33Math NotesWe’ll discuss many of the concepts in this chapter in depth later. But for now, we need a brief review ofthese concepts for many of the problems that follow.1.To compare two fractions, cross-multiply.The larger product will be on the same side as thelarger fraction.Example:Given56vs.67.Cross-multiplying gives5⋅7vs.6⋅6, or 35 vs. 36.Now 36 is largerthan 35, so67is larger than56.2.Taking the square root of a fraction between 0 and 1 makes it larger.Example:14=12and12is greater than14.Caution:This is not true for fractions greater than 1.For example,94=32.But32<94.3.Squaring a fraction between 0 and 1 makes it smaller.Example:122=14and14is less than12.4.ax2≠ax()2.In fact,a2x2=ax()2.Example:3⋅22=3⋅4=12.But3⋅2()2=62=36.This mistake is often seen in the following form:-x2= -x()2.To see more clearly why this is wrong, write-x2= -1()x2, which is negative.But-x()2= -x()-x()=x2, which is positive.Example:-52= -1()52= -1()25= -25.But-5()2= -5()-5()=5⋅5=25.5.1ab≠1ab.In fact,1ab=1aband1ab=ba.Example:123=12⋅13=16.But123=1⋅32=32.6.–(a+b)≠–a+b.In fact, –(a+b) = –a–b.Example:–(2 + 3) = –5.But –2 + 3 = 1.Example:–(2 +x) = –2 –x.7.Memorize the following factoring formulas—they occur frequently on the GRE.A.x2-y2=x+y()x-y()B.x2±2xy+y2=x±y()2C.a(b+c) =ab+acKolby, Jeff, and Derrick Vaughn. GRE Math Bible, Nova Press, 2008. ProQuest Ebook Central, .Created from gmu on 2018-01-28 05:42:58.Copyright © 2008. Nova Press. All rights reserved.