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.Aware of his own precocity, Galois noted, I have carried outresearches which will halt many savants in theirs. For over a centurythat proved to be the case.Benj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 122122 Secrets of Mental MathMORE TIPS ON TIPSAs we indicated in Chapter 0, it is easy to figure out tips formost situations.For example, to figure out a 10% tip, wemerely multiply the bill by 0.1 (or divide the bill by 10).Forexample, if a bill came to $42, then a 10% tip would be $4.20.To determine a 20% tip, you simply multiply the bill by 0.2, ordouble the amount of a 10% tip.Thus a 20% tip on a $42 billwould be $8.40.To determine a 15% tip, we have a few options.If you havemastered the techniques of Chapter 2, and are comfortable withmultiplying by 15 5 3, you can simply multiply the bill by15, then divide by 100.For example, with a $42 bill, we have42 15 42 5 3 210 3 630, which when divided by100, gives us a tip of $6.30.Another method is to take the aver-age of a 10% tip and a 20% tip.From our earlier calculation,this would be$4.20 $8.40 $12.60$6.302 2Perhaps the most popular approach to taking a 15% tip is totake 10% of the bill, cut that amount in half (which would be a5% tip), then add those two numbers together.So, for instance,with a $42 bill, you would add $4.20 plus half that amount,$2.10, to get$4.20 $2.10 $6.30Let s use all three methods to compute 15% on a bill that is$67.By the direct method, 67 3 5 201 5 1005,which when divided by 100 gives us $10.05.By the averagingBenj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 123Good Enough: The Art of Guesstimation 123method, we average the 10% tip of $6.70 with the 20% tip of$13.40, to get$6.70 $13.40 $20.10$10.052 2Using the last method, we add $6.70 to half that amount,$3.35 to get$6.70 $3.35 $10.05Finally, to calculate a 25% tip, we offer two methods.Eithermultiply the amount by 25, then divide by 100, or divide theamount by 4 (perhaps by cutting the amount in half twice).Forexample, with a $42 bill, you can compute 42 25 42 55 210 5 1050, which when divided by 100 produces a tipof $10.50.Or you can divide the original amount directly by 4,or cut in half twice: half of $42 is $21, and half of that is$10.50.With a $67 bill, I would probably divide by 4 directly:3since 67 4 16 , we get a 25% tip of $16.75.4NOT-TOO-TAXING CALCULATIONSIn this section, I will show you my method for mentally estimat-ing sales tax.For some tax rates, like 5% or 6% or 10%, thecalculation is straightforward.For example, to calculate 6%tax, just multiply by 6, then divide by 100.For instance, if thesale came to $58, then 58 6 348, which when divided by100 gives the exact sales tax of $3.48.(So your total amountwould be $61.48.)1But how would you calculate a sales tax of 6 % on $58?2Benj_0307338401_4p_c05_r1.r.qxd 5/4/06 1:42 PM Page 124124 Secrets of Mental MathI will show you several ways to do this calculation, and youchoose the one that seems easiest for you.Perhaps the easiestway to add half of a percent to any dollar amount is to simplycut the dollar amount in half, then turn it into cents.For exam-ple, with $58, since half of 58 is 29, simply add 29 cents to the6% tax (already computed as $3.48) to get a sales tax of $3.77.Another way to calculate the answer (or a good mental esti-mate) is to take the 6% tax, divide it by 12, then add those twonumbers.For example, since 6% of $58 is $3.48, and 12 goesinto 348 almost 30 times, then add 30 cents for an estimate of$3.78, which is only off by a penny.If you would rather divideby 10 instead of 12, go ahead and do it.You will be calculating66.6% instead of 6.5% (since 0.6) but that should still be a10very good estimate.Here, you would take $3.48 and add 34¢ toget $3.82.Let s try some other sales tax percentages.How can we calcu-1late 7 % sales tax on $124? Begin by computing 7% of 124.4From the methods shown in Chapter 2, you know that 1247 868, so 7% of 124 is $8.68.To add a quarter percent, youcan divide the original dollar amount by 4 (or cut it in half,twice) and turn the dollars into cents.Here, 124 4 31, soadd 31¢ to $8.68 to get an exact sales tax of $8.99.Another way to arrive at 31¢ is to take your 7% sales tax,7$8.68, and divide it by 28.The reason this works is because281.For a quick mental estimate, I would probably divide $8.684by 30, to get about 29¢, for an approximate total sales tax of$8.97.When you divide by 30, then you are actually computing a7tax of 7 %, which is approximately 7.23% instead of 7.25%.30How would you calculate a sales tax of 7
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