Add two-digit numbers - with regrouping
Theory
Adding two-digit numbers with regrouping is a Year 3 maths skill: add the ones first, and when they make ten or more, swap ten ones for one ten and carry it into the tens column. This page explains regrouping, the column method, the split strategy and the number line jump strategy, including totals past 100. Curriculum: VC2M3N04 / AC9M3N03.
To add two-digit numbers you add the ones first, then the tens. Sometimes the ones make ten or more. Ten ones is really one full ten, so you regroup: keep the extra ones and move the ten to the tens column. Moving that ten across is called carrying.
For \(46 + 29\), the ones make \(6 + 9 = 15\). That is 1 ten and 5 ones, so write the 5 and carry the 1 ten. Then the tens make \(4 + 2 + 1 = 7\), which gives \(75\).
There is more than one way to add. The column method lines the digits up and adds each column. The split strategy adds the tens and ones on their own, then joins them. The jump strategy starts at the first number on a number line and jumps the tens, then the ones.
Regrouping rests on a few place value facts. Keep these in mind whenever a column reaches ten.
How to add two-digit numbers with regrouping
- Line up the columns. Write the numbers so ones sit under ones and tens under tens.
- Add the ones. If they make ten or more, write the ones digit and carry 1 ten above the tens column.
- Add the tens. Add the tens digits and the carried ten. Write the total to get your answer.
| \(\text{ones: }5 + 8\) | \(=\) | \(13\) |
| \(\text{write }3,\text{ carry }1\text{ ten}\) | ||
| \(\text{tens: }6 + 1\) | \(=\) | \(7\) |
So \(65 + 8 = 73\).
| \(\text{tens: }50 + 20\) | \(=\) | \(70\) |
| \(\text{ones: }7 + 6\) | \(=\) | \(13\) |
| \(70 + 13\) | \(=\) | \(83\) |
The ten inside \(13\) joins the tens, so \(57 + 26 = 83\).
| \(35 + 20\) | \(=\) | \(55\) |
| \(55 + 9\) | \(=\) | \(64\) |
Jump \(+20\), then \(+9\) crosses \(60\): \(35 + 29 = 64\).
| \(\text{ones: }8 + 6\) | \(=\) | \(14\ (\text{carry }1)\) |
| \(\text{tens: }5 + 4 + 1\) | \(=\) | \(10\) |
| \(58 + 46\) | \(=\) | \(104\) |
The ten in the tens column moves into the hundreds. The total is \(\$104\).
| \(26 + 4\) | \(=\) | \(30\) |
| \(30 + 40\) | \(=\) | \(70\) |
| \(70 + 1\) | \(=\) | \(71\) |
| \(4 + 40 + 1\) | \(=\) | \(45\) |
The missing number is \(45\). Check: \(26 + 45 = 71\).
(i) How many pieces of fruit is that altogether?
(ii) How many more pieces would make \(150\)?
| \(34 + 48\) | \(=\) | \(82\) |
| \(82 + 26\) | \(=\) | \(108\) |
| \(108 + 2\) | \(=\) | \(110\) |
| \(110 + 40\) | \(=\) | \(150\) |
(i) \(108\) pieces of fruit.
(ii) Count on from \(108\) to \(150\): \(2 + 40 = 42\) more.
Common pitfalls
Frequently asked questions
How do you add two-digit numbers with regrouping?
Add the ones first. If they make ten or more, write the ones digit and carry 1 ten into the tens column. Then add the tens, including the carried ten. For \(46 + 29\), the ones make \(15\), so write 5 and carry 1 ten, then \(4 + 2 + 1 = 7\), giving \(75\).
What does regrouping or carrying mean in addition?
Regrouping means swapping ten ones for one ten. When a column adds to ten or more, you keep the extra ones in that column and carry the ten into the next column to the left.
When do you need to regroup when adding?
You regroup whenever a column adds to ten or more. Check the ones first: if the ones digits add to \(10\) or more, you must carry a ten. For \(36 + 48\) the ones are \(6 + 8 = 14\), so you regroup.
What is the split strategy for addition?
The split strategy adds the tens and the ones separately, then joins them. For \(57 + 26\), add \(50 + 20 = 70\) and \(7 + 6 = 13\), then \(70 + 13 = 83\). The ten inside \(13\) joins the tens.
How do you add on a number line using the jump strategy?
Start at the first number, then jump the tens and the ones. For \(35 + 29\), start at \(35\), jump \(+20\) to reach \(55\), then jump \(+9\) to land on \(64\).
What is 46 + 29?
\(46 + 29 = 75\). The ones make \(6 + 9 = 15\), so write 5 and carry 1 ten. The tens make \(4 + 2 + 1 = 7\), so the answer is \(75\).