Odd and even numbers: the pairing test and the last-digit rule
The pairing test
Take some blocks and match them into pairs. If every block has a partner, the number is even. If one block is left on its own, the number is odd. Twelve blocks make six pairs: even. Nine blocks make four pairs and one left over: odd.
Why only the last digit matters
Every ten can be split into five pairs, and so can every hundred and every thousand. So the tens, hundreds and thousands are always even and never leave a block over. Only the ones can leave a block over. That is why you can check 3,457 by looking at the 7 alone: it ends in an odd digit, so the whole number is odd.
| Even if it ends in | Odd if it ends in |
|---|---|
| 0, 2, 4, 6, 8 | 1, 3, 5, 7, 9 |
Adding odd and even numbers
| Sum | Result | Why |
|---|---|---|
| even + even | even | Both sets pair up completely. |
| odd + odd | even | The two leftover blocks pair with each other. |
| odd + even | odd | Only one leftover block, with no partner. |
This is a handy check on homework. If a child adds 37 + 25 and gets 61, you can tell something went wrong before working it out: odd plus odd must be even. (The correct answer is 62.)
What about zero?
Zero is even. It ends in 0, and zero blocks leave no block without a partner. It also sits between two odd numbers, -1 and 1, just like every other even number.
Try 3457 and 3458 in the Number Blocks Tool and compare the odd/even line. Open the tool with 3,457
Odd or even?
Decide whether each number or sum is odd or even, and say how you know.
- 86
- 1,003
- 45 + 27
- 19 + 30
Show answers
- Even (ends in 6).
- Odd (ends in 3).
- Even: 72. Odd plus odd is even.
- Odd: 49. Odd plus even is odd.