This is just something that occurred to me today; I haven’t yet had the time to really explore it. Once I do, I’m fairly certain that it’s range of use will expand however, for the time being, please note the limitation listed below.

Technique for performing mental multiplication for larger numbers.

This applies to any natural number that falls within 10 less than the next multiple of 50. For example, it will work with 248 but not 234; 495 but not 476, etc. There are definite patterns that emerge once you apply the technique to numbers outside of this restriction, so I’m quite sure that I will be able to modify it to work with all natural numbers once I have a moment to look at it again… but for now, it’s a good quick trick for those ranges to which it applies.

Take your two numbers, I’ll use 497 and 343 as an example. For the purpose of clarity, let us refer to the first value; 497, as a and the second; 343, as b.

Round a and b to the nearest multiple of 50 and find their product:
500 x 350 = 175000

Next, take the difference of the rounded a minus a and multiply it by the rounded b:
500 - 497 = 3
3 x 350 = 1050
Let’s call that product x.

Now, do the same, but reverse a and b; rounded b minus b multiplied by a:
350 - 343 = 7
7 x 500 = 3500
Let’s call that product y.

Now, add x and y together and subtract the sum from your initial product of the rounded values:
1050 + 3500 = 4550
175000 - 4550 = 170450

We’re almost there. The last step is to find the product of the difference of the ones from 10 in the first values…so:
497, the value of ones is 7, so:
10 - 7 = 3
343, the value of ones is 3, so:
10 - 3 = 7
Now, find the product of those differences:
3 x 7 = 21

Add this to the large product above and you have your answer:
170450 + 21 = 170471

I’ll leave it to you to explore this technique on larger numbers with more digits.

It may look tedious when written out in this manner, but it’s quite quick and easy to follow when running through the steps in your head.

Hope that helps!

Math mental math