doing math

courses › Mental Arithmetic

Two-digit add & subtract

level 4 course

Add and subtract two- and three-digit numbers in one pass.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 4.

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Builds on: Small facts

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

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.

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

Adding two two-digit numbers.

  1. Keep the first number whole.
  2. Add the tens of the second number.
  3. Then add its ones, crossing the next ten if you need to.
worked example

Example: 47 + 36

  1. 47 + 30 = 77.
  2. 77 + 6 = 83.

Answer: 83

Count up to subtract

Subtracting two-digit numbers when the ones would need borrowing.

  1. Start at the smaller number and jump to the next ten.
  2. Jump from there to the bigger number.
  3. Add the jumps. That total is the difference.
worked example

Example: 82 − 47

  1. 47 up to 50 is 3.
  2. 50 up to 82 is 32.
  3. 3 + 32 = 35.

Answer: 35

Round, then fix

One number is within 3 of a round number, like 29, 58 or 397.

  1. Swap that number for the round one: 29 becomes 30.
  2. Add or subtract with the round number.
  3. Ask whether that made the answer too big or too small, and fix it by the difference.
  4. Subtracting too much leaves too little, so add the difference back.
worked example

Example: 612 − 397

  1. 612 − 400 = 212.
  2. That took away 3 too many.
  3. Add them back: 212 + 3 = 215.

Answer: 215

Tips by skill

  • TipTwo-digit addition: Add the tens first, then the ones. If a number ends in 8 or 9, round it up and take the extra back.
  • TipTwo-digit subtraction: Count up from the smaller number to the bigger one, through the next ten if you pass it. Add the jumps.
  • TipThree-digit compensation: Subtract the nearest round number, then fix it. Took away too much? Add it back. Too little? Take away more.

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.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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