Subtraction — Definition, Formula & Examples
Subtraction is the operation of taking one number away from another to find the difference between them. For example, subtracting 3 from 8 gives 5.
Subtraction is a binary arithmetic operation, denoted by the minus sign (−), in which a quantity called the subtrahend is removed from a quantity called the minuend to produce a result called the difference. For any real numbers and , subtraction is defined as the addition of the additive inverse: .
Key Formula
Where:
- = The minuend — the number you start with
- = The subtrahend — the number being taken away
- = The difference — the result of the subtraction
How It Works
To subtract, you start with the first number (the minuend) and take away the second number (the subtrahend). The result is called the difference. If you have 10 apples and give away 4, you subtract to find you have 6 left. Subtraction is the inverse of addition — if , then . Unlike addition, subtraction is not commutative, meaning the order of the numbers matters: is not the same as .
Worked Example
Problem: A store has 52 oranges. A customer buys 17. How many oranges are left?
Set up: Write the subtraction problem with the minuend and subtrahend.
Subtract the ones: You cannot take 7 from 2, so borrow 1 ten from the 5 tens. Now the ones column is 12 minus 7.
Subtract the tens: After borrowing, the tens column is 4 minus 1.
Combine: Put the digits together to get the difference.
Answer: There are 35 oranges left.
Another Example
Problem: Find the difference: 200 − 85.
Set up: Write the problem in column form.
Borrow: You need to borrow twice. Borrow from the hundreds to make the tens 10, then borrow from the tens to make the ones 10. The hundreds digit becomes 1, the tens digit becomes 9, and the ones digit becomes 10.
Subtract each column: Ones: 10 − 5 = 5. Tens: 9 − 8 = 1. Hundreds: 1 − 0 = 1.
Answer: The difference is 115.
Why It Matters
Subtraction is one of the four basic operations you use throughout all of math, from elementary arithmetic to algebra and beyond. In everyday life, you rely on subtraction when making change, measuring how much is left, or comparing quantities. Mastering subtraction with borrowing and regrouping builds the foundation you need for multi-digit problems in later grades.
Common Mistakes
Mistake: Forgetting to borrow (regroup) when a digit in the minuend is smaller than the corresponding digit in the subtrahend.
Correction: Always compare digits column by column from right to left. If the top digit is smaller, borrow 1 from the next column to the left before subtracting.
Mistake: Switching the order of the numbers and getting the wrong sign, such as writing instead of .
Correction: Remember that subtraction is not commutative. The order matters: is not the same as unless .