So you want to get faster at long-hand math.
There may be several reasons for this. You may be an elementary school student (or the parent of one), or perhaps you are an adult who has found a new need for basic math (sans calculator).
If you need to take a test like the SATs, an EEI aptitude test (for employment/hiring screening in technical professions), or indeed any employment or academic test that requires timed math and doesn’t allow a calculator, what you really need is to cut down the wasted time you spend on facts that you could have memorized without much trouble.
For example, getting the multiplication table down cold is really sensible, and also fairly easy to do, since there are many simple and free online resources that will test you on single digit multiplication. (I.E. 6×8, 1×10, etc.)
However, I’m tackling a more obscure area in this blog post: subtraction facts.
Take for example the subtraction problem 794 minus 356.
If you are doing it long-hand, you have to borrow once: the first thing you have to solve is 4 minus 6, which is, of course, nonsense (in this context). Instead, you borrow from the nine in the 10’s column to turn your first task into 14 minus 6, rather than 4 minus 6.
Quick: what’s 14 minus 6?
Well, 6 plus 6 is 12, so if you added 2, that makes 14, and 6 plus 2 is 8, so 14 minus 6 must be 8…
(Um, that stream of reasoning was SO not fast enough.)
So here’s my premise: there are a fairly limited number of basic subtraction facts you need to outright memorize for long-hand subtraction.
For example, you would be wise to memorize 4 minus 3. (That seems obvious.) However, it is just as important to memorize 14 minus 6, because if you ever get 4 minus 6 in the middle of a longhand subtraction problem, you know you are just going to borrow from the next column and turn it into 14 minus 6.
On the other hand, it would be a waste of energy to memorize 14 minus 2, because in long-hand subtraction, you would not need to borrow from the next column to solve “4 minus 2.”
Following me so far?
Here’s my suggestion. If you can’t look at a subtraction problem (that you would run into in the course of long-hand subtraction) and instantly know the answer, put that subtraction fact on a flash card, with the answer on the other side. Do this for all the ones you don’t know instantly (or just do all of them for extra review, or if you’re only starting out in math and don’t know any of them that well yet).
Take that set of flash cards and shuffle them. Look at the first one. If you get it right, put it in the discard pile. If you get it wrong, stick it somewhere in the stack of cards you haven’t seen yet (this means you’ll get the harder cards more frequently and therefore get a little more practice in the areas you need it).
Keep going through your deck over and over until you reach the point where you don’t even stop to think, you just rattle off each number the moment you read it.
At that point, your subtraction fact fundamentals will be solid and you will fly through long-hand subtraction problems, because you don’t have to slow down to reason.
Remember, every second counts when a test only gives you 50 seconds to solve an entire math problem, including figuring out what information you actually need from a graph, and what operation you then need to perform on it! (This is a similar problem to sight-reading music, in fact, where speed is also paramount.)
So, I’ve figured out all the basic subtraction facts that fit my guidelines, and I’ve listed them below.
Note that you only need to memorize one “18 minus” fact, but you need two “17 minus” facts, and the list for each number keeps getting bigger until “9 minus,” which has 10 associated facts, including 9 minus 0. Then you hit “8 minus” and with each remaining one digit number, the list of facts per number gets shorter again.
Note: I’ve included everything for completeness. Most people already know that 0 minus 0 is 0, or that 9 minus 0 is 9. If you already have a particular fact down cold, you probably don’t need a card for it.
Second note: You may notice I have not provided solutions for these facts. I suggest that for making the flash cards, you should use a calculator to solve these if you don’t know how to solve them on your own. (And double check each one afterward so you know you didn’t enter it wrong!)
If you see anything wrong with this list (or this article in general), shout it out to me in the comments. Good luck to you all on your fundamentals!