Regrouping, sometimes called “borrowing” or “carrying,” is a math skill that helps us handle numbers that cross place value boundaries, which makes addition and subtraction much easier.
Today, Mathnasium tutors walk you through what regrouping is, how to visualize it, and how to use it in addition and subtraction, with step-by-step examples and practice problems to build confidence along the way.
Let’s get started!
Here's what you need to know about regrouping at a glance:
Also known as: Carrying (addition), borrowing (subtraction)
What it does: Reorganizes numbers across place value columns to make addition and subtraction possible
Skills it builds: Place value understanding, multi-digit addition and subtraction, preparation for long multiplication and division
Best for: Addition and subtraction problems where a column exceeds 9 or the top digit is smaller than the bottom digit
Next step: Long multiplication and division
Regrouping is a way of reorganizing numbers to make addition and subtraction easier.
If a number in one place value column is too large or too small to work with directly, we reorganize it by moving the value between columns.
In addition, we call the regrouping process ‘'carrying’’. If the sum in a column reaches 10 or more, we carry the extra amount over to the next place value.
If we are subtracting, we call it ‘’borrowing’’. If the top digit is smaller than the bottom digit, we borrow from the next column to make the subtraction possible.
Regrouping is also a building block for more advanced math, so getting comfortable with it early sets us up well for everything that comes next.
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Regrouping works with two-digit numbers, three-digit numbers, and even larger numbers. To get a feel for it before diving into the steps, we can use a few simple tools:
Base-ten blocks: Each small block represents 1, and each rod represents 10. In addition, if we end up with 10 or more small blocks in the ones column, we swap them for one rod and move it to the tens column. In subtraction, if we don't have enough small blocks to subtract, we break one rod into 10 small blocks and move them to the ones column.
Place value mats: A place value mat is a sheet divided into labeled columns: ones, tens, and hundreds. We place blocks or counters in the correct column, then physically move them between columns when regrouping is needed.
Drawings: We draw a simple table with three columns labeled "Ones," "Tens," and "Hundreds." We use circles or tally marks to represent each digit, then cross out and redraw them in the right column when regrouping takes place.
These tools help us see how regrouping works before we try it with pencil and paper.
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In both addition and subtraction, regrouping means moving values between place value columns. Let's walk through each one step by step.
We use regrouping in addition when the sum in a place value column reaches 10 or more. Let's add 47 and 28.
Align the numbers by place value, ones under ones and tens under tens.
Add the ones column: 7 + 8 = 15. Write down 5 in the ones place and ‘’carry’’ the 1 to the tens column.
Add the tens column, including the carried 1: 4 + 2 + 1 = 7.
Our answer is 75.
We use regrouping in subtraction when the top digit in a place value column is smaller than the bottom digit. Now, let's subtract 19 from 42.
Align the numbers by place value, ones under ones and tens under tens.
Look at the ones column: 2 is smaller than 9, so we borrow 1 from the tens column. The 4 in the tens place becomes 3, and the 2 in the ones place becomes 12.
Subtract the ones column: 12 - 9 = 3.
Subtract the tens column: 3 - 1 = 2.
Our answer is 23.
Let's put regrouping into practice. Here are five examples we can work through together, starting with addition and moving into subtraction.
We are adding three-digit numbers (276 and 138), so we work column by column from right to left.
In the ones column, we add 6 + 8 = 14, write down 4, and carry the 1.
In the tens column, let’s do one more addition 7 + 3 + 1 = 11. We carried 1 from the ones column, so we write down 1, and carry the 1 to the hundreds column.
In the hundreds column, we do one more addition 2 + 1 + 1 = 4. We carried 1.
Our final answer is 414.
Let’s subtract 287 from 503. In this case, we are subtracting from a number with a zero in the tens place, so we need to borrow twice.
In the ones column, number 3 is smaller than 7, so we borrow from the tens place. The tens digit is 0, so we first borrow from the hundreds place. The 5 in the hundreds place becomes 4, and the 0 in the tens place becomes 10.
Now, we borrow 1 from the tens place for the ones place. The 10 in the tens place becomes 9, and the 3 in the ones place becomes 13.
In the ones column, we do the subtraction 13 - 7 = 6.
Next, we move to the tens column and do the subtraction there 9 - 8 = 1.
In the hundreds column, we need one more subtraction 4 - 2 = 2.
We get our answer, which is 216.
Let’s do one more addition: 37 and 25. These are two-digit numbers with regrouping in the ones column.
In the ones column, we first add 7 + 5 = 12. Write down 2, carry the 1.
