| I had my own math shortcuts when I was a | | | | mind immediately focuses on the 9. Why? |
| child. Using these meant that I didn't "show | | | | Because it is close to 10, and multiplying by |
| my work" in math class, as was required. This | | | | 10 is easy. 68 x 10 is 680, from which I just |
| annoyed many of the teachers, and lowered my | | | | have subtract the extra 68 to arrive at the |
| grades. I did get the correct solutions to my | | | | solution of 612. Always look for the numbers |
| math problems, however. I was simply using | | | | that are close to 10 or 100 or 1000, and |
| different algorithms, ones which I had a hard | | | | you'll find the easier way to do the math, |
| time expressing on paper. | | | | especially if you are trying to do it in your |
| | | | head. |
| In my thinking, for example, 97 x 16 became | | | | |
| 100 x 16 (1600) minus 3 x 16 (48). It was | | | | Percentages can be trickier to do as mental |
| easier that way, and thinking this way became | | | | math, but there are ways. Suppose, for |
| almost automatic. As a result, I might just | | | | example, that you want to figure what the |
| write down 1552 even though I couldn't | | | | 4.6% sales tax will amount to on your $29 |
| explain very well how I arrived at the | | | | book. One quick way to estimate it is to take |
| answer. My teachers called that a problem, | | | | 10%, or $2.90, cut that in half to arrive at |
| but many years later such math shortcuts were | | | | 5%, or $1.45, and then just guess at around |
| being sold in seminars and books. | | | | $1.35, because you know 4.6% is a little less |
| | | | than 5%. Alternately, you could think of 5% |
| Making Your Own Math Shortcuts | | | | as a 20th of the price - if this is easier - |
| | | | and then round that figure down a bit. |
| You can make your own math shortcuts. The | | | | |
| following may give you some ideas on how to | | | | What if you want a more precise solution? 1% |
| do that. Alternately, you can try any of the | | | | of $29 is easy to arrive at (.29), so |
| shortcuts and algorithms you read about and | | | | multiply that by 4 to arrive at $1.16. (You |
| adopt the ones that are best suited to you. | | | | might think of this as (4 x 30) - 4.) Now you |
| There are no perfect techniques for all | | | | just need to add .6% to that. Think 6 x 29 = |
| people, because our minds work in slightly | | | | 174, and then put the decimal in the right |
| different ways. | | | | place: .174. Add that .18 (round it up as the |
| | | | store will likely do) to the 1.16 and you |
| For example, suppose you want to multiply 68 | | | | have $1.34 in sale's tax, pretty close to our |
| x 6. My mind immediately thinks "60 x 6 = 360 | | | | quick estimate. This is not as difficult as |
| and 8 x 6 = 48, and 360 + 48 is 408." That is | | | | it might seem once you practice these |
| one way to quickly arrive at a solution | | | | shortcuts a bit. |
| without pen and paper. It is essentially | | | | |
| this: (60 x 6) + (8 x 6) = 408. | | | | These simple methods do require a basic |
| | | | understanding of math. If you don't |
| Want another way? Think of it as (70 x 6) - | | | | understand that 123 multiplied by 199 is just |
| (2 x 6). The "internal dialog" might be | | | | adding 123 to itself 199 times - that |
| something like this: "70 x 6 = 420, but that | | | | multiplication is just another way to do |
| is two "sixes" too many, so take away two | | | | addition - you will have problems with these |
| sixes (12) and I have 408." The point is that | | | | math shortcuts. In that case, you may want to |
| there is often more than one way, and you can | | | | simply use the easiest math shortcut of all - |
| use whichever math shortcut is easier for | | | | a calculator. |
| you. | | | | |
| | | | Oh and the solution to that last one is |
| If the problem was 68 x 9, by the way, my | | | | 24,477. And yes, I did do that in my head. |