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Adding Right to Left

Grades 1–3 Addition The schoolbook method

This is the way most people first learn to add on paper: you start with the ones column (the smallest digits, on the right) and work leftward. Whenever a column adds up to 10 or more, you carry the extra ten into the next column.

Why it works

Every digit in a number stands for a different amount. In 467, the 4 is really 400, the 6 is really 60, and the 7 is just 7. When the ones column overflows past 9, ten ones wrap up into one ten — so you hand it to the next column. Nothing is lost; you're just moving the overflow leftward.

Worked example: 467 + 285

1 1 467 + 2 8 5 = 7 5 2
  1. Ones column: 7 + 5 = 12. Write the 2, carry the 1 (ten) into the tens column.
  2. Tens column: 6 + 8 + carried 1 = 15. Write the 5, carry the 1 (hundred) into the hundreds column.
  3. Hundreds column: 4 + 2 + carried 1 = 7. Write 7.
  4. Answer: 752. Check: 467 + 285 = 400 + 200 + 60 + 80 + 7 + 5 = 600 + 140 + 12 = 752. ✓
The golden rule Always line numbers up by the ones place (right edge), not by the left edge. 34 + 5 means the 5 sits under the 4 — never under the 3.

Carrying more than once

Bigger numbers work exactly the same — the carry just keeps moving left:

1 1 1 7 9 8 + 4 6 5 = 1 2 6 3

8 + 5 = 13 (carry 1) → 9 + 6 + 1 = 16 (carry 1) → 7 + 4 + 1 = 12 (write 2, carry 1 → a new thousands column appears) → answer 1263.

Try it yourself:
  1. 58 + 37  (answer: 95)
  2. 246 + 189  (answer: 435)
  3. 3,572 + 2,859  (answer: 6,431)

The other direction: some people prefer to add the biggest digits first and work rightward — see the left-to-right method. Both give the same answer; pick the one that feels natural.

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