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Did you enjoy our last set of <\/span>GRE Math Misconceptions<\/span><\/a>? Here are four more to watch out for.<\/span><\/p>\n Mistake:<\/b> If you raise a negative number to a negative exponent, the answer will definitely be negative.<\/span><\/p>\n Fact: <\/b>Weirdly enough, a negative number with a negative exponent can come out positive. Check out this expression:<\/span><\/p>\n To simplify it, remember that a negative exponent is \u201cshorthand\u201d for an exponent in the bottom of a fraction. This is what the expression really means:<\/span><\/p>\n What happens when you raise -2 to the 4<\/span>th<\/span> power?<\/span><\/p>\n The answer comes out positive. \u00a0<\/span><\/p>\n Why?: <\/b>All that matters is whether the exponent is even or odd. If the exponent is even, the result will always be positive. That\u2019s true even if the exponent is a <\/span>negative<\/span><\/i> even number. When you see a negative number and a negative exponent, don\u2019t automatically assume that the answer will be negative too. Check whether the exponent is odd or even first. <\/span><\/p>\n \u00a0<\/p>\n Mistake: <\/b>-1\/3 is smaller than -1\/2. <\/span><\/p>\n Fact: <\/b>-1\/3 is actually greater than -1\/2. <\/span><\/p>\n Why?: <\/b>Draw a number line:<\/span><\/p>\n On a number line, numbers to the left are always smaller than numbers to the right. Counterintuitively, since -1\/2 is to the left of -1\/3, -1\/2 is smaller. (A quick way to check this is to decide which one should be further away from zero.) So, if you\u2019re writing an inequality, it should look like this: <\/span><\/p>\n This is a good example of something that might seem clear now, but that can easily trick you if you\u2019re working quickly. If you\u2019re comparing negative numbers on the GRE, especially negative fractions, consider drawing a quick number line. At the very least, slow down for a moment!<\/span><\/p>\n \u00a0<\/p>\n Mistake:<\/b> There are 12 numbers between 8 and 20, inclusive. (By the way, \u2018inclusive\u2019 just means \u2018including the numbers at the ends,\u2019 which are 8 and 20 themselves.) \u00a0<\/span><\/p>\n Fact: <\/b>There are actually 13 numbers in that range. To be completely certain, count them: <\/span><\/p>\n 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20<\/strong><\/p>\n Why?: <\/b>The issue arises when you just subtract 8 from 20 and get 12. Just subtracting doesn\u2019t give you the right number of terms. You need to add 1 to whatever you got. <\/span><\/p>\n To see why this happens, go back to the number line. Place a token on every integer from 1 to 20:<\/span><\/p>\n When you subtract 8 from 20, that\u2019s the equivalent of removing the first 8 tokens:<\/span><\/p>\n When you do that, though, you don\u2019t have tokens on the numbers from 8 to 20, inclusive! You\u2019re actually missing one token: the one that\u2019s supposed to be on 8. That\u2019s why your result will turn out 1 too low. When you subtracted, you \u2018removed\u2019 one too many tokens.<\/span><\/p>\n \u00a0<\/p>\n Mistake: <\/b>To find the solution to this equation: <\/span><\/p>\n x<\/em> (<\/span>3x<\/em> – 1)\u00a0<\/span>= 8x<\/em><\/span><\/p>\n Start by dividing both sides of the equation by <\/span>x<\/span><\/i>. <\/span><\/p>\n Fact: <\/b>Hold on! The equation actually has two solutions: x<\/em> = 3, <\/span>and<\/span><\/i> x<\/em> = 0. But if you start by dividing both sides by x<\/em>, you only find the first solution. That could cause you to miss the right answer. <\/span><\/p>\n Why?: <\/b>On the GRE, you\u2019re never allowed to divide by 0. Since x<\/em> is a variable, you don\u2019t know <\/span>what<\/span><\/i> it equals: it could be 5, 100, -3, or even 0. If you divide by x<\/em>, you could be dividing by 0 accidentally. That\u2019s an \u2018illegal move\u2019 and will cause your math to come out wrong. <\/span><\/p>\n To avoid accidentally dividing by 0, don\u2019t divide both sides of an equation by a variable unless you\u2019re sure it doesn\u2019t equal 0. Instead, simplify using addition, subtraction, and multiplication: <\/span><\/p>\n x<\/em> (<\/span>3x<\/em> – 1)\u00a0<\/span>= 8x<\/em><\/span><\/p>\n 3<\/span>x<\/span><\/em>\u00b2 <\/span>– x<\/em> = 8x<\/em><\/span><\/p>\n 3<\/span>x<\/span><\/em>\u00b2 <\/span>– 9x<\/em> = 0<\/span><\/p>\n x<\/em> (<\/span>3x<\/em> – 9)\u00a0<\/span>= 0<\/span><\/p>\n Now, either x<\/em> equals 0, or 3x<\/em> \u2013 9 equals 0 (in which case x<\/em> is 3). ?<\/span><\/p>\n See that \u201cSUBSCRIBE\u201d button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!<\/i><\/b><\/p>\n Chelsey Cooley<\/a> Did you enjoy our last set of GRE Math Misconceptions? Here are four more to watch out for.<\/p>\n","protected":false},"author":127,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,474284,921840,6,7,733451,9,733445],"tags":[1362555],"yst_prominent_words":[1362656,1362654,1362643,1362644,1362646,1362648,1362658,1362659,1362657,1362649,1362652,1362650,1362645,1362651,1362647,1362653,1362642,1362641],"class_list":["post-12071","post","type-post","status-publish","format-standard","hentry","category-challenge-problems","category-current-studiers","category-gre-prep-2","category-gre-strategies","category-how-to-study","category-life-hacks","category-math-gre-strategies","category-study-tips-2","tag-gre-math-misconceptions"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/users\/127"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/comments?post=12071"}],"version-history":[{"count":3,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12071\/revisions"}],"predecessor-version":[{"id":12091,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/posts\/12071\/revisions\/12091"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/media?parent=12071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/categories?post=12071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/tags?post=12071"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gre\/wp-json\/wp\/v2\/yst_prominent_words?post=12071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"Manhattan](\"https:\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2018\/10\/cc-81-image-1.png\")
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\n![\"Chelsey](\"https:\/\/cdn2.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2015\/11\/chelsey-cooley-150x150.jpg\" "\\"Chelsey")
<\/a>\u00a0is 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 170Q\/170V on the GRE.\u00a0<\/em><\/i>Check out Chelsey\u2019s upcoming GRE prep offerings here<\/a>.<\/em><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"