Mental Math

Nowadays, kids rely heavily upon their calculator for simple arithmetic. Most of us know our multiplication tables and how to multiple or divide some easier numbers. When the numbers start to get more complex thought, people get very frustrated and don’t even attempt to figure it out without a calculator. Here are some tips for doing mental math:

Say we wanted to multiply 12 by 23. Not too hard to do by hand or calculator, but when most are asked what the answer is without a calculator, their response is without thought, “I do not know”. You can always break these numbers down into problems that are much easier to do in your head:

First let’s look at something like 12×20. 20 is 2×10, so 12×20 is just 12x(2×10). Since 12×2 is 24 and 24×10 is 240, 12×20=240.

Now, let’s look at 12×23. The trick here is to rewrite one of the numbers as the sum of two numbers we can easily multiply, then use distributive property to make the one multiplication the sum of two easier multiplications. We can write 23 at 20+3. So, 12(23) = 12(20+3) which by the distributive property is 12(20) +12(3) = 240 +36 = 276. Since 12×20 and 12×3 are easy to do in the head, multiplying 12×23 can be just as easy if you can keep track of a few extra numbers.

Similarly 12 = 10+2, so (12)23= (10+2)23 = 10(23) +2(23) = 230+46 = 276. Either way, it isn’t as hard as most people think it is.

The next trick is to change the numbers we are multiplying. What is 15×18? Well, 18=2×9, so 15×18 = 15x(2×9) = (15×2)x9 = 30×9. Again, 30 = 3×10, so 30×9 is 10x(3×9) = 10×27 = 270. While this may seem like a lot of steps, once you get the hang of it, you can do this really quickly in your head.

These tricks work well for numbers under 100. When you get above 100, the tricks work the same, there are just more numbers to keep track of. Once you get the hang of keeping track of all the numbers, bigger numbers will become just as easy to multiply.

Try these in your head:

18×32 [18=20-2 so 18×32 = (20-2)x32 = 20(32)-2(32)= 640-64=576]

22×35 [22=2×11 so 22×35 = 11x2x35 = 11×70 = 770]

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