Subtraction
Subtraction is finding the difference between two numbers by taking one away from the other. It is the inverse (opposite) of addition.
Subtraction Formula
Minuend − Subtrahend = Difference
You can check subtraction by adding: Difference + Subtrahend = Minuend.
Concept Explanation
When we subtract, we start with a larger number (the minuend) and remove a smaller number (the subtrahend) to find what is left (the difference).
Unlike addition, subtraction is NOT commutative — 9 − 4 is not the same as 4 − 9. Order matters!
When the digit on top is smaller than the digit below, we borrow from the next column to the left. This is called regrouping.
Word problems use subtraction when you see clue words like: "how many are left," "how many more," "difference," "fewer," "remain," or "take away."
Worked Examples
Subtract ones
3 < 7, so borrow: 13 − 7 = 6.
Subtract tens
7 (after borrowing) − 4 = 3.
Combine
83 − 47 = 36.
Answer: 36
Key Terms
Minuend
The starting number in subtraction. In 9 − 4, the minuend is 9.
Subtrahend
The number being subtracted. In 9 − 4, the subtrahend is 4.
Difference
The result of subtraction. 9 − 4 = 5, so 5 is the difference.
Regrouping (Borrowing)
Taking 1 ten from the tens column and adding 10 to the ones column when the top digit is smaller.
Inverse Operation
The opposite operation. Addition and subtraction are inverse operations of each other.
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Subtraction