My head hurts when I have to do calculations, even trivial additions and subtractions. However, I've always wanted to be able to do simple calculations in my head, and I admire those who can. What do they know that I don't? Is it too late to learn?

Mental Arithmetic

It turns out there are simple strategies that can be applied to solving what seems like complex problems.

Multiply and Divide by 10, 100, 100...

To multiply any number by a factor of 10, just add a zero to the end of the number we are multiplying, if it's a whole number or move the decimal point to the right, if it's a fraction.

For example: 2 * 10 = 20, since 10 has one zero, we move one place to the right. 2 * 100 = 200. We add two zeroes to the end. And for fractions: 0.2 * 10 = 2, 0.02 * 10 = 0.2, 0.02 * 100 = 0.2 * 10 = 2.

To divide any number by a factor of 10, we move decimal point to the left according the number of zeroes. So 2 / 10 = 0.2, since 10 has one zero, we move the decimal point one place to the left. 2 / 100 = 0.02, two zeroes, two places to the left.

Multiples of 10s, 100s and more

What if you need to multiply or divide by multiples of 10s? Say for example, 15 * 50. The strategy here is to first multiply by 5 then by 10 since 50 is 5 * 10. Breaking it down it becomes 15 * 5 = 75 * 10 = 750. Same thing for fractional amounts 0.25 * 20. First we multiply by 2: 0.25 * 2 = 0.50 The we multiply the result by 10: 0.50 * 10 = 5.

Already breaking it out like this, I can see that it's easier to work out in my head.

How do we handle division of decimals by multiples of 10s, 100s...?

For example: 0.25 / 20. The strategy is similar. In this case, we divide by 2 first and then by 10. So it becomes 0.24 / 2 = 0.12 0.12 / 10 = 0.012

There are many strategies like this that you can use to improve your ability to do calculations in your head. I intend to practice these strategies and reach for a calculator less if I can help it.

See Mental Arithmetic for more.