Steps to calcuate the sum of two one-digit numbers?

Hi All,

I’m not sure how to ask this question, but I think I do several unnecessary mental steps when adding two one digit numbers when the sum is greater than 10. I guess, I picked up this method when I was a kid, and now it’s a strong habit. I would like to know how to stop doing this!

Let me explain what I mean. I’ll write what happens in my head in quotes.

5 + 9 --> " 5 minus 1 is 4 --> 14"
so, with 9, I subtract one

5 + 7 --> “10 minus 7 is 3, 5 minus 3 is 2 --> 12”

On the other hand, I tend to recognize any two numbers add up to ten without any steps.
E.g. 6+4 --> “10”

What can I do, so that I just know the answer without doing an additional subtraction step?

Thank you for any ideas!!

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Memorize them.
There are not that many possibilities of adding 2 one digit numbers.

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I agree with @Kinma on that. Two things you could try to help with that:

  • number shape
  • major system

Look at 5 + 8 and try and figure out why the new unit digit will be 3:

So 5 is half of 10… the key being half. Also it looks a bit like a sickle (number shape)… something you can use to cut things in half with.

Now imagine what 8 would look like if you took the 5 and cut it in half… you get an E on the left and a 3 on the right. Ignore the “e” or read it as “equals” if you like… the answer is the 3 on the right.

Alternatively, you can go over the words they form when using the major system:

  • 7 + 5 = _2 for KLN
  • 5 + 7 = _2 for LKN

KLN could be read as “clown” and LKN could be read as “licking”… so make that a picture of two clowns licking each other.


Thank you this is very helpful.

After going through Domenic’s You Have A Brilliant Memory. I can memorize facts (crazy linked imagery within a loci) and figures that relate to facts (by including PAO characters in the scene). However, I don’t have an off-the-cuff solution to remembering how numbers relate to each other.

Of course, the default would be drill it by rote, but it seems that whenever I use memory tricks it’s faster and “sticks better.”

I tried number-shape, but the different images felt too similar to keep distinct within my mind. I’ll try major. I’ve never used major except for generating PAO character names and decoding them, so that’ll be good practice.

One more question. What’s a good way to remember that this major phrase relates to addition? I might do something similar with multiplication too and I’d like to keep them distinct.

Thank you!!

I’m going to try stock mnemonics for addition: a salt shaker and multiplication: Shakespeare (since he coined “multitudinous”)

If you are really only talking about adding two single digit numbers and you can’t recognize the sum by sight, then I have a radical suggestions.

Just count!

Use your fingers if you have to. It will be far quicker and easier than some convoluted solution for adding two single digit numbers.

Well, this all started from cracking open “The Secrets of Mental Math,” where Art describes what are the thinking steps. I saw that counting and my current method add additional steps. More importantly, they take up some of my short term memory. That makes me a little nervous, … and I think that nervousness slows me down and reduces my “memory power.”

Does that make sense?

E.g., when adding large sums left-to-right you end up with a long thing to keep in mind, then finally you’re adding a two single digit numbers. More concretely, with 1234 + 838, eventually, in my head I’d hear “two thousand sixty four plus 8” At this point, I’d like to avoid counting or thinking about “10-8=2” so then let’s take 4 minus 2 is 2 therefore it’s 2060 + 12.

It does make sense!

If I look at the same calculation, I go “two thousand. Sixty。 Seventy … Two”.

In this calculation I don’t really calculate. I merely put together. When I see 1,200 and 800 I immediately see 2,000. I have done this calculation so many times that I just see the numbers and see the result. This comes with experience. It is like muscle memory.

Same with 4+8. Even if I want to calculate it, I see 12 earlier than trying to go from 8 to 10 and then realizing I need 2 more to get to 12.

And yes, you are right. Pulling the result from memory saves up short term memory.
So my advice is to keep practicing.

Maybe try this.
First do 4+8 with 10 as the in between step, like you showed in the OP.

While doing this, remember you start with 8, ask yourself how to get to 10, and then realize you need 2 more and get to 12. Then say the calculation again without the in between steps.

So the last step should be saying out loud eight plus 4 equals 12.
Repeat that last step until it sticks.