UC MATH 1A - Chapter 5 Turning Algebra into Arithmetic

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Chapter 5 Turning Algebra into Arithmetic THE PROBLEM WITH ALGEBRA Knowing algebraic manipulation is important for your success on the GRE But the truth is unless you study and work with algebra regularly you re probably much more comfortable with arithmetic Using algebra when you are unfamiliar with it is likely to lead to errors that could have been avoided Let Us Count the Ways A basic appreciation of algebra is crucial for a good quantitative score on the GRE But whenever you have the option you should use arithmetic instead of algebra for a number of reasons Algebra is based on abstract unknowns while arithmetic is a concrete system of numbers you can You started doing arithmetic long before you even knew what algebra was so arithmetic is far more visualize x apples versus 2 apples ingrained in your brain You probably haven t done a lick of algebra in a very long time but you perform some sort of arithmetic every day whether you realize it or not so arithmetic is far more familiar Your calculator can help you with arithmetic calculations but it s useless for algebraic manipulations Some of you out there might think your algebra skills are passable and that you re not worried about making mistakes That may well be but the possibility of a mistake is greatly heightened by the manipulation of algebra and greatly diminished by the use of arithmetic The other bad thing about algebra is that often when you re performing it you can mess something up and not even know it GRE question writers are experts at predicting common mistakes that students will make using algebra They ll use that prediction to create incorrect answer choices to trap those students who made that mistake Plugging In So what should you do to try to avoid algebra as much as possible You should plug in actual numbers Plugging In is a lot like writing your own novel rather than wonder how many candies Phil has in his hand assume the power to write the narrative Decide for yourself how many he has The Steps to Plugging In There are two dead giveaways when you re identifying problems that you can solve using your own numbers The problems often feature the phrase in terms of The answer choices have variables in them 1 Recognize the Opportunity to Plug In If you have variables in the answer choices Plug In If there is an unknown quantity in a problem that cannot be solved for Plug In 2 Set Up Your Scratch Paper Write down letters for each answer choice and any important information from the problem 3 Plug In an Easy Number for the Variable Choose an easy number such as 2 3 5 10 or 100 for one of the variables If the problem gives you certain limitations for the value of the variable such as odd integer larger than 30 be sure to choose a number that follows those limitations If there are multiple variables in a problem see if you can solve for the other variables once you ve plugged in for the first one If you can t Plug In for those variables as well 4 Find Your Target Number Solve the question using your numbers Whatever is asked at the end of the question is your target number It s helpful to write this number down as well as the numbers you used to Plug In so you don t forget them 5 Check All of the Answer Choices Using the numbers that you plugged in for the variable or unknown in the question try out every answer choice You must check every answer Most of the time only one answer choice will work out but if you end up with two or more answer choices that give you your target number plug in a new set of numbers find a new target number and check the remaining answer choices Try an example Here s How to Crack It Look at the answer choices first You should recognize the opportunity to Plug In as soon as you see answer choices like those There are variables in all of our answer choices which means this is a perfect Plug In problem Since our variable is j let s plug in an easy number for Juan s age Let s say Juan is 5 so j 5 Now work through the problem Take it apart piece by piece The first part of the problem states that George is twice as old as Mary which is nice for George and Mary but you know only how old Juan is Leave that part of the problem alone and move on The next part of the sentence states that Mary is three years older than Juan Since Juan is 5 and Mary is three years older than Juan Mary must be 8 If George is twice as old as Mary then George is 16 years old Now you can answer the question If Juan is j years old then in terms of j how old will George be in 10 years Ignore the phrase in terms of Whenever you see that in a problem it is just another sign to Plug In If George is 16 now how old will he be in 10 years He ll be 26 years old so that s the target number Write down 26 and circle it Now check all of the answer choices A 2 5 4 6 Nope Replace j with 5 in each of the answer choices the one that gives you an answer of 26 is the correct answer B C D E 2 5 14 4 Nope 2 5 13 23 Nope 2 5 16 26 Correct 2 5 26 36 Nope Since D is the only answer that yielded the target number of 26 that s the correct answer If you had solved this algebraically you might have added j and 3 then doubled it to 2 j 3 then distributed it to become 2j 6 then added 10 and gotten the right answer But say you forgot to distribute the 2 and 2 j 3 became 2j 3 and you added 10 to get 2j 13 You could have chosen C and moved merrily along unaware of your mistake because ETS anticipated it Instead you solved the problem using only arithmetic that you can double check with your calculator if need be and you avoided all of the traps Try another Here s How to Crack It There are variables in the answer choices so Plug In Choose an easy number to plug in There are 60 minutes in an hour so make the math a little easier by choosing either a factor of 60 such as 30 or a multiple of 60 Plug in y 30 In 60 minutes one machine makes 3 000 golf balls In that case in 30 minutes one machine would make 1 500 golf balls The question asks how many golf balls four machines can make in 30 minutes which is 1 500 4 6 000 golf balls Write down 6 000 golf …


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