Monday, October 12, 2009
Learn The Math - Part 1
Saving Money Tip #197 - Learn The Math – Part 1. I know many people groan when they hear the word “math.” Something about numbers seems very overwhelming for some people. While I might sound like an elementary school math teacher, I have to say, if you don’t understand some fundamental math skills, then it is time to learn them. I am not talking about higher order math here – no geometry, trigonometry or calculus – just basic bath. Learning these basic skills will help you in saving money. For example, calculating percentages are important to figuring out sales prices and stock price changes. Being able to do division helps you figure out price per unit on items you are purchasing. Being able to calculate fractions allows you to double, triple, or halve recipes. Understanding multiplication can help you figure out interest rates and how much your money will be worth in the future on bank CDs.
So let’s learn the math. First up is calculating percentages. Let’s say you walk into a store with two coupons – one for $5 off any $15 item and one for 20% off any one item and. You see a teapot you need (and you cannot find one at the thrift store) for $20. Is it better to use the $5 off coupon or the 20% coupon? Let’s see. Obviously, the $5 off coupon will result in the teapot costing $15. The math is $20 - $5 = $15. But how about the 20% off coupon? Do you remember how to calculate percentages? The mathematical way to do it is move the decimal point of the percentage two places to the left. So 20% would become .20. (Remember 20% is 20.00% so the decimal place is at the end of the whole number). Now we take .20 and multiply it by $20. Do the long multiplication. (Multiplying 20 x .20, the first line is 00. The second line is 400. Add them together to get 400 and then move the decimal point two places to the left because there are two decimal places in the original number.) We come up with 4 or $4. Subtract $4 from $20 and we get $16. So clearly, the $5 coupon is more worth it in this case.
Now unless you bring a calculator with you to the store, which you could do, you might not have the time or materials to write out the problem on a piece of paper. How about we calculate a percentage a quick and dirty way? Did you know you can generally figure out percentages by dropping off the last digit or two digits of the number? When taking 10% of a number, you can generally drop off the last digit. For example, 10% of $200 is $20. 10% of $50 is 5. See all I did was drop off the last digit. But that only works perfectly if the last digit is 0 (zero). If the last digit is anything but 0 (zero) then you will only get an approximate percentage or you can use a fraction to get the exact percentage. Ten percent of 205 is not exactly 20. It’s actually 20.5. Ten percent of $518 is $51.8 or $51.80. (Remember the long way to do this would be to take the percentage and move the decimal two places to the left so 10% becomes .10. Then multiply .10 by $518 and voila you get the same number I did as in the quick and dirty way – $51.80.) Luckily in stores, most items are rounded to the dollar or if they are priced at $4.99 you can just pretend it’s $5.00 to do the quick and dirty percentages.
Okay, so figuring out 10% is easy. But how about we want to do 20% or 15% or 45%? Well 20% is just dropping off the last digit and doubling. So in our example above, 20% of $200 is $40 (start with $200, drop the last digit so that it’s $20 and then multiply by 2 or double to get $40). Twenty percent of $50 is $10 (drop the last digit to get $5 and then multiply by 2 to get $10). Forty percent would be four times the 10% number. So 40% of $200 is $20 x 4 or $80. Forty percent of $50 is $5 x 4 or $20. Easy, huh? Now let’s say you want to figure out 5% of something. Just take half of the 10% number. Five percent of $200 is half of the 10% figure. So drop the last digit and then divide by two or cut in half. So you have $200 and drop the last digit to get 10% or $20 and then divide by 2 to get $10. So 5% of $200 is $10. If you need to figure out 25%, which is a common sales figure then double the 10% figure and then add half the 10% figure. Twenty-five percent of $200 is $40 (20%) + $10 (5%) or $50. See, I doubled the 10% figure ($20) to get 20% ($40) and then I took half of the 10% figure ($20) to get the 5% ($10) and then added them together.
Generally in stores there usually isn’t less than a 10% sale or sales for odd numbers other than those ending in 5s – such as 25%. But sometimes there are rebates of 1% or 3% or sales of 1/3 off which is 33.3% off. And for sake of being complete, let’s figure out how to figure out 1% of something and more. Remember, I said that the quick and easy way to figure out percentages is to drop the last digit or two digits. Well, we’ve seen we drop the last digit, in general, to figure out 10%. To figure out 1%, we drop the last two digits. So 1% of $200 is $2. One percent of $50 is uh oh, we only have two digits. Okay, let’s do these smaller numbers another way. To get 1% of smaller numbers take 10% off first. 10% of $50 is $5. To get 1%, move the decimal one digit to the left to get .5 or 50 cents in money terms. So 1% of $50 is 50 cents. Let’s try another small number like $3.50. Ten percent of $3.50 is 35 cents or .35. So 1% of $3.50 is 3.5 cents. I just moved the decimal point from .35 one digit to the left to get 3.5.
If you want to check your work, just remember that 10% of something is a number divided by 10. So there would be 10 equal parts to get to the original number. I like to think of it in terms of money. 10% of $2.00 is 20 cents. If we did 20 cents 10 times we’d come up with the original $2.00. Ten percent of $1.00 is ten cents or .10. And there are 10 dimes in a dollar. To get 1% of something, divide by 100. That is, 1% times 100 is the original number. There are 100 pennies in a dollar. And 1% of $1.00 is 1 cent or .01. Twenty-five percent of something is also the same as taking one quarter of it or ¼ of a number of dividing by 4. Just like a quarter is 25% of a dollar (.25 x $1.00 = 25 cents). Twenty-five percent of $50 is $12.50. If we did $12.50 four times then we’d come back with our original $50. Of if we divided 200 by 4 we'd get 50. It’s all very logical. And if you practice with percentages over and over, it will become second nature to you, that you won’t even need a calculator or pencil and paper. Good luck!
In Real Life (IRL) – I’ve droned on and on about numbers, that you probably don’t want to hear about any real life stories. So suffice it to say that I am a math geek and always loved figuring out easy ways to come up with the correct answers in math class. I think I like it so much because there is only one correct answer to mathematic problems. And if I can go back and check my work like I did in the last paragraph above then I can be confident I did the problems correctly.
Recently I was in Old Navy exchanging a birthday gift my son received. I happened to time it when they were having a big sale. And while I was waiting in line the person in front of me had a couple of coupons. And it was one of those either/or scenarios that I addressed earlier. She was able to get 20% off an item or a certain dollar amount off an item. And I cringed when the person behind the front desk had to ask the other person behind the desk which one was better for this woman to use. She could not figure out the percentage problem. Actually, that is what gave me the idea for this post. I figured if the two people behind the desk and the person using the coupon were having trouble doing this math, that there were probably a lot more people out there who have trouble with percentages. And, it really is a good skill to know off the top of your head to make wise decisions in your purchases. If I didn’t explain anything clearly, please ask me in the comments. In the next post, we’ll do some other math problems to help us save money.