I came across a tweet earlier today that received a surprisingly large reaction for a relatively simple math shortcut: “Percentages are reversible. 8% of 25 is the as 25% of 8 and one of them is much easier to do in your head.” I followed it up with one of my own: “Similar one is use factors of 10. Want to divide by 5? Multiply by 2 and shift decimal point. 24/5=24*2/10=4.8 same with 4 and 25., 8 and 125, etc”
Despite nearly everyone having incredibly powerful calculators in our pockets these math shortcuts are valuable useful to have. It makes it that much easier to do back-of-the-envelope calculations and quickly validate some assumptions without disrupting the flow with a screen. It also keeps the brain sharp and fights the natural inclination to be lazy.
A few other helpful math tricks I’ve used over the years:
- Round and then adjust. When numbers are close to multiples of 10 or 5 just round them and then adjust after the calculation. For example: 49 * 14 = (50 * 15) - (14 + 49) - 1. This relies on knowing that that (x+1)(y+1) = x*y + x + y + 1 and solving for x * y = (x+1)(y+1) - x - y - 1.
- Multiplying numbers that differ by 2. For example, 14 * 16. Another algebraic identity is (x-1)(x+1) = xx - 1. In this case we can do 1515 - 1 = 224.
- There are countless others designed for specific numbers - for example squaring numbers ending in 5, multiplying by 11, etc - but I find them to be too unique to be useful.
More often than not, a simple approximation done quickly is more valuable than the perfect answer even a minute later. It’s a way of validating or invalidating your intuition and having a few techniques is often good enough and allows you to quickly move on to the next thought.