Add two-digit numbers - no regrouping
Theory
Adding two-digit numbers with no regrouping is a Year 3 maths skill: the ones add to less than ten, so no ten is carried into the tens column. This page shows the split strategy, the column method and the jump strategy on a number line, plus missing numbers and word problems. Adding one- and two-digit numbers starts in Year 2 (Level 2 in Victoria), so this page also revises that work. Curriculum: VC2M3N04 / AC9M3N03.
A two-digit number is built from tens and ones. In 61 the 6 means 6 tens and the 1 means 1 one. To add two of these numbers, you add the matching places: ones with ones, and tens with tens.
Regrouping (also called carrying) happens when the ones add to 10 or more and a ten has to be moved into the tens column. When there is no regrouping, the ones add to less than 10, so nothing is carried and the answer is built straight from the two column totals. For example, \(61 + 27\): the ones are \(1 + 7 = 8\) and the tens are \(6 + 2 = 8\), giving \(88\).
Two handy ways to add are the split strategy (break each number into tens and ones, add each part, then join them) and the jump strategy on a number line (start on the first number and jump forward by the tens, then the ones).
How to add two-digit numbers with no regrouping
- Line up the places. Put tens under tens and ones under ones, or split each number into its tens and ones.
- Add the ones. They add to less than 10, so write the ones total. Nothing is carried.
- Add the tens. Add the tens digits to get the tens total.
- Put it together. Join the tens total and the ones total to get the answer.
| \(5\) | is in the ones place | |
| \(4 + 5\) | \(=\) | \(9\text{ ones}\) |
| \(74 + 5\) | \(=\) | \(79\) |
The tens digit \(7\) does not change, so the answer is \(79\).
| \(50 + 20\) | \(=\) | \(70\ (\text{tens})\) |
| \(3 + 6\) | \(=\) | \(9\ (\text{ones})\) |
| \(70 + 9\) | \(=\) | \(79\) |
Add the tens and ones separately, then join them: \(79\).
| \(\text{ones: }2 + 5\) | \(=\) | \(7\) |
| \(\text{tens: }6 + 3\) | \(=\) | \(9\) |
| \(62 + 35\) | \(=\) | \(97\) |
Each column adds to less than ten, so the answer is \(97\).
| \(30 + 40\) | \(=\) | \(70\) |
| \(2 + 5\) | \(=\) | \(7\) |
| \(32 + 45\) | \(=\) | \(77\) |
The total cost is \(\$77\).
| \(\text{tens: }3 + 4\) | \(=\) | \(7\) |
| \(\text{ones: }4 + 5\) | \(=\) | \(9\) |
| \(34 + 45\) | \(=\) | \(79\) |
The box needs \(4\) tens and \(5\) ones, so the missing number is \(45\).
(i) How many books are there altogether?
(ii) How many more books would make \(100\)?
| \(23 + 14\) | \(=\) | \(37\) |
| \(37 + 31\) | \(=\) | \(68\) |
| \(68 + 2\) | \(=\) | \(70\) |
| \(70 + 30\) | \(=\) | \(100\) |
(i) \(68\) books.
(ii) Count on from \(68\) to \(100\): \(2 + 30 = 32\) more books.
Common pitfalls
Frequently asked questions
What does no regrouping mean in addition?
No regrouping, also called no carrying, means the ones digits add to less than 10, so you never carry a ten into the tens column. For example, in \(61 + 27\) the ones are \(1 + 7 = 8\).
What is the split strategy for adding two-digit numbers?
The split strategy breaks each number into tens and ones. Add the tens, add the ones, then put them together. For \(45 + 32\), add \(40 + 30 = 70\) and \(5 + 2 = 7\), so the total is \(77\).
Do you add the tens or the ones first?
Either order works when there is no regrouping, but adding the ones first is a good habit. If the ones ever add to 10 or more you will see straight away that the sum needs regrouping.
How do you add two-digit numbers on a number line?
Use the jump strategy. Start on the first number, jump forward by the tens of the second number, then jump forward by its ones. For \(51 + 27\), start at \(51\), jump \(20\) to \(71\), then jump \(7\) to \(78\).
How do you know if an addition needs regrouping?
Add the ones digits. If they total less than 10 there is no regrouping. If they total 10 or more you must carry a ten into the tens column, which is regrouping.