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Topic: Mental Math and my job search
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I intend to include this with my resume, certificates and cover letter when applying for teaching positions in physics chemistry or math. It will be printed on card stock 8.5 by 11 inches. The card will be folded in half. This will be on the inside. The the folded card will be used intstead of an envelope. My resume will be folded in half. The bottom of the resume will be taped the bottom of the card with scotch tape. 25% of the way up from the bottom the resume and outer card will be taped together. My certificates will go in that pocket. On top of the Resume and my cover letter will be secured in the same fashion as the resume was secured to outer card stock. The outercard resume and cover letter folded in half will secured with a thin piece of tape on right left and bottom. On the outside of the card stock on the side that does not have the address will be an analysis of an atwood machine. The other side will have the employers adress on the right and my picture on the left.
Mental Math by (name witheld to protect my anonimity on Queen Alice)
Have you ever had difficulty calculate percent off sales, or a tip? In elementary School you learned the value of rounding numbers. My intended audience is professionals who majored in a non math intensive subject. I have been developing these techniques for years after majoring in math and Physics at SUNY Stony Brook and earning a Masters in Physics from Wesleyan University. I did all the math in my head while writing this. With practice you will be able to do these calculations in your head also. However, while you are learning the technique you should use paper and pencil to follow and verify my calculations. Using approximation techniques you can calculate tax or tip valid to 1% o 2% percent. You can also do 3 digit arithmetic, for example 165 x 150 or 144 / 30. Square roots are possible. When asked the square root of 70. I said 8.4. It is even possible to calculate car loan payments.
Suppose you want to buy a pair of jeans. The regular price is $22.95 and they are 10% off. 22.95 is very close to 23. The trick to calculate 10% is move the decimal point. 10% of 23 is 2.3. 23-2.3= 20.7 The original price was $22.95 not $23. If you are concerned that the original price was $22.95 and not $23, ask yourself if a nickel will determine if you buy the jeans. There may be times that you need to know 90% of 22.95 and can’t afford to be off by 0.05. With more effort you can do better. If 10% is 2.3, 1% is 0.23; 0.1% 0.023; 0.2% is twice 0.1%. 0.2% of 23.95 is 0.046 and that is very close to 0.05. Think of 22.95 as 23 – about 0.2%. Let’s subtract 0.2% from 20.7 our preliminary answer. 1% of 20.7 dollars is 20.7 pennies. 0.1% is 2.07 pennies. 0.2% is 4.07pennies. So we need to adjust our answer of 20.7 down 4 pennies. The jeans will cost 20.66. We can do even better but if the vast majority cases it is adequate to correct to 1 part in 10,000.
Suppose the jeans are 20% off. 20% is twice 10%. After you move the decimal point double the result. 20% means you save $5.4. The jeans will cost $17.6. If your dinner came to $22.95 and you want to give a 15% tip, think of 15% as 10% plus 5%. 5% is half of 10%. Half of 2.3 is 1.15. The sum of 2.3 and 1.15 is 3.45. That’s the tip $3.45.
Let’s turn our attention to 165 x 150. If you adopt my techniques you’ll learn the value of knowing 132=169, 142=196, 152=225 … 192=361. Returning to the product of 165 and 150, 150 is 15 x 10. 165 is 1.1(15x10). Now our problem is 15x10x1.1x15x10. Do you remember the commutative property of multiplication? We can change the order that we multiply. 165 x 150 = 1.1 x 152 x 102 = 1.1 x 225 x 100 = 1.1 x 22,500. Now we need to add 10% to 22500. 10% of 22500 is 2250. We add 2250 to 22500 and our answer is 24750.
144/30 is even easier. 144=122. 30=3x10. 144/30 = (12 x 12) / (3 x 10) = (12/3) x (120/10) = 4x12/10 =48/10 = 4.8
I will save calculating square roots and car loan payments for part 2. Please contact me if you want to read part 2.
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