Regrouping in Math: Definition & Examples

Definitionnoun

What is regrouping in math?

Regrouping is trading 10 of one place value for 1 of the next larger place, or 1 for 10 of the next smaller place, so that column addition or subtraction works. In 47 + 38, the 15 ones become 1 ten and 5 ones; in 52 − 27, 1 ten becomes 10 ones. It is also called carrying and borrowing.

In Spanish: reagrupación
Also called: carrying, borrowing, trading, renaming, composing and decomposing tens
Grade level: K-5

Grade 1Grade 2Grade 3Grade 4CCSS 1.NBT.C.4CCSS 2.NBT.B.7CCSS 4.NBT.B.4TABE

Regrouping in a picture

In addition, ten ones are grouped into one ten and carried left. In subtraction, one ten is broken into ten ones so there are enough to take away.

Formal definition and notation

Regrouping rewrites a number in an equivalent place value form: since 10 ones = 1 ten, 10 tens = 1 hundred, and so on, a digit total of 10 or more in a column is composed into one unit of the next place (carrying), and one unit of a place is decomposed into 10 units of the place to its right (borrowing). The value of the number never changes; only how its parts are grouped does.

Symbol	Read it as	Meaning
small 1 above a column	carried one	1 group of ten moved to the next place on the left
crossed-out digit	regrouped digit	a place that gave 1 unit to the place on its right, now 1 less

Key facts

Regrouping is needed in addition when a column adds to 10 or more, and in subtraction when a top digit is smaller than the digit below it.
Regrouping never changes the number: 5 tens 2 ones and 4 tens 12 ones both equal 52.
Old names: “carrying” for addition and “borrowing” for subtraction. Nothing is really borrowed; a ten is broken into ten ones.
Across zeros, regroup step by step: 503 = 4 hundreds, 9 tens, 13 ones.
The same trades work with decimals: 10 hundredths = 1 tenth, 10 tenths = 1 one.

The trading rule

10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand

adding: if a column totals 10 or more, write the ones digit and carry the tens digit left
subtracting: if the top digit is smaller, take 1 from the place on the left and add 10 to this place

When the place on the left is 0, regroup from farther left first: 400 = 3 hundreds, 9 tens, 10 ones.

Regrouping examples, step by step

Example 1: Adding with one regroup

Warm-up

Find 58 + 27.

Ones: 8 + 7 = 15. Write 5, carry 1 ten.
Tens: 5 + 2 + 1 = 8.

Answer: 58 + 27 = 85.

Example 2: Subtracting across a zero

Core

Find 403 − 156.

Ones: 3 − 6 needs more ones, but the tens place is 0.
Regroup 1 hundred: 4 hundreds 0 tens → 3 hundreds 10 tens.
Regroup 1 ten: 10 tens 3 ones → 9 tens 13 ones.
Subtract: 13 − 6 = 7, 9 − 5 = 4, 3 − 1 = 2.

Answer: 403 − 156 = 247.

Example 3: Regrouping in several places

Test-style

A library had 2,345 books and received 1,879 more. How many books does it have now?

Ones: 5 + 9 = 14: write 4, carry 1.
Tens: 4 + 7 + 1 = 12: write 2, carry 1.
Hundreds: 3 + 8 + 1 = 12: write 2, carry 1.
Thousands: 2 + 1 + 1 = 4.

Answer: The library has 4,224 books.

Common mistakes

✗ MistakeForgetting the carried 1: 58 + 27 = 75.

✓ InsteadAdd the carried ten: 5 + 2 + 1 = 8 tens, so 85.

The extra ten from the ones column is part of the sum. Write the small 1 above the tens column so you do not lose it.

✗ MistakeSubtracting the smaller digit from the larger in each column: 52 − 27 = 35 (because 7 − 2 = 5).

✓ InsteadRegroup: 4 tens 12 ones − 2 tens 7 ones = 2 tens 5 ones = 25.

Each column must be top minus bottom. When the top digit is smaller, regroup instead of flipping the order.

✗ MistakeAcross a zero, taking 1 from the zero: 403 − 156 written with the 0 turned into −1.

✓ InsteadRegroup from the hundreds first: 403 = 3 hundreds, 9 tens, 13 ones; answer 247.

A place holding 0 has nothing to give, so it must first get 10 from the place to its left.

✗ MistakeWriting the whole column sum: 47 + 38 = 715 (4 + 3 = 7 and 7 + 8 = 15).

✓ InsteadCarry the 1 ten: 47 + 38 = 85.

Each place can hold only one digit, 0 to 9. A 15 in the ones column must become 1 ten and 5 ones.

Not to be confused with

Regroupingvs.Rounding

Rounding changes a number to a nearby simpler one (47 → 50). Regrouping keeps the exact value (47 = 3 tens 17 ones).

Regroupingvs.Decompose

Decomposing is any split into parts. Regrouping is the specific trade of 1 unit of a place for 10 of the next smaller place (or the reverse).

Quick check: 3 questions

Question 1 of 3

What is 36 + 48?

Show answer and explanation

Answer: C. Ones: 6 + 8 = 14, write 4 and carry 1. Tens: 3 + 4 + 1 = 8. Answer 84. 74 forgets the carry, 714 writes the whole 14, and 82 makes an adding slip.

Question 2 of 3

What is 71 − 46?