Then, in the tens column, we do one more addition 3 + 2 + 1 = 6. We carried 1.
Our answer for this one is 62.
We are subtracting two-digit numbers (18 from 42) with regrouping in the ones column.
In the ones column, we notice that 2 is smaller than 8, so we borrow 1 from the tens place. The 4 in the tens place becomes 3, and the 2 in the ones place becomes 12.
Now, in the ones column, we subtract 8 from 12, and the result is 4.
Next, in the tens column, we are dealing with one more subtraction: 3 - 1 = 2.
Our answer is 24.
Let’s add 58 and 36. As they are two-digit numbers, we are regrouping in the ones column.
First, in the ones column, we add 8 + 6 = 14. Write down 4, carry the 1.
Then, in the tens column, we have one more addition 5 + 3 + 1 = 9. We carried 1.
Our final answer is 94.
Ready to test what we’ve covered? Try these practice problems on your own and check your answers at the bottom of the guide.
38 + 27
52 - 15
45 + 38
71 - 36
63 + 29
If you don't have any math tools like blocks or counters, you can draw your own regrouping table. Here's how:
Draw three columns: Label them "Hundreds," "Tens," and "Ones."
Draw boxes or circles in each column to represent the numbers.
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Even the most careful mathematicians make mistakes while learning something new. Here are the three most common ones to watch out for when regrouping.
If the sum in a column reaches 10 or more, we need to carry that value to the next column. We skip this step, and the entire answer changes.
If we want to add 47 to 28 and forget to carry the 1 from the ones column, we get 65 instead of 75. One missed step can cost us the right answer.
Before we start, we need to make sure ones line up with ones, tens with tens, and hundreds with hundreds. Misaligned columns lead to errors before we even begin calculating.
For example, if we write 47 + 8 and accidentally line up the 8 under the tens column instead of the ones column, we end up adding 8 to 4 instead of 8 to 7, and the entire calculation goes off track.
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If we carry a number to the next column, we need to include it in that column's calculation. Leaving it out is one of the most common regrouping mistakes in addition.
Let’s take 47 + 28 as an example. After carrying the 1 to the tens column, we need to add 4 + 2 + 1. If we forget the carried 1 and only add 4 and 2, we get 65 instead of 75.
Mathnasium's specially trained tutors guide students through the addition and subtraction regrouping process in a supportive, engaging environment.
Mathnasium is the only math-only learning center helping K-12 students of all skill levels learn and master regrouping and any other math concept.
To help students build a deep understanding of any math topic, we use a proprietary teaching approach called the Mathnasium Method™.
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Each student starts with a diagnostic assessment that helps us identify their current skills, knowledge gaps, and learning goals. From there, we build a personalized learning plan tailored to exactly where they are and where they need to go.
Our specially trained tutors then guide students through concepts like regrouping using plain language and a combination of verbal, visual, tactile, and written techniques. This helps students see the concept from different perspectives and truly understand how it works.
When a student gets stuck, we break the problem down into smaller, manageable steps and focus on both the “how” and the “why” behind the concept. Over time, students build strong problem-solving skills and critical thinking tools that help them approach new math challenges independently.
Fun is an important part of how we work. Sessions often include game-based and hands-on activities that keep students engaged and learning enjoyable. Students earn rewards along the way, and every bit of progress gets celebrated, so confidence grows alongside mastery.
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If you worked through the practice problems, here are the answers:
1. 38 + 27
Ones column: 8 + 7 = 15. We write down 5, carry the 1.
Tens column: 3 + 2 + 1 = 6. We carried the 1 from the ones column.
The answer is 65.
2. 52 - 15
Ones column: 2 is smaller than 5, so we borrow 1 from the tens place. The 5 in the tens place becomes 4, and the 2 in the ones place becomes 12.
Ones column: 12 − 5 = 7
Tens column: 4 − 1 = 3
The answer is 37.
3. 45 + 38
Ones column: 5 + 8 = 13. Write down 3, carry the 1.
Tens column: 4 + 3 + 1 = 8. We carried the 1 from the ones column.
The final answer is 83.
4. 71 - 36
Ones column: 1 is smaller than 6, so we borrow 1 from the tens place. The 7 in the tens place becomes 6, and the 1 in the ones place becomes 11.
Ones column: 11 − 6 = 5
Tens column: 6 − 3 = 3
Our answer is 35.
5. 63 + 29
Ones column: 3 + 9 = 12. Write down 2, carry the 1.
Tens column: 6 + 2 + 1 = 9. We carried the 1 from the ones column.
Our answer is 92.
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