What Is Regrouping in Math? Carrying and Borrowing

How Does Regrouping Work In Addition?

Regrouping in addition happens when a column adds up to 10 or more. You keep the ones digit of that column's total and move the ten (or tens) into the next column to the left as a single unit.

Take $46 + 37$, written in columns:

$\begin{array}{r}46\\+37\\\hline83\end{array}$

1. Ones column: $6 + 7 = 13$. Thirteen ones is 1 ten and 3 ones. Write 3 in the ones place and carry the 1 ten.

2. Tens column: $4 + 3 + 1 = 8$ tens. Write 8.

3. Answer: $46 + 37 = 83$.

The carried 1 is the part most children get wrong, and the reason is language. "Carry the one" sounds like a stray digit. Said as "carry one ten", it becomes a quantity your child can picture: ten ones snapped into a rod and slid one column over.

How Does Regrouping Work In Subtraction?

Regrouping in subtraction happens when the top digit in a column is smaller than the bottom digit. You take 1 from the next column to the left and turn it into 10 of the current unit, so the subtraction in that column becomes possible.

Take $52 - 27$:

$\begin{array}{r}52\\-27\\\hline25\end{array}$

1. Ones column: 2 ones is not enough to take away 7. Regroup 1 ten from the 5 tens, leaving 4 tens, and add 10 ones to the 2 ones to make 12.

2. Ones again: $12 - 7 = 5$.

3. Tens column: $4 - 2 = 2$.

4. Answer: $52 - 27 = 25$. Check by adding back: $25 + 27 = 52$.

Nothing was really "borrowed", because nothing is ever paid back. Fifty-two was simply renamed as 4 tens and 12 ones, which is still 52. Teachers increasingly prefer "regroup" or "trade" over "borrow" for exactly that reason.

Is Regrouping The Same As Borrowing Or Carrying?

Yes. Regrouping is the umbrella word; carrying is regrouping in addition and borrowing is regrouping in subtraction. Some textbooks also say "trading", "exchanging" or "renaming", and in the UK you will often hear "exchanging" alongside the formal written method called columnar addition and subtraction.

The words matter more than they look. A child taught "borrow" sometimes expects to "give it back" later, and adds a stray 1 to the answer; a child taught "regroup" just sees the same number sorted differently. This is one of the reasons the Common Core math vs traditional math debate is often a debate about vocabulary rather than about different arithmetic.

What Is Regrouping In Math Really Doing, And Why Is It Important?

Regrouping does one job: it keeps a single digit, 0 to 9, in each place, which is the only thing our number system allows. That is why it is important. The moment a column reaches ten, that ten has to be written as a 1 in the next place, so regrouping is not an extra rule bolted onto addition; it is what place value forces.

Three ideas sit underneath every regrouping step:

• Each place is worth ten of the place to its right. One ten equals ten ones, one hundred equals ten tens. That fixed ratio is what makes the trade fair.

• A number can be written in more than one way. $52 = 5 \text{ tens} + 2 \text{ ones} = 4 \text{ tens} + 12 \text{ ones}$. Both are true, and regrouping just picks the version that makes the column work.

• The written method is a record of the trades. The vertical algorithm your child learns is a compact way of writing down exchanges that could be done with blocks or coins.

Here is the part that is easy to miss, even for adults who do it fluently. The column method is not faster because it is clever; it is faster because it lets you work one digit at a time, and regrouping is the price of that convenience. Mental strategies such as adding tens first (the kind in how to add mentally) avoid regrouping altogether by keeping the whole number in view.

How Do You Teach Regrouping With Base Ten Blocks?

You teach regrouping with base-ten blocks by letting your child do the physical trade before writing anything: ten small cubes are swapped for one rod, or one rod is swapped for ten cubes. The written method comes only after the trade feels obvious.

A simple sequence for home:

1. Build both numbers. For $46 + 37$, lay out 4 rods and 6 cubes, then 3 rods and 7 cubes.

2. Push the cubes together and count them. Thirteen cubes. Ask: "Can we make a rod?" Your child counts out ten, swaps them for one rod, and 3 cubes are left.