Show answer and explanation

Answer: B. Regroup 1 ten: 6 tens 11 ones − 4 tens 6 ones = 2 tens 5 ones = 25. 35 subtracts 1 from 6 in the ones, 24 makes a slip, and 117 adds.

Question 3 of 3

To subtract 600 − 248, how is 600 regrouped?

Show answer and explanation

Answer: C. Take 1 hundred to make 10 tens, then 1 of those tens to make 10 ones: 5 hundreds, 9 tens, 10 ones (still 600). Choice B stops one step early, and D adds value that was never there (700).

Regrouping: frequently asked questions

Is regrouping the same as carrying and borrowing?

Yes. “Carrying” is regrouping in addition: 10 ones are grouped into 1 ten and moved to the tens column. “Borrowing” is regrouping in subtraction: 1 ten is broken into 10 ones. Many teachers prefer “regrouping” because nothing is really borrowed or paid back; the number is just written in a different but equal way.

When do you need to regroup?

In addition, regroup when the digits in a column add to 10 or more, as in 7 + 6 = 13. In subtraction, regroup when the top digit in a column is smaller than the bottom digit, as in 3 − 8. If neither happens, as in 54 + 32 or 87 − 41, no regrouping is needed.

How do you subtract across zeros?

Go left until you find a nonzero digit, take 1 from it, and pass the trade back to the right. For 500 − 168, rewrite 500 as 4 hundreds, 9 tens and 10 ones. Then subtract: 10 − 8 = 2, 9 − 6 = 3, 4 − 1 = 3, giving 332. Check by adding: 332 + 168 = 500.

Practice and tools

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 1.NBT.C.4, CCSS 2.NBT.B.7, CCSS 4.NBT.B.4

Cite this entry

Effortless Math Team. “Regrouping.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/regrouping/

Flashcard

TermRegroupingcarrying and borrowing

DefinitionTrading 10 of one place for 1 of the next place, or the reverse, in column math. In 47 + 38, 15 ones become 1 ten and 5 ones.

Study the full deck

Browse all terms in the Math Dictionary · More operations terms · Random term

NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3HundredthsHundredths are the parts you get when one whole is split into 100 equal parts; one hundredth is 1100 or 0.01. The hundredths place is the second digit to the right of the decimal point, so in 3.47 the 7 means 7 hundredths. One cent is one hundredth of a dollar.Number System · Grade 4, Grade 5, Grade 6TenthsTenths are the parts you get when one whole is split into 10 equal parts; each part is one tenth, written 110 or 0.1. The tenths place is the first digit to the right of the decimal point, so in 4.7 the 7 means 7 tenths, or 0.7.Number System · Grade 3, Grade 4, Grade 5RoundingRounding replaces a number with a nearby number that is easier to use, to a chosen place value. Look at the digit immediately to the right of that place: 5 or more rounds up, 4 or less rounds down. So 47 rounds to 50 to the nearest ten, and 3.68 rounds to 3.7 to the nearest tenth.Number System · Grade 3, Grade 4, Grade 5DecomposeDecompose means to break a number or shape into smaller parts that together make the whole. You can decompose 8 into 5 + 3, decompose 347 into 300 + 40 + 7, or decompose 34 into 14 + 24. Most numbers can be decomposed in many ways, and the parts always add back to the original.Number System · Kindergarten, Grade 1, Grade 2DigitA digit is one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write every number. The number 507 has three digits: 5, 0 and 7. What a digit is worth depends on its place: in 507, the 5 stands for 5 hundreds, or 500.Number System · Grade 1, Grade 2, Grade 3Standard AlgorithmThe standard algorithm is the usual written column method for adding, subtracting, multiplying or dividing multi-digit numbers. You line up digits by place value, work one place at a time, and regroup (carry or borrow) when a place overflows or runs short. For 478 + 365 it gives 843 in three short steps.Operations · Grade 4, Grade 5, Grade 6SumA sum is the result you get when you add two or more numbers. In 8 + 5 = 13, the numbers 8 and 5 are the addends and 13 is the sum. The order does not change it: 5 + 8 is also 13. Word problems ask for a sum with words like total, in all and altogether.Operations · Grade 1, Grade 2, Grade 3DifferenceA difference is the result of subtracting one number from another. In 12 − 7 = 5, the difference is 5. It tells how much bigger one number is than another, or how far apart they are on a number line. “The difference of a and b” means a − b, in that order.Operations · Grade 1, Grade 2, Grade 3Expanded FormExpanded form is a way of writing a number as the sum of the values of its digits. Each digit is multiplied by its place value, so 4072 = 4000 + 70 + 2, or 4 × 1000 + 7 × 10 + 2 × 1. It shows what every digit is worth. Zeros add nothing, so they are usually left out.Number System · Grade 2, Grade 3, Grade 4

Regrouping

What is regrouping in math?

Regrouping in a picture

Formal definition and notation

Key facts

The trading rule

Regrouping examples, step by step

Example 1: Adding with one regroup

Example 2: Subtracting across a zero

Example 3: Regrouping in several places

Common mistakes

Not to be confused with

Quick check: 3 questions

Regrouping: frequently asked questions

Is regrouping the same as carrying and borrowing?

When do you need to regroup?

How do you subtract across zeros?

Related terms

Practice and tools

Sources

Flashcard

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