Even and odd numbers

Sharing into two

Try sharing some counters fairly between two people.

• If everyone gets the same and nothing is left over, the number is even.
• If there is one left over, the number is odd.

Making pairs

Another way: try to put the counters into pairs. If every counter has a partner, the number is even. If one counter is alone, the number is odd.

●● ●● ●● → 6 is even

●● ●● ●● ● → 7 is odd

The ones digit shortcut

You only need to look at the ones digit (the last digit):

So 3,458 is even (ends in 8) and 1,001 is odd (ends in 1). It doesn’t matter how big the number is.

Why does this work? Every ten can be split into two fives with nothing left over. So only the ones can cause a leftover.

Even and odd patterns

On a number line, numbers take turns: odd, even, odd, even…

1 2 3 4 5 6 7 8 9 10

• Counting by 2s from 2 lands on even numbers.
• Counting by 2s from 1 lands on odd numbers.

When you add:

Is zero even?

Yes. Zero can be split into two equal groups of zero with nothing left over, and it ends in 0.

Worked examples

Example 1: Is 14 even or odd?

The ones digit is 4: even.

Example 2: Is 89 even or odd?

The ones digit is 9: odd.

Example 3: Without adding, is 15 + 27 even or odd?

odd + odd = even. Check: 42 is even. ✓

Common mistakes

• Looking at the tens digit instead of the ones digit. 41 is odd, even though 4 is even.
• Thinking 0 is neither. Zero is even.
• Thinking big numbers are always even.

Try it yourself

1. Is 26 even or odd?
2. Is 103 even or odd?
3. List the odd numbers between 10 and 20.
4. Is 8 + 9 even or odd?

Answers: 1) even 2) odd 3) 11, 13, 15, 17, 19 4) odd

Quick recap

• Even numbers split into equal groups of two; odd numbers have one left over.
• Check the ones digit: 0, 2, 4, 6, 8 are even.
• Even and odd numbers alternate.