Addition with regrouping is a technique used in Maths when adding together two or more numbers of any size. It is used with the column method of addition, where sums are arranged vertically, and numbers are added one column at a time.
You may also hear regrouping referred to as “carrying over.” If you add all the numbers in a column, and the total is ten or more, then the number is carried over to the next place value column. For example, you would reach thirteen if there are four and a nine in the one’s column. Here, you would write the three in the one’s column and carry the one over to the tens column.
When do you use regrouping?
As mentioned above, regrouping is used when the sum of the values in one place value column is more than nine. This technique of carrying a number over to the next place value column can be used with any addition or subtraction question – regardless of how many numbers are involved in the question or how many digits each number has.
If you’re completing a question where the sum of the values in each place value column is nine or less, then there is no need to use the regrouping method. This is because there are no numbers that need to be carried over. An example of this would be for a question like 12 + 24. In this situation, the numbers in the ones and the tens columns total less than nine. This makes for an excellent, simple column addition where you can easily find the answer – in this case, 36.
Example of addition with regrouping:
An example is the best way to see addition with regrouping in action. This helps us to see precisely how we might complete the sum and when we would need to use regrouping.
So, as an example, take the sum 38 + 14.
We can line these numbers up vertically in their place value columns, just as we would do for any column method addition.
3 8
1 4 +
——–
Next, we can begin adding the numbers in the one’s column. This is the far right column containing the eight and the 4. The sum of these two numbers is 12. In line with the regrouping method, we’d write the 2 in the one’s column underneath the line and carry the one over to the tens column, writing it above the other two numbers. After this stage, you’ll have something that looks like this:
1
3 8
1 4 +
———
2
After this step, you’re free to add the digits in the tens column – the three from the original numbers and the one you’ve just carried over. Then, from the simple sum 1 + 3 + 1, you’ll have the answer 5. You can then write this in the tens column of your solution.
1
3 8
1 4 +
——–
5 2
And there you have it! The answer to this question is 52.
Regrouping with more than two digits:
This simple addition method with regrouping can be used with numbers of any size. The same principles still apply – the only difference is that numbers might need to be carried over to the hundreds, thousands, or even ten of thousands of columns.
You can also use addition with regrouping if you add more than two numbers, such as the sum 26 + 37 + 18. Here, you need to line three numbers up in a column and add them up the same way. In this example, adding up the one’s column (6 + 7 + 8) results in the answer of 21. In this case, you’d write the 1 in the one’s column and then carry the two over to the tens. Once you’ve completed your calculations, you should have the answer of 81.
Can regrouping be used with subtraction?
Yes! The process for subtracting with regrouping is slightly different, but the overall principle is the same. It still involves splitting numbers into ones, tens, and hundreds and making your calculations one column at a time – using the column method.
The main difference between addition and subtraction using regrouping is that instead of carrying over numbers, you might need to borrow numbers from the column to the left.
Let’s use an example to show what we mean. Taking the sum 31 – 14, we can write the question in columns as usual.
3 1
1 4 –
——-
However, when we complete our first step, we’re faced with 1 – 4. We can’t do this sum without going into minus numbers, so we borrow one lot of ten from the column to the left, leaving us with a two instead of a 3. This allows us to transform one into 11 and calculate 11 – 4. Here’s how we’d write this:
32 11
1 4 –
———-
1 7
Then, by filling in the columns as usual and starting from the left, we reach the answer that 31 – 14 = 17.
