Two-digit add & subtract
Add and subtract two- and three-digit numbers in one pass.
Best in your head · no pen, no calculator why?
Opens at level 4. You're level 1. You can read and practice here now.
the idea
On paper you start at the ones column. In your head it is faster to go left to right: add the tens, then the ones, and keep a single running total.
more of the idea
A number a little under a round one, like 29 or 398, is quicker to use as the round number, followed by a small fix.
For subtraction you can also count up. The difference between two numbers is the distance from the smaller one to the bigger one, and counting up lets every jump land on a round number, so nothing needs borrowing.
techniques
Tens first, then ones
- Keep the first number whole.
- Add the tens of the second number.
- Then add its ones, crossing the next ten if you need to.
47 + 36
- 47 + 30 = 77.
- 77 + 6 = 83.
Answer: 83
Count up to subtract
- Start at the smaller number and jump to the next ten.
- Jump from there to the bigger number.
- Add the jumps. That total is the difference.
82 − 47
- 47 up to 50 is 3.
- 50 up to 82 is 32.
- 3 + 32 = 35.
Answer: 35
Round, then fix
- Swap that number for the round one: 29 becomes 30.
- Add or subtract with the round number.
- Ask whether that made the answer too big or too small, and fix it by the difference.
- Subtracting too much leaves too little, so add the difference back.
612 − 397
- 612 − 400 = 212.
- That took away 3 too many.
- Add them back: 212 + 3 = 215.
Answer: 215
watch out for
- Dropping the carried ten. In 58 + 19 the ones make 17, so a ten carries over: the answer is 77, not 67.
- Taking the smaller ones digit from the bigger one, wherever it sits. For 91 − 54 that gives 43; counting up gives 37.
- Fixing the rounding the wrong way. For 503 − 278, taking 280 removes 2 too many, so add 2 back: 225, not 221.
practice
New here? Start the four-problem warm-up. No sign-up.
Two-digit addition
worked example
79 + 18
- Round and compensate: 79 + 20 = 99, then take back the extra 2: 97.
Answer: 97
Two-digit subtraction
worked example
44 − 28
- Count up from 28: 2 gets to 30, then 14 more gets to 44.
- 2 + 14 = 16.
Answer: 16
Three-digit compensation
worked example
449 − 382
- Subtract a round number, then fix it: 449 − 380 = 69.
- That took away 2 too few, so take away 2 more: 67.
Answer: 67