IMOClass 3 › Addition & Subtraction

Addition & Subtraction

Addition With and Without Regrouping

To add large numbers, line up the Ones, Tens, Hundreds and Thousands and add each column from the right. When a column adds up to 10 or more, we regroup (carry) 1 to the next column.

For 2,567 + 1,848: ones 7 + 8 = 15 (write 5, carry 1), tens 6 + 4 + 1 = 11 (write 1, carry 1), hundreds 5 + 8 + 1 = 14 (write 4, carry 1), thousands 2 + 1 + 1 = 4. The sum is 4,415.

Example 1: Add 3,245 + 1,632.
No carrying: ones 7, tens 7, hundreds 8, thousands 4 → 4,877.
Example 2: Add 2,567 + 1,848.
With carrying at each step the sum is 4,415.
Quick recap
  • Add column by column from the Ones place.
  • If a column makes 10 or more, carry 1 to the next column.
✓ Quick check
Add: 234 + 158 = ?
Ones 4 + 8 = 12 (carry 1), tens 3 + 5 + 1 = 9, hundreds 2 + 1 = 3 → 392.
Add: 4,123 + 2,345 = ?
No carrying needed: 6,468.

Subtraction With Borrowing & Checking

To subtract, line up the places and subtract each column from the right. When the top digit is smaller, borrow 1 from the next column.

We can check a subtraction by adding the answer to the number we subtracted — it should give back the first number. For 645 − 278 = 367, check: 367 + 278 = 645.

Example 1: Subtract 645 − 278.
With borrowing, 645 − 278 = 367. Check: 367 + 278 = 645.
Example 2: Subtract 5,000 − 2,367.
5,000 − 2,367 = 2,633. Check: 2,633 + 2,367 = 5,000.
Quick recap
  • Borrow 1 from the next column when the top digit is too small.
  • Check subtraction: answer + number subtracted = first number.
✓ Quick check
Subtract: 803 − 547 = ?
With borrowing, 803 − 547 = 256.
Is 912 − 458 = 454 correct?
Check: 454 + 458 = 912, so the answer is correct.

Estimation & Word Problems

Estimation gives a quick, close answer. To estimate a sum or difference, first round each number to the nearest ten or hundred, then add or subtract. For example, 312 + 489 is about 300 + 500 = 800.

In word problems, words like in all and altogether mean add, while left, remaining and how many more mean subtract.

Example 1: Round 467 to the nearest hundred.
467 is closer to 500 than to 400, so it rounds to 500.
Example 2: A shop sold 1,245 items in the morning and 2,180 in the evening. How many in all?
1,245 + 2,180 = 3,425 items.
Quick recap
  • Round to the nearest ten/hundred, then estimate.
  • 'In all' means add; 'left / how many more' means subtract.
✓ Quick check
Round 738 to the nearest ten.
The ones digit 8 is 5 or more, so 738 rounds up to 740.
A box has 156 red and 248 blue beads. How many beads in all?
156 + 248 = 404 beads.
Ready to test this chapter?
Take the Chapter Test →