Odd and Even Numbers

Pair them up

Here are $8$ socks, put in pairs.

Every sock has a partner. None is left over. So $8$ is even.

Now try $7$.

Three pairs, and one sock is left over. So $7$ is odd.

Count by 2s

Count by $2$s: $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $18$, $20$. These are the even numbers.

The numbers you skip are the odd numbers: $1$, $3$, $5$, $7$, $9$, $11$, $13$, $15$, $17$, $19$.

Even and odd take turns: even, odd, even, odd, all the way up.

Why even numbers are doubles

Take the pairs apart. Put one sock from each pair on the left and the other on the right. Both sides get the same number.

So an even number is always a number plus itself: a double.

$$8 = 4 + 4 \qquad 12 = 6 + 6 \qquad 18 = 9 + 9$$

An odd number can not be split that way. For $7$, one sock is always left over: $7 = 3 + 3 + 1$.

Bigger numbers

A ten is $5$ pairs, with none left over. So the tens in a number always pair up.

That means only the ones digit decides. If it is $0$, $2$, $4$, $6$ or $8$, the number is even. If it is $1$, $3$, $5$, $7$ or $9$, the number is odd.

$16$ is even, because $6$ is even. $13$ is odd, because $3$ is odd.

Worked examples

Common mistakes

Practice problems