IQ Test Labs

Math shortcuts to amaze your friends

Author: Steve Gillman

I had my own math shortcuts when I was a child. Using these meant that I didn't "show my work" in math class, as was required. This annoyed many of the teachers, and lowered my grades. I did get the correct solutions to my math problems, however. I was simply using different algorithms, ones which I had a hard time expressing on paper.

In my thinking, for example, 97 x 16 became 100 x 16 (1600) minus 3 x 16 (48). It was easier that way, and thinking this way became almost automatic. As a result, I might just write down 1552 even though I couldn't explain very well how I arrived at the answer. My teachers called that a problem, but many years later such math shortcuts were being sold in seminars and books.

You can make your own math shortcuts. The following may give you some ideas on how to do that. Alternately, you can try any of the shortcuts and algorithms you read about and adopt the ones that are best suited to you. There are no perfect techniques for all people, because our minds work in slightly different ways.

For example, suppose you want to multiply 68 x 6. My mind immediately thinks "60 x 6 = 360 and 8 x 6 = 48, and 360 + 48 is 408." That is one way to quickly arrive at a solution without pen and paper. It is essentially this: (60 x 6) + (8 x 6) = 408.

Want another way? Think of it as (70 x 6) - (2 x 6). The "internal dialog" might be something like this: "70 x 6 = 420, but that is two "sixes" too many, so take away two sixes (12) and I have 408." The point is that there is often more than one way, and you can use whichever math shortcut is easier for you.

If the problem was 68 x 9, by the way, my mind immediately focuses on the 9. Why? Because it is close to 10, and multiplying by 10 is easy. 68 x 10 is 680, from which I just have subtract the extra 68 to arrive at the solution of 612. Always look for the numbers that are close to 10 or 100 or 1000, and you'll find the easier way to do the math, especially if you are trying to do it in your head.

Percentages can be trickier to do as mental math, but there are ways. Suppose, for example, that you want to figure what the 4.6% sales tax will amount to on your \$29 book. One quick way to estimate it is to take 10%, or \$2.90, cut that in half to arrive at 5%, or \$1.45, and then just guess at around \$1.35, because you know 4.6% is a little less than 5%. Alternately, you could think of 5% as a 20th of the price - if this is easier - and then round that figure down a bit.

What if you want a more precise solution? 1% of \$29 is easy to arrive at (.29), so multiply that by 4 to arrive at \$1.16. (You might think of this as (4 x 30) - 4.) Now you just need to add .6% to that. Think 6 x 29 = 174, and then put the decimal in the right place: .174. Add that .18 (round it up as the store will likely do) to the 1.16 and you have \$1.34 in sale's tax, pretty close to our quick estimate. This is not as difficult as it might seem once you practice these shortcuts a bit.