What are the numbers in a subtraction called?

The number you subtract from is the minuend, the number you take away is the subtrahend, and the result is the difference. In a − b = c, a is the minuend, b the subtrahend and c the difference.

Can you swap the numbers in subtraction?

No. Subtraction is not commutative: a − b is generally not equal to b − a. For example 7 − 3 = 4, but 3 − 7 = −4. The order matters.

How do you check a subtraction?

Add the subtrahend to the difference — you should get back the minuend. Since a − b = c, we have b + c = a. For example 15 − 6 = 9, because 6 + 9 = 15.

What is borrowing in column subtraction?

When a digit of the minuend in a column is smaller than the digit of the subtrahend, borrow one ten from the column to the left: the current digit grows by 10 and the neighbour shrinks by 1. In 52 − 27 the ones: 2 is smaller than 7, so we borrow — 12 − 7 = 5, and the tens become 4 − 2 = 2.

Basic level

Subtraction

Subtraction is the inverse of addition — take the subtrahend away from the minuend to get the difference. Learn the names, the properties, the link to addition and how to subtract in columns with borrowing.

Before you start

This topic builds on earlier ideas. Before you start, it's worth working through the lessons below — they'll make everything click:

AdditionAddition combines two or more numbers into one — the sum. Learn the names of the parts, the laws of addition (commutativity, associativity, identity element) and how to add in columns with carrying.

Where this is used

Real situations where you count exactly the way this lesson teaches:

Household budget
Take a 4,200 payday, subtract the fixed bills — 1,350 rent, 280 electricity, 90 internet — and the 2,480 left over is what the month actually has to work with.
Warehouse
Stock reconciliation is one subtraction: 480 units on the shelf less the 137 picked this morning leaves 343 — which settles whether an order for 350 can ship today.
Weather forecasting
The daily temperature range means subtracting a negative: from −7 °C at night to 3 °C at noon is 3 − (−7) = 10 degrees.
Convert it here: Temperature

All formulas

Difference
$a - b = c$
minuend − subtrahend = difference
Check
$a - b = c \iff b + c = a$
check subtraction with addition
Subtracting zero
$a - 0 = a$
zero leaves the number unchanged
Difference of equals
$a - a = 0$
a number minus itself is zero

Subtraction is the inverse of addition: you take away one number from another to find out how much is left. The notation $a - b = c$ reads "a minus b equals c". The number $a$ is the minuend, $b$ is the subtrahend, and $c$ is the difference.

The names in subtraction

minuend — the number you subtract from ( $a$ ),
subtrahend — the number you take away ( $b$ ),
difference — the result ( $c$ ).

For example, in $8 - 5 = 3$ the number $8$ is the minuend, $5$ the subtrahend and $3$ the difference.

Subtraction on the number line

The easiest way to see subtraction is on a number line: start at the minuend and step back to the left as many times as the subtrahend says. The number you land on is the difference.

12 − 7 = 5 — from 12 you step 7 places to the left.

Addition moves you to the right along the line, subtraction to the left — which is why the difference is never larger than the minuend (as long as you subtract a positive number). Step back past zero and you enter the negative numbers: $3 - 7 = -4$ .

Subtraction and addition

Subtraction and addition are inverse operations — one "undoes" the other. That lets you check every subtraction with addition:

a - b = c \iff b + c = a

Since $15 - 6 = 9$ , it must be that $6 + 9 = 15$ — and it is. This is the simplest way to be sure a result is correct.

Check whether 84 − 37 = 47.

Properties of subtraction

Unlike addition, subtraction is neither commutative nor associative — order and grouping matter:

a - b \neq b - a

For example $7 - 3 = 4$ , but $3 - 7 = -4$ . There are, however, two handy properties:

subtracting zero leaves the number unchanged: $a - 0 = a$ ,
a number minus itself is zero: $a - a = 0$ .

Column subtraction

Larger numbers are subtracted in columns — digit under digit, right to left. When a digit of the minuend is smaller than the digit below it, we borrow one ten from the column to the left.

Take $52 - 27$ . Ones: $2$ is smaller than $7$ , so we borrow a ten — compute $12 - 7 = 5$ . Tens: after the borrow $4$ is left, so $4 - 2 = 2$ . The result is $25$ .

Practice

Work through a set of exercises — they get harder as you go. At the end you'll see your score and the mistakes worth reviewing.

Exercise 1 of 8Score: 0

6 − 2 =

Common mistakes

Forgetting the borrow — if you don't reduce the neighbouring digit by 1 after borrowing, the result comes out too large.
Subtracting the smaller digit from the larger "as a shortcut" — in a column you always subtract the subtrahend's digit from the minuend's, not the other way round; when you can't, you borrow.
Mixing up the order — $a - b$ is not the same as $b - a$ .

Formula card

Topic: Subtraction

Difference
$a - b = c$
minuend − subtrahend = difference
Check
$a - b = c \iff b + c = a$
check subtraction with addition
Subtracting zero
$a - 0 = a$
zero leaves the number unchanged
Difference of equals
$a - a = 0$
a number minus itself is zero

12 − 7 = 5 — subtraction moves you left along the number line.

Frequently asked questions

Plus, minus, times and division signs and digits floating in a geometric grid, joined by emerald lines of the order of operations, against a cosmic nebula in violet and magenta

Arithmetic

The grammar of arithmetic — why the order of operations is a convention

Nobody invented +, −, × and ÷ overnight, and the fight over 6 ÷ 2(1+2) still splits the internet. Here is why the notation of arithmetic is a human convention, the results are absolute truth, and division by zero simply cannot be defined.

10 min