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I.4 Subtract two numbers up to five digits

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Subtraction with five digit numbers

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.

Example:
45,327
- 12,145
33,182
Note

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.

Subtracting without regrouping

When each digit in the top number is larger than the digit below it, we subtract directly without any regrouping.

Example:
78,964
- 3,521
75,443

Start from the right: 4-1=3, 6-2=4, 9-5=4, 8-3=5, 7-0=7

Note

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.

Subtracting with regrouping

When a digit in the top number is smaller than the digit below it, we need to regroup from the next higher place value.

Example:
52,413
- 36,728
15,685

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

Note

Remember: when you regroup, the digit you take from becomes one less, and the digit you're helping becomes ten more.

Subtracting across zeros

When you need to regroup but encounter zeros in the top number, you may need to regroup across multiple place values.

Example:
40,005
- 7,328
32,677

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

Note

When regrouping across zeros, work from left to right until you reach the place value that needs help.

Checking your subtraction

You can check your subtraction by adding your answer to the number you subtracted. The sum should equal the original number.

Example:

If 63,842 - 27,519 = 36,323, then check:

36,323
+ 27,519
63,842
Note

Always check your work! This helps catch mistakes and builds confidence in your answers.

Real-World Subtraction Problems

Five-digit subtraction helps solve real problems like calculating distances, managing budgets, or comparing large quantities.

Example:

A library has 85,427 books. If 23,658 books are checked out, how many remain on the shelves?

85,427
- 23,658
61,769

Answer: 61,769 books remain on the shelves.

Note

Read word problems carefully to identify what numbers to subtract and in what order.