F.3 Subtract two multi-digit whole numbers
What does it mean to subtract multi‑digit whole numbers?
Subtraction means finding the difference between two numbers. When we subtract multi‑digit whole numbers, we work with numbers that have more than one digit (like 52, 371, or 6,045). The answer is called the difference.
- If you have 58 pencils and you give away 23, you are subtracting: 58 − 23 = 35.
- The difference is 35.
Always line up the digits by place value: ones under ones, tens under tens, hundreds under hundreds. This keeps the numbers organized.
Writing a subtraction problem correctly
Write the larger number (minuend) on top. Write the smaller number (subtrahend) below it. Draw a line. The answer (difference) goes below the line.
- 87- 2463
- 5,238- 1,1144,124
When numbers have different lengths, always align the rightmost digits. For 3,892 − 47, write 3,892 above 0047 (think of 47 as 0047).
Subtract without regrouping (simple subtraction)
When each digit in the top number is greater than or equal to the digit below it, subtract column by column from right to left.
- 69- 2544
- Ones: 9 − 5 = 4
Tens: 6 − 2 = 4
- 7,582- 2,4315,151
- Ones: 2 − 1 = 1
Tens: 8 − 3 = 5
Hundreds: 5 − 4 = 1
Thousands: 7 − 2 = 5
Always start at the ones column. Work your way to the left: ones, tens, hundreds, thousands, and so on.
Subtract with regrouping (borrowing) – the big idea
Sometimes a digit on top is smaller than the digit below it. Then you need to regroup (borrow) from the next column to the left.
- Ones: 2 − 7 — you cannot do 2 − 7.
- Borrow 1 ten from the 5 tens. That ten becomes 10 ones. Now the tens column has 4 tens, and the ones become 12 ones.
- Now subtract: 12 − 7 = 5; tens: 4 − 2 = 2. Difference = 25.
Borrowing is like “unpacking” a higher place value to help a smaller column. You borrow 1 from the neighbor, which is worth 10 in the current column.
Step‑by‑step: subtract 423 − 156 (with regrouping)
Follow each place value column, regrouping when needed.
- 423- 156
- Ones: 3 − 6 – need to regroup. Borrow 1 ten from the tens (2 becomes 1 ten; the 3 becomes 13 ones). 13 − 6 = 7.
- Tens: Now 1 ten (after borrowing) − 5? Can't do 1 − 5. Borrow 1 hundred from the hundreds (4 becomes 3 hundreds; the 1 ten becomes 11 tens). 11 − 5 = 6.
- Hundreds: 3 − 1 = 2.
- Difference = 267. Check: 423- 156267
When you borrow, always adjust the digit you borrowed from (down by 1) and the digit you borrowed for (up by 10).
Subtracting with zeros in the top number
When a zero is on top and you need to borrow, you must look to the next non‑zero column. This is called “borrowing across zero.”
- 702- 458
- Ones: 2 − 8 – need to borrow. But tens column is 0! So look to hundreds: borrow 1 hundred (7 becomes 6). That hundred moves to tens: 0 becomes 10 tens. Now borrow 1 ten from the 10 tens (becomes 9 tens) and give it to ones: ones become 12. Now subtract: 12 − 8 = 4; tens: 9 − 5 = 4; hundreds: 6 − 4 = 2.
- Final: 702- 458244
Zeros can be tricky. Remember: if you need to borrow from a zero, you go to the next non‑zero column, turn the zero into 10, then borrow from that 10.
Subtracting larger numbers – up to 7 digits
The same rules apply no matter how many digits: line up, subtract column by column, regroup when necessary.
- 5,364,281- 2,175,093
- Ones: 1 − 3 – borrow from tens (8 becomes 7; ones 11 − 3 = 8)
- Tens: 7 − 9 – need to borrow. Look to hundreds: 2 becomes 1; tens become 17; 17 − 9 = 8
- Hundreds: 1 − 0 = 1
- Thousands: 4 − 5 – borrow from ten‑thousands (6 becomes 5; thousands become 14; 14 − 5 = 9)
- Ten‑thousands: 5 − 7 – borrow from hundred‑thousands (3 becomes 2; ten‑thousands become 15; 15 − 7 = 8)
- Hundred‑thousands: 2 − 1 = 1
- Millions: 5 − 2 = 3
- Result: 5,364,281- 2,175,0933,189,188
Always write commas to separate thousands – this helps you see the place values clearly. Work slowly and check each column.
Checking subtraction with addition
You can check your answer by adding the difference (answer) to the number you subtracted (subtrahend). You should get the original top number (minuend).
- Add 1,326 + 2,877:
- 1,326+ 2,8774,203
- It matches! The subtraction is correct.
Use addition to check your work. This helps catch mistakes and builds number sense.
Common pitfalls to avoid
Even careful mathematicians make errors. Watch for these common mistakes.
- Misaligned digits: When subtracting vertically, line up the digits by place value. In 4,592 − 37, the 7 must go under the 2 (ones column), not under the 9.
- Forgetting to borrow from zero correctly: In 605 − 128, don’t just subtract 0 − 2; borrow properly.
- Subtracting top from bottom: Always subtract bottom digit from top after regrouping, never reverse.
- Dropping digits: After borrowing, you might forget to reduce the digit you borrowed from. Always cross out and write the new number.
Practice with grid paper or lined paper to keep columns straight. Double‑check each column.
Real‑world word problems with multi‑digit subtraction
Subtraction helps solve everyday problems: money, distance, inventory, and more.
- A city had 235,849 people. Over a year, 2,761 people moved away. What is the new population?
- 235,849 − 2,761 = 233,088
- 235,849- 2,761233,088
- A school raised $15,372 for new computers. They spent $8,945. How much money is left?
- $15,372 − $8,945 = $6,427
- 15,372- 8,9456,427
When you see “how many more,” “how many left,” “fewer than,” or “difference,” it often means subtraction.
Practice problems you can try (with answers hidden)
Use scratch paper to solve these. Then check by adding.
- 1) 784 − 392 = ?
- 2) 5,006 − 2,478 = ?
- 3) 32,541 − 18,763 = ?
- 4) 908,173 − 529,485 = ?
- 5) 6,421,035 − 3,876,291 = ?
Take your time. If you get stuck, go back to the step-by-step examples. Practice is the key to mastering subtraction.
- 1) 784 − 392 = 392
- 2) 5,006 − 2,478 = 2,528
- 3) 32,541 − 18,763 = 13,778
- 4) 908,173 − 529,485 = 378,688
- 5) 6,421,035 − 3,876,291 = 2,544,744
Final checklist for subtraction success
Before you say you’re done, ask yourself these questions.
- ❏ Did I line up the digits by place value (ones under ones, etc.)?
- ❏ Did I start subtracting from the ones column?
- ❏ If I borrowed, did I correctly update both columns?
- ❏ Did I remember to reduce the digit I borrowed from?
- ❏ Did I check my answer with addition?
Make this checklist a habit. Soon it will become automatic.
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.4 – Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.4. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.