3. Count the rods. Eight rods, three cubes: 83.

4. Write it alongside. Only now, write the column sum and point to where each trade appears: the carried 1 is the rod your child just made.

5. Reverse it for subtraction. Build 52, try to take away 7 cubes from 2, get stuck, and break a rod into ten cubes.

No blocks at home? Bundled straws or lolly sticks in elastic bands work, and so do coins (ten 1-unit coins for one 10-unit coin). The IES practice guide Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (March 2021) rates the use of "a well-chosen set of concrete and semi-concrete representations" as supported by strong evidence, which is the research name for exactly this blocks-then-drawings-then-digits route.

How Can You Tell When Regrouping Is Needed?

Regrouping is needed in addition when a column's digits add to 10 or more, and in subtraction when the top digit in a column is smaller than the digit below it. Your child can check every column before starting, which stops the most common guessing.

Is Regrouping Needed To Subtract 32 - 19?

Yes. In the ones column, 2 is smaller than 9, so 1 ten must be regrouped.

$$32 = 2 \text{ tens} + 12 \text{ ones}$$

$$12 - 9 = 3$$

$$2 - 1 = 1$$

So $32 - 19 = 13$. Check: $13 + 19 = 32$.

By the same test, $65 - 43$ needs no regrouping ($5 \geq 3$ and $6 \geq 4$, answer 22), and neither does $346 - 123$ (answer 223). Asking "does any column need a trade?" before starting is a small habit that makes the rest of the calculation calmer. For small numbers, mental subtraction strategies such as counting up from 19 to 32 skip the trade entirely.

How Do You Subtract Across Zeros?

To subtract across zeros, you regroup from the first non-zero place to the left and pass the trade down through each zero, so every zero becomes a 9 and the ones place gains 10. It looks like a new rule, but it is the same trade made twice in a row.

Take $400 - 163$. The ones place has 0, and so does the tens place, so there is nothing to borrow from next door.

1. Regroup 1 hundred. 4 hundreds becomes 3 hundreds and 10 tens.

2. Regroup 1 of those tens. 10 tens becomes 9 tens and 10 ones.

3. The number now reads $400 = 3 \text{ hundreds} + 9 \text{ tens} + 10 \text{ ones}$.

4. Subtract column by column: $10 - 3 = 7$, then $9 - 6 = 3$, then $3 - 1 = 2$.

5. Answer: $400 - 163 = 237$. Check: $237 + 163 = 400$.

A useful shortcut for parents to know: $400$ is $399 + 1$. Subtract from 399 (no regrouping at all: $399 - 163 = 236$) and add the 1 back to get 237. It is a good way to check, and some children prefer it as their main method.

Does Regrouping Happen In Multiplication And Decimals?

Yes. Any written method that works one column at a time needs regrouping whenever a column reaches ten or more, so it shows up in multiplication, in decimals and later in long division.

• Multiplication: For $27 \times 4$, the ones give $7 \times 4 = 28$, so write 8 and regroup 2 tens. The tens give $2 \times 4 = 8$ tens, plus the 2 regrouped tens, which is 10 tens: $27 \times 4 = 108$. The same habit appears when your child moves on to how to teach multiplication with bigger numbers.

• Decimals: Tenths and hundredths follow the same ten-for-one rule. $0.6 + 0.7 = 1.3$, because 13 tenths is 1 one and 3 tenths.

• Mixed numbers: Fractions regroup too, but the trade is 1 whole for a full set of parts (1 whole is $\frac{4}{4}$ when you work in quarters), not 1 for 10.

Examples Of Regrouping In Math

These six examples move from a single carry to two regroupings, across zeros, and into money. Each answer has been checked by the inverse operation.

Example 1

Add $58 + 25$.

Ones: $8 + 5 = 13$, so write 3 and carry 1 ten.

Tens: $5 + 2 + 1 = 8$.

Final answer: 83. Check: $83 - 25 = 58$.

Example 2

Subtract $63 - 28$.

