Subtraction

Subtraction is the opposite of adding: instead of putting amounts together, it takes some away and asks what is left. Imagine you bake 5 cookies and then gobble up 2 of them. How many cookies are still on the plate? You cross off the two you ate and count the rest: 3.

cookie cookie cookie ✖ eaten cookie ✖ = 3 cookies left

We write subtraction with a minus sign, -. If you start with a things and take b of them away, the amount left over c is:

a - b = c

So our cookies are 5 - 2 = 3 Read it aloud as "five minus two equals three", or "five take away two is three".

Way 1: take away

The first picture of subtraction is take away. You start with a group, you cross out the ones that leave, and you count whoever is still standing. Here are 6 birds on a wire — then 4 of them flap away:

bird bird ✖ bird flying away ✖ ✖ ✖ = 2 birds left, so 6 - 4 = 2.

The picture below shows the same idea with counters. Some are crossed out — those are the ones taken away — and the ones still solid are the answer. Press Refresh for a brand-new take-away to work out: count the whole group, count the crosses, then count what is left.

Way 2: counting back

Another way to picture subtraction is to start at a on a number line and take b steps to the left — this is called counting back. Press play, then replay it: each time it starts at a new random number and takes a different amount away, reading each number aloud as it hops. The dots still standing at the end are the answer.

Khan Academy walks through basic subtraction here:

Way 3: the difference — how many more?

Subtraction has a second job that doesn't look like "taking away" at all. When you compare two amounts and ask "how many more?" or "how many fewer?", the answer is also a subtraction. The gap between the two numbers is called the difference.

Suppose you have 7 fish and your friend has 3 fish. How many more do you have? Line them up and look at the gap:

You: fish fish fish fish fish fish fish

Friend: fish fish fish

The first 3 match up, and you have 4 left over with no partner — that is the difference. So 7 - 3 = 4: you have 4 more fish. Whether you think "take 3 away from 7" or "what is the gap from 3 up to 7?", the minus sign gives the same answer.

Three subtractions to try

Once you can take away and count back, every subtraction works the same way:

9 - 4 = 5 — start at 9 and count back four: "8, 7, 6, 5". You land on 5.
8 - 8 = 0 — take away everything and nothing is left. Eight cookies, eat all eight, and the plate is empty: zero.
6 - 0 = 6 — take away nothing and the group is unchanged. Six stars, remove none, and you still have all six.

Two traps that catch out new subtractors:

Order matters! Unlike addition, you cannot swap the two numbers around. 7 - 2 = 5, but 2 - 7 is not 5 — you cannot take 7 cookies away when you only have 2. Always take the second number away FROM the first, in the order they are written.
Subtraction is not commutative: 5 - 3 is not the same as 3 - 5. The bigger number goes first when you are taking away.

If you start with 4 cookies and eat all 4, the plate is bare. Taking a whole group away leaves zero: 4 - 4 = 0. Any number take away itself is always zero, because there is nothing left over.

eaten cookie = an empty plate (0 cookies)

With everyday counting you cannot take 5 birds away when only 2 are sitting there — you run out of birds! That is exactly why order matters: when you are taking away, the bigger number comes first. Later, when you meet negative numbers, you will discover that 2 - 5 does have an answer (it is below zero) — but for now, keep the larger number in front.

bird bird − 5 birds? There aren't enough to take away!