There are many secrets to mental mathematics and just a handful of techniques needed to multiply numbers in your head quickly and simply. Let’s begin with squaring, which as you know, is multiplying a number by itself. Squaring a single digit is easy, as simple as knowing the multiplication tables from 1 through 9, which is taught in elementary school. But how do we square two digit numbers? The following paragraphs explain how to quickly square two digit numbers ending in 5 and also extend the concept to multiplying any two digit numbers with the same first digit and second digits which add to 10.
To square a two digit number ending in 5, simply remember the following two things. First, the answer begins with multiplying the first digit by the next highest digit. The answer ends in 25. For example, let’s square 75, that is multiply 75 by 75. We take 7 times 8 to get 56 and end the answer with 25 to get 5,625. Let’s try another example. Take 95 times 95. We take 9 times 10 to get 90 and end the answer with 25 to get 9,025. Very easy and quick mental math used to solve such problems.
We can extend this concept to multiply any two digit number with the same first digit and second digits which add to 10. We begin the process the same way as when squaring two numbers ending in five. For example, let’s multiply 76 and 74. Take 7 times 8 to get 56. Now take the last two digits and multiply to get the end of the answer, therefore 6 times 4 equals 24, so the answer is 5,624. Now try another example. Multiply 62 and 68. Take 6 times 7 to get 42. Now take 2 times 8 to get 16. The answer is 4,216.
We can also multiply two digit numbers with the same first numbers, even if the last two numbers do not add to 10. The method is fairly easy. We want to make one of the numbers to a base number ending in zero, because multiplication is simple using those numbers. For example, let’s take 23 times 22. Change 23 into 20 and we did so by subtracting 3. Since we subtracted 3 from 23, we will add 3 to 22 to get 25. Next multiply 20 and 25 to get 500. Add 3 times 2 (the last two numbers multiplied together) and the answer is 506. Try another example, take 68 times 63. Change 68 to 60 by subtracting 8. Now add 8 to 63 to get 71. We multiply 60 by 71 to get 4,260. Now multiply 8 and 3 to get 24 and add to 4,260 to get 4,284. Basically we subtract down from the higher number to get to the base number ending in 0. Then add the same number to the other number before beginning the multiplication process.
These are some tricks I have come across during my years of studying and tutoring math. I always try to make math simpler and more interesting for my students. There will be more methods of mental math in future articles.