Can I master mental arithmetic in one month? Day 11
I figured I should start by learning the ‘correct’ technique for fast mental arithmetic (if such a thing even exists) as a first step. I’d read a few articles which mentioned the book ‘Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks’, so I downloaded it and started reading. I’m 25% of the way through now, and here’s what I’ve learned so far:
Addition: work from left-to-right. e.g. 581+264 = 581+200+60+4. I think I was doing a mixture of left-to-right and right-to-left calculations beforehand, so good to know the best technique as I start to practice.
Subtraction: work from left-to-right unless it involves carrying digits. For simple subtraction use the same process as addition e.g. 574–361 = 574–300–60–1 (all of the digits of the second number are lower than the corresponding digits in the first number). However for a more complex problem e.g. 574–396 it is easier to ‘round up’ and do 574–400+4
Multiplying by 11: Sum the digits and insert them in the middle. E.g. for 53*11. Sum the digits of 53 ->5+3=8 and insert it in the middle i.e. 583. Quite a handy trick.
Multiplication: work from left-to-right. E.g. 342*7=300*7+40*7+7*7.
Squaring numbers ending in 5: multiply the first digit by itself +1 then add 25. E.g. 45² = 40*50+25 = 2,000+25
Multiplication: look for symmetry around a nice round number. E.g. 42*38 — both numbers have a difference of 2 from 40. i.e. (40+2)(40–2) = 40²–4² =1,600–4
Though I haven’t dedicated more than an hour or so putting these techniques into practice so far, there are a few things I’ve noticed. Firstly, simple calculations aren’t as second-nature for me as I’d originally thought. For example if I do 7+8, instead of instantly thinking 15, the process goes something like this: the difference between 7 and 10 is 3, and 8–3 is 5 so the answer is 15. In normal life this isn’t too much of an issue, but it starts to become an issue when you’re doing more complex calculations. Likewise, when I’m calculating multiples of 9, my natural process for n*9 is that the first digit is n-1 and the second digit is 9-(n-1). Again, happens very quickly but I can’t afford to waste memory space in doing these micro-calculations when I’m trying to solve bigger problems. I’m going to need to force myself to remember all of the basic calculations and have them ready for instant recall if I want to increase my speed and accuracy.
One of the elements I’ve found most difficult so far is remembering all the numbers. I’m trying to answer the questions by only looking at the numbers once then looking away until I have the answer which requires remembering a lot of numbers. For example in a 3x1 digit multiplication 387*8, that’s 4 digits to remember immediately. While you’re calculating that 300*8 is 2400 you still need to remember the 87. So now you need to remember 2400, 87 and 8. While calculating 80*8 as 640 and adding to the 2400 you need to keep remembering to add 8*7 at the end. As you can imagine, this becomes more complex when you have to carry numbers. Still, according to the book the more you practice the easier this will become.
