Mental Strategies

You do not always need pen and paper. With a few tricks you can add and subtract small numbers in your head. The idea is always the same: break a hard sum into easy pieces you already know.

Partitioning splits each number into its tens and ones, adds the tens together and the ones together, then combines the two parts. This leans on place value:

47 + 38 = (40 + 30) + (7 + 8) = 70 + 15 = 85

Near doubles turns a sum into a double you know by heart, plus a small adjustment. Since 6 + 6 = 12, the next sum is just one more:

6 + 7 = (6 + 6) + 1 = 12 + 1 = 13

Subtraction has its own shortcut. Instead of taking away, count up from the smaller number to the bigger one — the difference is how far you travelled. To work out 71 - 68, count on from 68 to 71: that is 3 steps, so the answer is 3.

71 - 68 = 3 \quad (68 \to 69 \to 70 \to 71)

Compensation rounds an awkward number to a tidy one, does the easy sum, then adjusts back. Adding 99 is hard, but adding 100 is easy — so add 100 and take one back:

99 + 46 = (100 + 46) - 1 = 146 - 1 = 145

Four tricks for adding and subtracting in your head:

Partitioning — split into tens and ones, add each part, then combine: 47 + 38 = 70 + 15 = 85.
Near doubles — use a double you know, then adjust: 6 + 7 = (6 + 6) + 1 = 13.
Counting up — for subtraction, count on from the smaller number to the bigger: 71 - 68 = 3.
Compensation — round to a tidy number, then correct: 99 + 46 = (100 + 46) - 1 = 145.