Addition and subtraction up to 10,000 — mental strategies

Addition and subtraction up to 10,000 — mental strategies

Mental strategies — round numbers and clever tricks

The column method always works, but for round numbers (or numbers close to round) you're wasting time on paper. Let's learn when you can just do it in your head.

Round thousands and hundreds

For round numbers, the same trick works as for single digits:

  • 4,000 + 5,000 = 9,000 — that's just 4 + 5 = 9, but "in thousands".
  • 8,000 − 3,000 = 5,000 — that's 8 − 3 = 5.
  • 2,300 + 1,400 = 3,700 — add thousands and hundreds separately: 2 + 1 = 3 and 300 + 400 = 700.

Adding hundreds and thousands

Often you need to add a round amount to a given number. That's a job for your head.

  • 5,247 + 1,000 — add 1 to the thousands: 6,247.
  • 3,856 + 200 — add 2 to the hundreds: 4,056 (we crossed into the next thousand!).
  • 7,480 − 300 — take 3 off the hundreds: 7,180.

Watch out when the hundreds and thousands both change. For example 3,856 + 200 turns into 4,056 — the hundreds "rolled over" past 9.

Trick: round to a friendly number

When you need to compute 3,998 + 4,005, make it an easier problem first. Round both numbers:

3,998  ≈  4,000
4,005  ≈  4,000

Add the round numbers: 4,000 + 4,000 = 8,000. Now fix the small differences:

  • 3,998 is 2 less than 4,000,
  • 4,005 is 5 more than 4,000.

Together you correct by +5 − 2 = +3. The answer is 8,003.

Patterns in addition and subtraction

When you look at a longer sequence, you can often spot a rule that speeds you up.

Example:

1,200 + 800 = 2,000
2,200 + 800 = 3,000
3,200 + 800 = 4,000
4,200 + 800 = ?

The first number goes up by 1,000 each time, the second stays the same — so the answer also goes up by 1,000. The answer is 5,000.

Another example, where the second number changes:

6,500 − 100 = 6,400
6,500 − 200 = 6,300
6,500 − 300 = 6,200
6,500 − 400 = ?

The second number goes up by 100, so the answer drops by 100. Answer: 6,100.

You can try these tricks here:

For context: intro to this topic.