Thursday, May 22, 2014

Edward H. Julius - Rapid Math: Tricks and Tips, 30 Days to Number Power (book review)

Note:  This is a review that's reposted from my Epinions account with a few minor modifications.

I’ve always been impressed by people that could write thousands of words on a topic when I could only get a few hundred. Many of these people knew a lot about the subject and had a lot to offer. I could only do this when I was reviewing something, such as a game, that required a lot of detail. Math is a subject that I know a lot about, so I’m about to reveal how and why some of the tricks work.

While going through the bookcase recently, I came across this book. My brother bought it many, many years ago. He seemed to like it, but hasn’t used it much since he left for college. The book promises greater calculating speed and over 2,000 practice problems. I figured that I’d take a look through it. Presumably, it’s meant to be done over the course of a month, since the subtitle is "30 days to number power". If you made it all the way to high-school math, the book won’t seem that  impressive.

Each day has two tricks. It starts off with multiplying and dividing with zeros. For example, if you have to multiply 50 by 30, remove the zeroes and multiply 5 by 3 to get 15, then put the two zeroes back to get 1500. That’s an entire trick. The next one is about multiplying and dividing with decimals. It’s the same concept with different powers of ten. You should have mastered this before leaving elementary school. Of course, both of these are on the first day. I don’t imagine that it would be a good idea to throw anything too difficult your way so soon.

Many of the ‘tricks’ could be consolidated. For instance, one trick is how to multiply two numbers that differ by 2. Almost a week later, you learn how to multiply two numbers that differ by 4. Both of these tricks rely on the same principle. Lets say you have two numbers, 31 and 29. According to the book, you multiply by the average of the two numbers and subtract 1, thus getting 899. If you have 32 and 28, you multiply the two numbers and subtract 4, thus getting 896. What the book doesn’t explain is that this works for any two numbers. (For the sake of convenience, it's generally only used for whole numbers that differ by an even number.) The rule is that (x+y)(x-y)=x?-y?. It’s just that the larger the difference between the two numbers, the less convenient it becomes. If you look closely, you’ll notice that this rule comes up several times throughout the book.

Look also at the trick for multiplying by 12. The author says to multiply by ten, then to double the amount so that 38 times 12 should be 380+76, which amounts to 456. The trick for multiplying by 11 is similar. To multiply by 11, take the number, split the digits and put the sum of the digits in the middle, carrying if you have to. 59 times 11 is 509+140, or 649. I have news for you: this is how you usually do math. The author is just pointing out two different cases that are easy to do in your head.

Multiplying a two-digit number by 101 is a similar case, where you just repeat the two-digit number. 48 times 101 becomes 4848. Multiplying by 99 is more of a trick which most people wouldn’t necessarily be able to figure out on their own. Instead of multiplying by 99, you multiply by 100 and subtract 1. 48 times 99 is done by multiplying 48 by 100 to get 4800. You then subtract 48 from 4800 to get 4752.

The author also points out that you can reassemble factors to make multiplying easier. Instead of 2 times 14, you can multiply 2 times 2 times 7, or 4 times 7. This is essentially the same thing as dripping zeroes. 30x50 is like 3x10x5x10, or 3x5x10x10. (It also works great until you hit prime numbers. If you have to multiply 13 by 7, you’ll have to find another way to do it.)

The author presents it in a way that is easy for someone to understand each trick, but the reader might not necessarily understand the underlying principle, and that’s the problem. The trick from the paragraph before last could be used with other numbers or in combination with other tricks. For instance, 48 times 98 would be like 48 times 100 minus twice 48, or 4702. The real lesson to be learned is to notice proximity to an easier number to multiply by.

I would say that if you paid attention in math up until high school, you’ll find about 30% of this book to be stuff that you could have figured out on your own. (I’d say that a person of average mathematical abilities will find at least a few tricks that they already have figured out on their own.) Another 20% will be stuff that will serve no practical purpose. For instance, the book has parlor tricks, which the author admits are nothing more than mathematical curiosities that are meant to amuse people at parties. One will allow you to tell the day of the week for any date in the 20th century.

There are also a few things, like adding large sets of numbers, which will probably still require pencil and paper of most people. On the whole, I’d say that among the 60 tricks in the book, very few of them are of any benefit to me. Many are of great use, but I already know much of the information contained herein. I think that it would have been better to write a book on why these tricks work.

No comments :