Wrong path first. A child working fast looks at the ones column, sees 3 and 8, and takes the smaller from the larger: $8 - 3 = 5$. Then the tens: $6 - 2 = 4$. The answer comes out as 45.

Check it by adding back: $45 + 28 = 73$, not 63. The answer is ten too big, which is the giveaway that a ten was never traded.

The rescue is to regroup. Rename 63 as 5 tens and 13 ones.

$$13 - 8 = 5$$

$$5 - 2 = 3$$

Final answer: 35. Check: $35 + 28 = 63$.

Example 3

Add $278 + 156$.

Ones: $8 + 6 = 14$, so write 4 and carry 1 ten.

Tens: $7 + 5 + 1 = 13$ tens, so write 3 and carry 1 hundred.

Hundreds: $2 + 1 + 1 = 4$.

Final answer: 434. Check: $434 - 156 = 278$.

Example 4

Subtract $305 - 128$.

Ones: 5 is smaller than 8, and the tens place is 0, so regroup from the hundreds first. 3 hundreds becomes 2 hundreds and 10 tens; then 10 tens becomes 9 tens and 10 more ones.

$$305 = 2 \text{ hundreds} + 9 \text{ tens} + 15 \text{ ones}$$

$$15 - 8 = 7$$

$$9 - 2 = 7$$

$$2 - 1 = 1$$

Final answer: 177. Check: $177 + 128 = 305$.

Example 5

A school library owns 1,003 books, and 268 are out on loan. How many are on the shelves?

Every place between the thousands and the ones is 0, so the trade passes through two zeros.

$$1003 = 9 \text{ hundreds} + 9 \text{ tens} + 13 \text{ ones}$$

$$13 - 8 = 5$$

$$9 - 6 = 3$$

$$9 - 2 = 7$$

Final answer: 735 books. Check: $735 + 268 = 1003$.

Example 6

Your child pays for a 2.35 snack with a 5.00 note. How much change comes back?

Line up the decimal points. The hundredths and tenths of 5.00 are both 0, so regroup 1 whole into 9 tenths and 10 hundredths.

$$5.00 = 4 \text{ ones} + 9 \text{ tenths} + 10 \text{ hundredths}$$

$$10 - 5 = 5 \text{ hundredths}$$

$$9 - 3 = 6 \text{ tenths}$$

$$4 - 2 = 2 \text{ ones}$$

Final answer: 2.65 in change. Check: $2.65 + 2.35 = 5.00$.

What Grade Is Regrouping Taught?

Regrouping is usually introduced in grade 1 (adding a two-digit and a one-digit number that "composes a ten"), becomes a main focus in grade 2, and is expected to be fluent with the standard written method by grade 4. The table pairs two curricula so you can match the stage to your child's school year.

Table: When regrouping appears in two curricula.

Sources: Common Core Grade 1 Number and Operations in Base Ten, Grade 2 NBT, Grade 4 NBT and the national curriculum in England mathematics programmes of study (updated 28 September 2021). The grade 3 and Year 5 rows describe typical practice rather than a single quoted standard. Ages are typical bands, not deadlines.

Where Do Children Go Wrong With Regrouping?

Most regrouping errors come from treating the method as a set of moves rather than a set of trades. The four below cover nearly every wrong answer a parent will see on homework, and each has a quick check.

Mistake 1: Subtracting The Smaller Digit From The Larger

Where it slips in: A column where the top digit is smaller, such as the ones in $63 - 28$.

Don't do this: Flip the digits and write $8 - 3 = 5$, giving 45.

The correct way: Check each column first; if the top digit is smaller, regroup a ten before subtracting. The first instinct here is that subtraction "goes" from big to small in every column, and adding the answer back ($45 + 28 = 73$) is the fastest way for a child to see it fail.

Mistake 2: Forgetting To Add The Carried Ten

Where it slips in: The rusher writes the 1 above the tens column and then adds only the two original tens digits.

Don't do this: For $46 + 37$, write $4 + 3 = 7$ in the tens and get 73.

