Practice
Mental Addition and Subtraction: 7 Methods With Worked Examples
By HumanCalc · Published · 4 min read
School teaches addition from right to left, carrying as you go. On paper that works well. In your head it is awkward, because you produce the answer backwards and have to hold every carried digit until the end.
The seven methods below avoid carrying in your head. Each one comes with a worked example you can check on a calculator.
1. Add from the left
Add the hundreds, then the tens, then the ones, and keep a single running total. You say the answer in the order you will write it, and the largest part is settled first.
347 + 285
- Hundreds: 300 + 200 = 500.
- Tens: 40 + 80 = 120. Running total 620.
- Ones: 7 + 5 = 12. Running total 632.
347 + 285 = 632
2. Round one number, then adjust
When a number sits just below a round value, add the round value and take back the difference. This turns a carrying problem into two easy steps.
398 + 176
- 398 is 2 less than 400.
- 400 + 176 = 576.
- Take back the 2: 576 − 2 = 574.
398 + 176 = 574
3. Make a ten first
Move just enough from one number to bring the other up to the next ten. Adding to a round number is easy.
46 + 28
- 46 needs 4 to reach 50.
- Take 4 from 28, which leaves 24.
- 50 + 24 = 74.
46 + 28 = 74
4. Subtract by counting up
To find a difference, start at the smaller number and count up to the larger one in friendly jumps. It is how many people count out change, and it is the fastest way to subtract from 100, 1,000 and similar round numbers.
1,000 − 367
- 367 to 400 is 33.
- 400 to 1,000 is 600.
- 33 + 600 = 633.
1,000 − 367 = 633
5. Subtract a round number, then give some back
Subtracting 597 is hard. Subtracting 600 is easy. You took away 3 too many, so add them back.
812 − 597
- 812 − 600 = 212.
- You subtracted 3 too many: 212 + 3 = 215.
812 − 597 = 215
6. Shift both numbers by the same amount
A difference does not change if you add the same amount to both numbers. Shift the number you are subtracting up to a round value and move the other one with it.
83 − 47
- Add 3 to both numbers.
- 83 − 47 becomes 86 − 50.
- 86 − 50 = 36.
83 − 47 = 36
7. Use a double you already know
Numbers that are close to each other are easier to add as a double plus or minus a little. Most people know their doubles far better than other sums.
36 + 37
- 36 + 36 = 72.
- 37 is one more than 36, so add 1.
36 + 37 = 73
Which method fits which problem
| The problem looks like | Try | Example |
|---|---|---|
| Two three-digit numbers | Add from the left | 254 + 318 = 572 |
| One number ends in 7, 8 or 9 | Round and adjust | 199 + 64 = 263 |
| A round number minus anything | Count up | 500 − 173 = 327 |
| Subtracting something near a round number | Subtract round, give back | 430 − 98 = 332 |
| Two numbers that are close together | Doubles | 45 + 46 = 91 |
Adding a list of numbers
For a list, keep only the running total and let each number go once you have added it. With 9, 7, 6, 8 and 4, the totals are 9, 16, 22, 30 and 34. Trying to remember the list while adding it is the most common reason people lose track.
Flash Anzan trains exactly this, with numbers that appear one at a time. Serial Addition is a twist on it: you add each number to the one just before it, not to the total.
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