Addition · Technique guide
Mental Addition with Big Numbers
By Robert Hansson, Kung Fu Math
On paper we add from right to left and carry digits. In your head that method is awkward, because you have to remember the answer backwards. Strong mental calculators do the opposite: they start with the biggest place value and keep a running total.
The goal is to hold as little as possible in working memory at once. Every technique here keeps the number of things you are juggling small, so you can add three and four-digit numbers without losing track.
01
Left to right
Add the hundreds first, then the tens, then the ones. You always hold one growing number, and you say the answer in the right order when you finish. Most people find this much easier to keep in their head than carrying from the right.
Worked example
647 + 285
- → 647 + 200 = 847
- → 847 + 80 = 927
- → 927 + 5 = 932
Answer: 932
Practice: Try 356 + 427, 718 + 164 and 2 345 + 1 678.
02
Round and compensate
If one number is close to a round number, add the round number instead and fix the difference afterwards. Adding 298 is the same as adding 300 and taking away 2.
Worked example
1 476 + 398
- → 398 is 400 − 2
- → 1 476 + 400 = 1 876
- → 1 876 − 2 = 1 874
Answer: 1 874
Practice: Try 563 + 197, 2 418 + 999 and 745 + 49.
03
Friendly pairs
When adding a list, look for numbers that make round totals together: 25 and 75, 37 and 63, 140 and 60. Add those pairs first. The order of addition does not matter, so you are free to choose the easiest path.
Worked example
37 + 48 + 63 + 52
- → 37 + 63 = 100
- → 48 + 52 = 100
- → 100 + 100 = 200
Answer: 200
Practice: Try 26 + 59 + 74 + 41 and 125 + 380 + 75 + 20.
04
Move to a round number
Shift a small amount from one number to the other so that one of them becomes round. 68 + 57 becomes 70 + 55. The total stays the same, but the sum is now easy.
Worked example
896 + 437
- → Move 4 from 437 to 896
- → 900 + 433 = 1 333
Answer: 1 333
Practice: Try 68 + 57, 495 + 238 and 1 997 + 586.
05
Decimals the same way
Decimals follow exactly the same rules. Line up whole numbers and tenths in your mind, add the whole numbers first, then the decimal parts, and carry if the decimals pass 1.
Worked example
4.7 + 3.8
- → 4 + 3 = 7
- → 0.7 + 0.8 = 1.5
- → 7 + 1.5 = 8.5
Answer: 8.5
Practice: Try 2.6 + 5.9, 12.75 + 3.5 and 0.48 + 0.67.
Common mistakes
- Losing a place value when going left to right. Say each partial total quietly, such as 847, then 927, to anchor it.
- Compensating in the wrong direction. If you added too much, take it back; if you added too little, add the rest.
- Mixing up tenths and hundredths in decimals. 0.5 + 0.25 is 0.75, not 0.30.
Summary
- Start with the largest place value and keep one running total.
- Use round numbers and fix the difference afterwards.
- Reorder and pair numbers to make tens and hundreds.
Into the dojo
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