Add three-digit numbers
Theory
Adding three-digit numbers is a Year 3 maths skill: combining numbers with the split strategy, the column (vertical) algorithm and the jump strategy on a number line. This page explains how to line up the hundreds, tens and ones, how to regroup (carry) when a column reaches ten, and how to add three numbers at once. Curriculum: VC2M3N04 / AC9M3N03.
To add two three-digit numbers you combine their hundreds, tens and ones. Line the numbers up so the same places sit under each other, then add one column at a time, starting from the ones.
The split strategy adds each place on its own: \(324 + 251\) is \(300 + 200\), then \(20 + 50\), then \(4 + 1\), joined to make \(575\). The column algorithm writes the numbers one above the other and adds each column. The jump strategy starts at the first number on a number line and jumps forward by the tens, then the ones.
Regrouping (also called carrying) happens when a column reaches ten or more. Because \(10\) ones make \(1\) ten and \(10\) tens make \(1\) hundred, you keep one digit and carry the extra 1 to the next place on the left.
Adding does not need formulas, but these place value facts tell you when to regroup and how the split strategy works.
How to add two three-digit numbers
- Line up the places. Write the numbers so hundreds sit under hundreds, tens under tens and ones under ones.
- Add from the ones. Add the ones column first, then the tens, then the hundreds.
- Check each column. Before you write a column's answer, ask: is it \(10\) or more? If so, that column regroups.
- Regroup when needed. If a column reaches ten or more, write the ones digit and carry \(1\) to the next place on the left, then add it in.
| \(300 + 200\) | \(=\) | \(500\) |
| \(20 + 50\) | \(=\) | \(70\) |
| \(4 + 1\) | \(=\) | \(5\) |
| \(500 + 70 + 5\) | \(=\) | \(575\) |
No column reaches ten, so \(324 + 251 = 575\).
| \(\text{ones: }8 + 6\) | \(=\) | \(14\ (\text{carry }1)\) |
| \(\text{tens: }5 + 3 + 1\) | \(=\) | \(9\) |
| \(\text{hundreds: }4 + 1\) | \(=\) | \(5\) |
So \(458 + 136 = 594\).
| \(253 + 40\) | \(=\) | \(293\) |
| \(293 + 5\) | \(=\) | \(298\) |
Jump the tens, then the ones: \(253 + 45 = 298\).
| \(\text{ones: }7 + 5\) | \(=\) | \(12\ (\text{carry }1)\) |
| \(\text{tens: }6 + 8 + 1\) | \(=\) | \(15\ (\text{carry }1)\) |
| \(\text{hundreds: }3 + 2 + 1\) | \(=\) | \(6\) |
The total raised is \(\$652\).
| \(\text{ones: }7 + 6\) | \(=\) | \(13\ (\text{carry }1)\) |
| \(\text{tens: }4 + 8 + 1\) | \(=\) | \(13\ (\text{carry }1)\) |
| \(\text{hundreds: }3 + 1 + 1\) | \(=\) | \(5\) |
The ones and the tens both reach \(10\) or more, so both regroup. The hundreds make \(5\), so they do not. \(347 + 186 = 533\).
| \(\text{hundreds: }200 + 200\) | \(=\) | \(400\) |
| \(\text{tens: }30 + 50\) | \(=\) | \(80\) |
| \(\text{ones: }0 + 6\) | \(=\) | \(6\) |
| \(230 + 256\) | \(=\) | \(486\) |
Work out what each place needs: \(2\) hundreds, \(5\) tens and \(6\) ones. The missing number is \(256\).
(i) How many tickets were sold altogether?
(ii) How many more tickets would make \(700\)?
| \(\text{ones: }4 + 3 + 1\) | \(=\) | \(8\) |
| \(\text{tens: }1 + 5 + 2\) | \(=\) | \(8\) |
| \(\text{hundreds: }2 + 1 + 3\) | \(=\) | \(6\) |
| \(688 + 12\) | \(=\) | \(700\) |
(i) Add all three columns: \(688\) tickets.
(ii) Count on from \(688\): \(2\) more makes \(690\) and \(10\) more makes \(700\), so \(12\) more tickets.
Common pitfalls
Frequently asked questions
How do you add three-digit numbers?
Line up the hundreds, tens and ones. Add the ones first, then the tens, then the hundreds. Whenever a column reaches ten or more, keep the ones digit and carry \(1\) to the next place.
What is regrouping or carrying in addition?
Regrouping means swapping ten of one place for one of the next. Ten ones become one ten and ten tens become one hundred. When a column totals ten or more you write the ones digit and carry the extra \(1\) to the next column on the left.
What is the split strategy for addition?
The split strategy adds each place separately. For \(324 + 251\) you add \(300 + 200\), then \(20 + 50\), then \(4 + 1\), and join the parts to get \(575\).
How do you add numbers on a number line?
Start at the first number and jump forward. Add the tens in one jump, then the ones in another. For \(253 + 45\) you jump \(40\) to reach \(293\), then \(5\) to reach \(298\).
When do you need to carry a one?
You carry a one whenever a column adds up to ten or more. For example, in the ones column \(8 + 6 = 14\), so you write \(4\) and carry \(1\) ten into the tens column.
How do you check an addition answer?
Add the numbers a second way, such as the split strategy, and see if you get the same total. You can also check that each column was regrouped correctly and that the carried ones were added.