7=20 is an <\/span>equation<\/span><\/i>. Remember this mnemonic: an <\/span>equation<\/b> contains an <\/span>equals<\/b> sign. PEMDAS can be useful when you solve equations, but it\u2019s really meant for expressions. When you\u2019re simplifying an expression, PEMDAS is a hard-and-fast rule. When you\u2019re solving equations, you might do things in a different order, and that\u2019s fine\u2014as long as you understand the arithmetic you\u2019re doing at each step.<\/span><\/p>\n You should learn PEMDAS so well that you rarely need to think about it. (For a lot more practice, check out <\/span>Foundations of GMAT Math<\/span><\/a>.) However, when you run into one of the special cases we\u2019ve gone over in this article, slow down and think about what to do. The GMAT test writers want to overwhelm you and get you to make silly mistakes. But if you memorize some of the special cases here, you\u2019ll greet them with confidence on test day. ?<\/span><\/p>\n Want more guidance from our GMAT gurus? You can attend the first session of any of our online or in-person GMAT courses absolutely free! We\u2019re not kidding. <\/i><\/b>Check out our upcoming courses here<\/i><\/b><\/a>.<\/i><\/b><\/p>\n Chelsey Cooley<\/a> Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We\u2019re not kidding! Check out our upcoming courses here. Here\u2019s a phrase that might bring back some memories from middle school math class: Please Excuse My Dear Aunt Sally, or PEMDAS. (If you went […]<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,873,18,929,874,52871,930,2,8],"tags":[53051],"yst_prominent_words":[],"class_list":["post-13770","post","type-post","status-publish","format-standard","hentry","category-manhattan-gmat-blog-algebra","category-for-current-studiers","category-manhattan-gmat-blog-fdp","category-gmat-prep","category-gmat-resources","category-gmat-strategies","category-gmat-study-guide","category-how-to-study","category-quant-on-gmat","tag-pemdas"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13770","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/127"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=13770"}],"version-history":[{"count":5,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13770\/revisions"}],"predecessor-version":[{"id":13851,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/13770\/revisions\/13851"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=13770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=13770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=13770"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=13770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nPEMDAS and Negative Numbers<\/b><\/h4>\n
PEMDAS and Fractions <\/b><\/h4>\n
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<\/p>\nPEMDAS and Equations<\/b><\/h4>\n
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\n![\"Chelsey](\"https:\/\/cdn2.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2015\/11\/chelsey-cooley-150x150.jpg\" "\\"Chelsey")
<\/a> is a Manhattan Prep instructor based in Seattle, Washington.<\/strong>\u00a0<\/em><\/i><\/b>Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master\u2019s degree in linguistics, a 790 on the GMAT, and a perfect 170\/170 on the GRE.\u00a0<\/em><\/i>Check out Chelsey\u2019s upcoming GRE prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"