Addition

Imagine you have 3 red apples in one hand and a friend gives you 2 green apples in the other. How many apples do you have altogether? You put them all in one basket and count: 1, 2, 3, 4, 5. That is addition — it combines two amounts into one total.

apple apple apple + apple apple = 5 apples

We write a plus sign + between the two amounts, and an equals sign = before the total. If you have a things and b more, the total c is:

a + b = c

So our apples are 3 + 2 = 5

Way 1: counting on

One way to add is to count on. Start at the first number and take little hops forward, one for each thing you are adding. To work out 3 + 2, start at 3 and hop on two more: "4… 5". You land on 5.

Press play below, then replay it — each time it starts at a new random number and adds a different amount, reading each number aloud as it hops along the number line.

To count on 2 + 9 you start at 2 and hop nine times — that's a lot of hopping! But 9 + 2 gives the very same answer with only two hops. Clever adders always start from the bigger number and count on the smaller, so there is less hopping to do.

duck duck + duck duck duck duck duck duck duck duck duck = 11 ducks — and it's still 11 whichever way round you add.

Way 2: combining two groups

Another way to add is to push two groups together and count the whole pile. Here are 4 fish and 3 fish swimming into one tank:

fish fish fish fish + fish fish fish = 7 fish

The picture below shows the same idea with counters. One group is one colour, the other group is a second colour — slide them together and count them all to find the total. Press Refresh for two brand-new groups to add.

Three sums to try

Once you can count on and combine groups, every sum works the same way:

3 + 4 = 7 — start at the bigger number 4 and hop on three more: 5, 6, 7.
6 + 5 = 11 — this one crosses past ten. Hop from 6: "7, 8, 9, 10…" and you still have one more hop, landing on 11. Crossing ten is nothing to fear — you just keep counting.
0 + 7 = 7 — adding nothing changes nothing. Seven stars plus no stars is still seven stars.

Two traps that catch out new adders:

When you count on, don't count the start number again. For 3 + 2 you start on 3 and hop "4, 5" — you do not say "3, 4" and stop at 4. The first number is your launch pad, not your first hop.
The order doesn't matter: 2 + 9 equals 9 + 2. Both make 11. So always start from the bigger number to save yourself hops.

Zero means "none". If you have 4 cookies and add 0 more cookies, nobody brought any — so you still have exactly 4.

cookie cookie cookie cookie + 0 = 4 cookies. Adding zero to any number leaves it exactly the same: n + 0 = n.

When a sum jumps over ten, a handy trick is to make ten first. To do 8 + 5, give 2 of the five to the eight to make a tidy ten — then you have 3 left over: 10 + 3 = 13. Ten is a friendly number to count from.

ball ball ball ball ball ball ball ball + ball ball ball ball ball = 13 balls

Khan Academy walks through basic addition here: