How To Do Long Subtraction | Borrowing Made Clear

Long subtraction can feel odd at first because the steps look strict on paper. Once you see what each step means, it stops being a “mystery method” and turns into a tidy routine you can trust.

This walkthrough keeps it practical: how to set the problem up, how borrowing works, what to do with zeros, and how to check your answer so you catch slips fast.

What Long Subtraction Is Doing Under The Hood

Subtraction asks, “How much is left?” When numbers have more than one digit, each digit has a place value: ones, tens, hundreds, and so on.

Long subtraction lines those places up so you subtract ones from ones, tens from tens, and hundreds from hundreds. You start on the right because the ones column is the smallest place value, so it’s safe to finish that part first.

Minuend And Subtrahend (The Two Numbers)

The top number is the one you start with. The bottom number is the one you take away. You subtract the bottom from the top, column by column.

If you want clean vocabulary for schoolwork, the top is often called the minuend, and the bottom is the subtrahend. You don’t need the terms to get the math right, but they can help when reading instructions.

Why Borrowing Works

Borrowing is really regrouping. You’re not “getting free numbers.” You’re trading value from one place to the next.

One ten equals ten ones. One hundred equals ten tens. When a top digit is too small to subtract a larger bottom digit, you trade one unit from the next place to make the current place larger.

Set Up The Problem So You Don’t Fight The Layout

Most subtraction mistakes come from messy setup. Fix the layout, and the arithmetic gets easier.

Line Up Place Values, Not Just The Ends

Write the numbers in a column with the ones digits stacked in the same column. Then stack tens under tens, hundreds under hundreds, and keep going left.

If one number has fewer digits, treat missing places as zeros. That keeps the columns aligned and stops you from subtracting tens from hundreds by accident.

Use A Clear Subtraction Bar

Draw a straight line under the second number. Leave space below for the answer digits so you don’t crowd your work.

If you borrow, write the changed digits small and neat above the original digit. Keeping the edits readable makes checking far easier.

How To Do Long Subtraction With Borrowing

This is the standard routine that works for 2-digit, 3-digit, and bigger problems.

Step-By-Step Method

1. Start at the ones column (far right). Subtract the bottom digit from the top digit.
2. If the top digit is smaller, regroup from the next column left. Reduce the next column by 1, and add 10 to the current top digit.
3. Write the result for that column. Put it directly below the column you just finished.
4. Move one column left. Repeat the subtract-or-regroup routine until you reach the last column.

Walkthrough: A Clean Borrowing Example

Try this: 432 − 158.

Ones: 2 − 8 can’t work without regrouping. Trade one ten from the 3 tens. The 3 becomes 2, and the 2 ones becomes 12 ones. Now do 12 − 8 = 4.

Tens: after the trade, you have 2 − 5. Trade one hundred from the 4 hundreds. The 4 becomes 3, and the 2 tens becomes 12 tens. Now do 12 − 5 = 7.

Hundreds: 3 − 1 = 2. Your answer is 274.

Fast Self-Check For Borrowing Problems

A quick way to check subtraction is to add your answer to the number you subtracted. If you get the original top number, your subtraction is consistent.

For 432 − 158 = 274, check 274 + 158 = 432.

Borrowing Across Zeros Without Getting Stuck

Zeros can feel like a roadblock because you can’t take 1 from 0 in a clean way. The fix is a chain of regrouping until you reach a column with value to trade.

What To Do When A Column Is Zero

Say you’re working on 5002 − 178. The ones column (2 − 8) needs regrouping, but the tens digit is 0.

Move left until you find a digit that isn’t zero. Borrow from that place, then “pass” the regrouping back to the right one column at a time.

Mini Walkthrough: 5002 − 178

Ones: 2 − 8 needs regrouping. Tens is 0, hundreds is 0, thousands is 5. Regroup from thousands: 5 becomes 4, and the hundreds place becomes 10 hundreds.

Now you still need tens. Regroup from the 10 hundreds: hundreds becomes 9 hundreds, tens becomes 10 tens.

Now you still need ones. Regroup from the 10 tens: tens becomes 9 tens, ones becomes 12 ones.

Finish columns: ones 12 − 8 = 4, tens 9 − 7 = 2, hundreds 9 − 1 = 8, thousands 4 − 0 = 4. Answer: 4824.

A Practical Tip For Zero Chains

Write each regrouping change as you go. If you try to hold all the changes in your head, it’s easy to subtract from the original digits by accident.

If your paper gets messy, rewrite the problem after regrouping, then subtract on the clean copy.

Common Mistakes And The Fix That Stops Them

Most errors follow a pattern. Once you know the pattern, you can spot it mid-problem and correct it on the spot.

Mistake: Borrowing But Forgetting To Reduce The Left Digit

If you turn 2 into 12 in the ones column, you must reduce the tens column by 1. If that reduction is missing, the final answer will be too large.

Fix: circle the digit you borrowed from and change it first. Then change the right digit to +10.

Mistake: Subtracting The Larger Digit From The Smaller Digit Anyway

Some students see 2 − 8 and write 6 because they subtract 8 − 2. That flips the direction and breaks the meaning of subtraction.

Fix: pause and say the sentence out loud: “two minus eight.” If it doesn’t make sense without regrouping, regroup before writing anything.

Mistake: Misaligned Columns

If the ones digits don’t sit in the same column, every later step can be wrong even if each mini-subtraction is correct.

Fix: draw a light place-value guide or use graph paper. Even one vertical line between ones and tens can clean things up.

Regrouping Cheat Sheet (Table 1)

Use this as a quick “what do I do next?” reference when you hit a snag mid-problem.

Situation You See	What To Do	Slip To Watch For
Top digit ≥ bottom digit	Subtract normally and write the result under the column	Writing the result in the wrong column
Top digit < bottom digit	Regroup 1 from the column to the left (add 10 to the current top digit)	Forgetting to reduce the left digit by 1
Left digit is 0 when you need to regroup	Move left until you find a non-zero digit, regroup, then pass the regrouping back right	Stopping too early and regrouping from a 0
Multiple regroups in a row	Make each change one at a time, writing the new digits above the old ones	Subtracting from the original digits after you changed them
Bottom number has fewer digits	Treat missing places as 0 and keep columns aligned	Shifting the bottom number too far left
Answer ends with leading zeros on the left	Drop leading zeros (write 045 as 45)	Dropping zeros in the middle (405 is not 45)
You doubt the result	Check by addition: difference + subtrahend = minuend	Adding with misaligned columns during the check
Regrouping feels abstract	Think “trade 1 ten for 10 ones” (or 1 hundred for 10 tens)	Calling it “borrowing” and thinking it must be paid back

Ways To Check Your Answer Without A Calculator

Checking isn’t busywork. It’s a fast habit that saves you from turning in a page of tiny errors.

Add-Back Check

Add your difference to the number you subtracted. If the sum matches the original top number, your work hangs together.

This check matches what subtraction means: you started with the top number, took away the bottom number, and the remainder is the answer.

Estimation Check (Quick Sanity Test)

Round each number to a nearby friendly number, then subtract in your head. Your exact answer should land near that rough result.

Say 782 − 396. A quick mental check is 800 − 400 = 400. The exact answer should be near 400, not 40 or 4,000.

Digit Reasonableness Check

Look at the ones digit. If you subtracted 8 from 2, you had to regroup, so the ones digit of the answer should feel consistent with 12 − 8 = 4.

This isn’t a full proof, but it can catch “I forgot to regroup” in seconds.

Practice Set With Built-In Answer Checks (Table 2)

Work these on paper. After each one, use the add-back check. That way you’re practicing the method and the checking habit at the same time.

Problem	Main Skill	Add-Back Check You Should See
64 − 28	Single regroup	(Answer) + 28 = 64
503 − 176	Regroup with a zero in tens	(Answer) + 176 = 503
900 − 457	Regroup across zeros	(Answer) + 457 = 900
1,204 − 689	Multiple regroups	(Answer) + 689 = 1,204
7,030 − 2,558	Zero chain regrouping	(Answer) + 2,558 = 7,030
50,002 − 9,875	Long zero chain regrouping	(Answer) + 9,875 = 50,002

When Long Subtraction Feels Hard, Try This Order

If you’re learning, it helps to build the skill in layers instead of jumping straight into zeros and five-digit numbers.

Layer 1: No Regrouping

Start with problems where every top digit is larger than the bottom digit in the same column. That builds clean column habits.

Try: 864 − 321, 975 − 642.

Layer 2: One Regroup

Move to problems with one regroup in the ones column. Keep the tens and hundreds subtraction simple so your attention stays on the regroup step.

Try: 742 − 315, 651 − 427.

Layer 3: Two Regroups

Next, use problems where regrouping happens in ones and tens. This trains you to track changes across columns without losing your place.

Try: 432 − 158, 703 − 489.

Layer 4: Zeros In The Middle

Now bring in zeros, but not a long chain yet. This teaches you to “go left, then pass it back right” without getting overwhelmed.

Try: 1,002 − 478, 2,040 − 895.

Layer 5: Long Zero Chains

Save the long chains for last. They’re not harder because the subtraction is different. They’re harder because the bookkeeping is longer.

Try: 10,000 − 6,789, 50,002 − 9,875.

A Clean Mental Picture For Borrowing

If borrowing still feels weird, switch the wording in your head from “borrow” to “trade.”

Trading matches place value: one ten becomes ten ones, one hundred becomes ten tens. Nothing is created, nothing is lost, it’s the same value written in a different form.

Khan Academy’s regrouping lessons show the same idea with clear place-value language, which can help the method click if you like seeing it explained step by step.

Wrap-Up Check Before You Turn It In

Before you submit homework or a test page, run this quick scan:

• Ones, tens, hundreds are lined up in straight columns.
• Each regroup reduced the left digit by 1 and added 10 to the current digit.
• Every column subtraction used the edited digits, not the original ones.
• Your final answer drops only leading zeros, not middle zeros.
• You checked at least the hardest problem by addition.