Subtraction Calculator — Minuend, Subtrahend & Difference with Steps

Welcome to Calcugo's subtraction calculator, where we'll tackle just what the name suggests: subtraction problems. In essence, the operation is the inverse of addition, but the properties of subtraction are quite different. We'll begin with some theory — the meaning of a difference in math, as well as the formal subtraction definition — and support it all with examples, including how to subtract numbers in some special cases of the minuend and subtrahend: decimals, negative numbers, and more.

Keep reading to learn:

• The subtraction definition in math — the minuend and the subtrahend;
• The properties of subtraction;
• How to subtract integers, decimals, and negative numbers; and
• How to use the subtraction calculator.

Subtraction definition in math; the minuend and the subtrahend

Subtraction is the opposite of addition. To be precise, if we have a sum:

a + b = c

then subtraction turns it around into:

c − a = b

In other words, instead of adding things to a pile, we steal some away. The formal yet basic subtraction math definition is the following:

💡 Subtraction is the arithmetic operation of taking several objects (the subtrahend) away from a pile of the same objects (the minuend). We represent it by the minus sign − and call the result the difference.

minuend − subtrahend = difference

For example, in 9 − 4 = 5, the number 9 is the minuend, 4 is the subtrahend, and 5 is the difference.

Properties of subtraction

Although subtraction is the inverse of addition, it does not share addition's convenient properties:

• Not commutative. The order matters: in general a − b ≠ b − a. For instance, 7 − 3 = 4 but 3 − 7 = −4.
• Not associative. The grouping matters: in general (a − b) − c ≠ a − (b − c). For instance, (10 − 4) − 2 = 4 but 10 − (4 − 2) = 8.
• Subtraction of zero. Taking nothing away changes nothing: a − 0 = a.
• Subtracting a number from itself. The result is always zero: a − a = 0.
• Inverse check. You can always verify a subtraction by adding: if c − a = b, then b + a = c.

Subtracting integers, decimals, and negative numbers

Integers. Line up the digits and subtract, borrowing from the next column when a digit is too small. Example: 52 − 27 = 25.

Decimals. Align the decimal points, then subtract as with whole numbers. Example: 8.5 − 3.2 = 5.3.

Negative numbers. Subtracting a negative is the same as adding its opposite: a − (−b) = a + b. For example, 6 − (−4) = 6 + 4 = 10. And when the subtrahend is larger than the minuend, the difference is negative: 3 − 8 = −5.

Using the subtraction calculator

1. Select the unit type — Plain Number, Currency, Imperial (US), or Metric measurement.
2. If using Currency, pick your preferred currency from the list (USD, RUB, EUR, GBP, JPY, and 20+ more).
3. If using Imperial or Metric, choose the specific unit (inches, feet, kilograms, meters, etc.).
4. Enter the minuend in the first field — the number you start with.
5. Enter the subtrahend(s) — the numbers to take away. The form automatically expands as you type, so you can subtract several numbers in a row (up to 10 terms). A live preview shows the running difference.
6. Click Calculate — the calculator shows the difference, labels the minuend, subtrahend, and difference, solves the subtraction step by step, and verifies the answer by adding it all back together.

FAQs

What is the minuend and the subtrahend?

In a subtraction a − b = c, the minuend is the number you start with (a), the subtrahend is the number being taken away (b), and the difference is the result (c).

Is subtraction commutative?

No. Unlike addition, subtraction is not commutative: a − b is generally not equal to b − a. For example, 9 − 5 = 4 but 5 − 9 = −4.

How do you subtract a negative number?

Subtracting a negative number is the same as adding its positive counterpart: a − (−b) = a + b. For example, 7 − (−3) = 7 + 3 = 10.

What happens when the subtrahend is bigger than the minuend?

The difference becomes negative. For example, 4 − 10 = −6. The calculator handles negative results automatically.

Can I subtract several numbers at once?

Yes. Enter the minuend first, then as many subtrahends as you need (up to 10 terms). The calculator subtracts them from left to right: a − b − c − …