Subtraction is taking one number away from another to find the difference. When working with five-digit numbers, we subtract each place value from right to left, starting with the ones place.
Always line up numbers by their place values before subtracting. The ones digits should be in the same column, tens with tens, hundreds with hundreds, and so on.
When each digit in the top number is larger than the digit below it, we subtract directly without any regrouping.
Start from the right: 4-1=3, 6-2=4, 9-5=4, 8-3=5, 7-0=7
When the second number has fewer digits, imagine zeros in the empty places. For example, 3,521 becomes 03,521 when lining up with a five-digit number.
When a digit in the top number is smaller than the digit below it, we need to regroup from the next higher place value.
Ones: 3-8 (can't do), regroup from tens → 13-8=5
Tens: 0-2 (can't do), regroup from hundreds → 10-2=8
Hundreds: 3-7 (can't do), regroup from thousands → 13-7=6
Thousands: 1-6 (can't do), regroup from ten thousands → 11-6=5
Ten thousands: 4-3=1
Remember: when you regroup, the digit you take from becomes one less, and the digit you're helping becomes ten more.
When you need to regroup but encounter zeros in the top number, you may need to regroup across multiple place values.
Ones: 5-8 (can't do), but tens, hundreds, and thousands are zero
Regroup from ten thousands: 4 becomes 3, then continue regrouping
Thousands: 10 becomes 9, hundreds get 10
Hundreds: 10 becomes 9, tens get 10
Tens: 10 becomes 9, ones get 10 → 15
Ones: 15 - 8 = 7
Tens: 9 - 2 = 7
Hundreds: 9 - 3 = 6
Thousands: 9 - 7 = 2
Ten Thousands: 3 - 0 = 3
Final Answer: 32,677
When regrouping across zeros, work from left to right until you reach the place value that needs help.
You can check your subtraction by adding your answer to the number you subtracted. The sum should equal the original number.
If 63,842 - 27,519 = 36,323, then check:
Always check your work! This helps catch mistakes and builds confidence in your answers.
Five-digit subtraction helps solve real problems like calculating distances, managing budgets, or comparing large quantities.
A library has 85,427 books. If 23,658 books are checked out, how many remain on the shelves?
Answer: 61,769 books remain on the shelves.
Read word problems carefully to identify what numbers to subtract and in what order.