This is a subject that makes many shudder. But why? Unlike language the rules of math have no exceptions, so once the rule is learned it never changes. Whereas language always has an exception to the rule – I before E, except after C, and words like neighbor and weigh, as an example. So why is it not language that is the issue instead? “Ah, but we use language every day, but not that dreaded math.” One could say. And if they did, they would be totally wrong. In fact we probably use math in its simplest form almost as much as language.

Don’t believe me? Okay then, here we go. When you buy that cup of coffee in the morning, you are unconsciously comparing what you have in your pocket, if you are not using either a debit or credit card, to see if indeed you have enough for maybe adding that donut. Or do I have enough gas to make this trip? Hmmm, let’s see. . . I get about this many miles to a gallon so I should be able to cover this distance before I need gas. Or, you have to shop for groceries for the week and is there enough money in the budget to get what I need, and maybe a little left over to get want I want? Then you go to the grocery store with that coupon in hand giving you $1 off if you purchase 2 – 16oz items. Looking you see that by using the coupon your final price for the 2 items would be $4. Then you happen to glance over and see that a single 32oz product is $3.69 saving you an additional 31 cents over the coupon. So you take the deal and put the coupon away for a later time. And of course I could continue on with examples, but there probably is no need. After all we look at spread sheets at work all the time, and what are they doing for us? Let me guess, results from math problems so we can make intelligent decisions.

So this is all in the perspective, and like language we really never think about how much we use such tools. And if you think about it, both math and language are tools. And both have their place and importance. And we in this modern society could not live without either. So I guess that when one looks at it from this point of view, then math is not so dreaded after all. So now that we have that out of the way, it is time to have some fun, and maybe learn a couple of things. Now, I’m the first to admit that I was never any math wiz, and never did very well with higher math. Yet, can I blame it on me, or can I blame it on the way math is taught? It matters not for me but as time has passed me by I learned a few things that makes everyday math easier.

Now, I don’t know about you, but multiplying by 9’s were always a problem. Yet, why? It is almost as easy as 10’s, and easy to check. 9*1=9. 9+0=9. 9*2=18. 1+8=9. 9*3=27. 2+7=9. Now what I am presenting for the 9’s is just that a way to make it easier and has nothing to do with the rules of math. Still there seems to be a pattern developing here. Actually there are 2 patterns. Fist the number to the left of the last number increases by one, and is one less than the number you are multiplying nine by. Second the result of adding the two numbers together is 9, and each time you go up the last number in the answer is one less. So for example if someone said the answer is 45 you would know by the first number that the number that is multiplied by nine is five, and that 4+5=9 confirms that it is a correct answer, and that the next multiple of nine would be what? Why it is 54, because the left goes up one, and the right goes down one. Ah but there appears to be one change to this and the answer is 11*9 giving us an answer of 99. When you add these together you get 18, but it is two numbers and we need only one. So again, if we add 18 we get 9, proving the answer. And that would cover 9’s all the way through the tens and then the last 2 – the elevens and twelves are easy, and this was all we were  required to memorize back in school. To repeat, it would be easy to determine what 9 has been multiplied by,  if one just looked at the first number. An example would this, 6 – that tells us that the number is 7, since 6 is one less that the actual number that was multiplied by 9, then we would know that we would have to add 3 since the total would have to equal 9 giving us 63. See how easy that was?

Now the next number manipulation I want to pass on has to do with what I call the rules of 5’s and 10’s. If you think about it, we can add and subtract easily anything that deals with fives and tens. This applies very well to the handling of money. I taught my children this, and when you first start doing it, it appears to be just too complicated. Yet, if you stick with it, in a short time, your mind will do it instantly without having to think about it at all. Okay, are you ready to stretch your mind? Mentally you  have to begin to look at differences and relationships of the numbers you are dealing with. For example, the position and difference of any number that falls between 10 and 15. How close is this number to either 10 or 15? And once you determine that, this is the number you will work with. Say that number is 13. 13 is 2 away from 15 and 3 away from ten. So we would use 15. We know for example, that to reach 20 is only 5 more away from 15, and it is easy to add 5 if our ultimate goal is 20. Say for example that it is, and you are wanting to know the difference or what you need to reach twenty. First we now know that it is 2 to reach 5 which reflects 15 to 20, and then 2+5=7. this is what we need to reach 20 from 13. I show you this to give you the concept of what we are doing. Okay, you are working a cash register and when the total is presented it states that you need to collect $13.27. The customer gives you a $20, instantly you know that the change would be $6.73, giving you a quick check on what the register says the change should be. And no, I did not grab a calculator to get the change amount shown here. I had the answer instantly, thank you. Here’s the mental manipulation involved: First I view the dollars, 13 to 15, which is 2, and 15 to 20, which is 5, giving me a total of 7. But that does not take the change into account. Since the change takes it above $13, then I now know that the dollar portion of this will be 1 less than the 7 or 6. This allows me to look at the change, and what is due, which is 27 cents. It takes 3 cents to make it 30 cents, and it takes 70 cents to make it $1. So 70+3= 73 cents. Thusly the change to the customer is $6.73. While I know that this is a simple example it works quite well for more complicated transactions or number groups. It just takes a little practice and after a while your mind will do all the manipulations automatically and you will instantly have the correct answer. And there are others, but that is for another blog. And you can have fun with this last one since you see the answer even before the cashier,or you if you are the cashier, sees what the register says you need  to make change.

Published in: on March 24, 2012 at 11:20 am  Comments (2)  
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