The correct way: Say the carried digit as "one ten" and add it first: $1 + 4 + 3 = 8$. Children who name the carried 1 as a ten stop dropping it, because a whole rod of blocks is harder to forget than a small mark.

Mistake 3: Leaving A Zero Untouched When Subtracting Across Zeros

Where it slips in: $400 - 163$, where the child takes 1 from the hundreds and moves it straight to the ones.

Don't do this: Change 400 to 3 hundreds, 0 tens and 10 ones, then get stuck on $0 - 6$ in the tens, or write the tens as 10 and the ones as 10 at once.

The correct way: Pass the trade down one place at a time: hundreds to tens (10 tens), then tens to ones (9 tens, 10 ones). The memorizer who learned "zeros turn into nines" without the reason often turns the ones zero into a 9 as well; asking "where did that ten go?" fixes it.

Mistake 4: Lining Up The Digits On The Left

Where it slips in: Numbers of different lengths, such as $305 - 28$ or $1003 - 268$.

Don't do this: Write 28 under the 3 and the 0 of 305, so tens sit under hundreds.

The correct way: Line up the ones on the right, always. Squared paper, one digit per square, removes the problem almost completely.

A real-world version of a carry with no room to go caused the Year 2000 problem. Many programs stored years with only their last two digits, so, in the words of the Wikipedia summary of the Year 2000 problem, the year 2000 became "indistinguishable from 1900": when 99 rolled over, the carried 1 had no column to land in. It is Mistake 2 at the scale of the world's computers.

When Should You Get Extra Help With Regrouping?

Most children need weeks, not days, for regrouping to settle, and a few wrong answers along the way are normal. It is worth talking to your child's teacher, or bringing in structured support, when several of these hold together:

• By the end of grade 2 (Year 3), your child still cannot say what the carried 1 is worth, even with blocks in front of them.

• Your child can follow the steps with an example open but cannot start a fresh problem alone.

• Answers that are exactly 10 or 100 out keep appearing after a month of regular practice.

• Homework with column subtraction regularly ends in tears or refusal, not just frustration.

Usually the gap sits one step earlier, in place value itself: a child who is not sure that 52 is 5 tens and 2 ones will find every trade mysterious.

How Does Bhanzu Teach Regrouping?

Bhanzu teaches regrouping the way this guide describes: the WHY first, with objects and pictures, before the written column. In live online classes, trainers use on-screen base-ten blocks so a child makes the trade, says what it is worth, and only then records it in the written method.

Every child starts from their real level rather than their school grade, so a child stuck on borrowing because place value never settled begins with place value. Bhanzu enrols children from UKG (around age 5) through Grade 10, learning in a live classroom with peers from 20+ countries. It fits families who want the reasoning taught alongside the method; it is not the right fit if you want a worksheet bank or a program that pushes speed before understanding.

Where Can Your Child Get Extra Help With Regrouping?

If regrouping has shown you a place-value gap worth closing, these pages are matched to the grades where it is taught:

• 2nd grade math tutor for two-digit carrying and borrowing.

• 3rd grade math tutor for three-digit numbers and subtracting across zeros.

• Elementary math tutor for place value and the written methods through grade 5.

• Mental maths for class 2 for the add-tens-first strategies that sit beside the column method.

The Short Version

• Regrouping in math is trading ten of one place value for one of the next, or one for ten, without changing the number.

• Carrying is regrouping in addition; borrowing is regrouping in subtraction.

• Subtracting across zeros is the same trade passed down one place at a time.

• The most common error is subtracting the smaller digit from the larger, and adding back catches it.

• Blocks first, drawings next, written columns last is the order that makes the method stick.

Can You Solve These Three Before Moving On?

Ask your child to try these, checking each one by the inverse operation: $67 + 25$, $81 - 46$ and $500 - 237$. The answers are 92, 35 and 263; if the last one goes wrong, go back to "How Do You Subtract Across Zeros?" and build 500 with blocks before trying again. Want a live trainer to take your child from place value to confident regrouping? Book a free demo class with Bhanzu.

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