Have you ever wondered how to solve tricky addition or subtraction problems when one column just doesn’t add up?
That’s where regrouping comes in!
Regrouping, sometimes called “borrowing” or “carrying,” is a math skill that helps you handle numbers that cross place value boundaries, making addition and subtraction much easier.
In this guide, we’ll walk you through everything you need to know about regrouping, starting with simple, kid-friendly definitions and a step by step guide, and topping it all off with solved examples, common mistakes, and practice problems to build your confidence.
Let’s get started!
Meet Our Top-Rated Math Tutors in Littleton, CO
Regrouping is a way of reorganizing numbers to make addition and subtraction easier.
When a number in one place value column (like the ones place) is too large, we "regroup" by carrying over the extra value to the next column.
In addition, this process is called carrying. When the sum in a column is 10 or more, we shift the extra amount to the next place value.
In subtraction, it’s known as borrowing. When the top digit is smaller than the bottom digit, we take from the next column to make the subtraction possible.
Think of regrouping like organizing toys: if one box is too full, you move some into a bigger box. This simple idea helps make math much easier!
Regrouping works with two-digit numbers, three-digit numbers, and even larger numbers.
To understand it better, try using:
Base-ten blocks – Stack and trade 10 small blocks for one bigger block to see regrouping in action.
Place value mats – Organize numbers into ones, tens, and hundreds to keep track of regrouping.
Drawings – Use circles, squares, or tally marks to represent numbers and visually regroup when needed.
By using these tools, you’ll see how regrouping helps simplify addition and subtraction, making math both fun and easy to understand!
Regrouping is used in addition and subtraction when a number in one place value column exceeds 9 or when you need to borrow from another column.
By organizing numbers into place value columns—ones, tens, hundreds, and beyond—you can clearly see where regrouping is needed.
Let’s break it down step by step with examples for both addition and subtraction!
We use regrouping in addition when we add numbers and the sum in a specific place value (like the ones place) is 10 or greater. When this happens, we "regroup" by carrying over the extra ten to the next higher place value (like the tens place).
Let's break down the steps to make regrouping easy!
We will add 47 and 28:
Start by aligning the numbers by place value (ones under ones, tens under tens): 7 + 8
Add the digits in the ones column: 7 + 8 = 15. Since the sum is 10 or greater, write down the ones digit (in this case, 5) and carry the tens digit (in this case, 1) to the next column.
Add the tens column (including any numbers carried over): 4 + 2 + 1 = 7
If necessary, repeat for hundreds, thousands, etc.
In our case, the sum of 47 and 28 is 75:
Sometimes when we subtract, we don't have enough in one place value.
For example, if we try to subtract 9 from 2 in the ones place, we can't do it directly. That's when we need to "borrow" from the next higher place value.
Let’s solve 42 - 19.
Align the numbers by place value: the ones 2 and 9, and the tens 4 and 1.
If the digit in the top row is smaller than the one below it, borrow 1 from the next column. In this case, 2 is smaller than 9, so we’ll “borrow” 1 from 4, and subtract 9 from 12 like so: 12 - 9 = 3
Reduce the number in the column you borrowed from by 1, like so: 4 - 1 = 3
Complete the subtraction. In our case, we borrowed 1 from 4, so now we are subtracting the tens of the top number (3) with the tens of the bottom number (1) like so: 3 - 1 = 2
Combine the resulting ones and tens, and our result is: 23
Imagine you're building a tall tower with blocks.
You need to make sure each level is strong and steady, right?
Regrouping is like building the foundation for your math tower!
It helps you understand how numbers work together. Just like you need to stack blocks carefully, you need to understand how to group and ungroup numbers.
It makes adding and subtracting big numbers much easier, like having a secret shortcut to reach the top of your tower!
It's a stepping stone for learning even harder math. Just like you can build a bigger tower on a strong foundation, you can learn more complex math when you understand regrouping.
Let's see regrouping in action with some solved examples!
Let’s practice a few examples:
Addition: 276 + 138
Subtraction: 503 - 287
Addition: 37 + 25
Subtraction: 42 - 18
Addition: 58 + 36
Now it's your turn to be a math magician! You've learned how to regroup with addition and subtraction, so let's put those skills to the test!
If you don't have any math tools like blocks or counters, don't worry! 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.
Now, solve these problem using regroupings:
Addition: 38 + 27 = ?
Subtraction: 52 - 15 = ?
Addition: 45 + 38 = ?
Subtraction: 71 - 36 = ?
Addition: 63 + 29 = ?
You can use your drawing to help you keep track of your numbers and regroup when needed.
When you are done, check your answers at the end of the page to see how you did!
Sometimes, even the best math detectives make mistakes! Here are a few things to watch out for:
Forgetting to "borrow" or "carry": This is like forgetting to get a new pack of cookies from the jar! You might not have enough to share.
Mixing up the numbers: Make sure your ones are lined up with ones, your tens with tens, and so on. It's like stacking blocks neatly!
Missing the extra number: When you "carry" a number, don't forget to add it to the next column. It's like adding that extra cookie you got from the jar!
Remember: Even if you make a mistake, it's okay! Just go back and check your work carefully.
Our specially trained math tutors help students of all skill levels to learn and master math concepts like regrouping.
Mathnasium of Littleton is a math-only learning center for K-12 students of all skill levels.
Our specially trained math tutors offer personalized instruction and online support to help students truly understand and enjoy math.
Discover our approach to elementary school tutoring:
Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of 4S Ranch today!
Schedule a Free Assessment at Mathnasium of Littleton
1. Addition: 38 + 27
Ones: 8 + 7 = 15
Write down 5, carry 1
Tens: 3 + 2 + 1 (carried over) = 6
Answer: 38 + 27 = 65
2. Subtraction: 52 - 15
Ones: We can't take 5 away from 2, so we borrow 1 ten from the tens place.
52 becomes 4 tens and 12 ones.
Ones: 12 - 5 = 7
Tens: 4 tens - 1 ten = 3 tens
Answer: 52 - 15 = 37
3. Addition: 45 + 38
Ones: 5 + 8 = 13
Write down 3, carry 1
Tens: 4 + 3 + 1 (carried over) = 8
Answer: 45 + 38 = 83
4. Subtraction: 71 - 36
Ones: We can't take 6 away from 1, so we borrow 1 ten from the tens place.
71 becomes 6 tens and 11 ones.
Ones: 11 - 6 = 5
Tens: 6 tens - 3 tens = 3 tens
Answer: 71 - 36 = 35
5. Addition: 63 + 29
Ones: 3 + 9 = 12
Write down 2, carry 1
Tens: 6 + 2 + 1 (carried over) = 9
Answer: 63 + 29 = 92
(303) 979-9077
(303) 979-9077
