Random mental math tricks (Part 1): Two-digit Numbers Multiplication
Introduction
Mental math refers to the calculation of simple arithmetic expressions in mind, without using any paper, pencils and calculators. We often encounter some simple arithmetic problems in our daily life — to calculate the bus fare, to do the changes, to split the bill among a group of friends etc.. This is a skill always good to acquire in order to make your life more convenient, or more importantly, to impress your friends by giving out an arithmetic answer before they switch to the calculator app in their phones.
On the other hand, this is an essential skill for those who work in a quantitative field. Traders who do trades in the financial market have to be very sensitive to numbers, and hence a mental math session is sometimes included in the interview procedures for the quantitative trader positions.
In this article series, I am going to share some of the quick mental math tricks and tips that I learned during my years of study. To demonstrate these tricks and tips, I am going to introduce several examples of arithmetic expressions and show you a go-through of how I process the question.
Two-digit Numbers Multiplication
Example 1
45 * 63 = ?
Before looking into better way to tackle these kinds of multiplication problem, let’s see how the conventional way taught in elementary schools would approach to this question:
When we have to do multiplication of two two-digit numbers in, we may intuitively split them into two problems of multiplication of a two-digit and a one-digit number. In the above example, the conventional way to do the math is to split it into 45*60+45*3.
Problem arise with the usual practice
However when we have to do the math without pencil and paper, we cannot mark any intermediate results and we often forget the result of 45*60 when we move onto calculate 45*3. Not to mention that we have to add up the two results in mind for the final answer. We have to find a better way that rely less on remembering intermediate results.
The method
The “rule of thumb” is like this:
“Outers * Inners, Tens * Tens, Ones * Ones”
Here is the explanation:
- Multiply the two “outer” digits (4 and 3) and two “inner” digits (5 and 6) then add them up: 4*3+5*6 = 42. This is the first intermediate result. In order not to let the intermediate result occupy your precious memory slots, you may want to remind yourself the number 42 by using hand gesture, so 4 on left hand and 2 on right hand.
- Moving on, we look at the two digits on the tens, and multiply them. 4*6=24. Look at your hand again, and imagine a number 24. Align the right-most digit with the ten on your hand and add them up as illustrated as below. You should get the number 282 and this is the number to remember now:
- Lastly, we look at the two digits on the ones and multiply them. 5*3=15. Remember the intermediate result 282? Align the left-most digit of 15 with the right-most digit in the intermediate result, and add them up. And this is the final answer: 2835.
This is regarded as an improved way to do two-digit numbers multiplication as we only require to remember at most two easy intermediate result at any instance. Also, we could remember less with the aid of hand gestures.
Example 2
Let’s do one more example:
79 * 23 = ?
The number that goes through your hand and head should be noted as follows:
- The first intermediate result from “Outers * Inners” should be 39.
- “Add” 14 to the first intermediate result and get 179.
- “Add” 27 to 179 to get 1817.
- Done!
Is this what you did in your mind?
At first, your speed of calculation using this trick might be a little slow, but I can guarantee that with a little practice, you will be able to come up with the answer quicker than your friend who tries to input the numbers into a calculator to get the result. This is a trick definitely worth practicing for a bit!
Conclusion
This is a little trick that helped me do the mental math slightly faster than an average person. Remember: practice makes perfect. Less reliance on calculator in daily life can significantly reduce your computational time when you encounter them in the midst of a computational-heavy math problem. Next, we will look at other little tricks for other types of question!
Other Parts of the Mental Math Series
Part 1: Two-digit Numbers Multiplication [This Article]
