Some groups can be shared fairly between two friends. Others always have one left over. Let’s find out which is which. Doubles will help.
A number is even when you can put all of its objects in pairs, with none left over. It is odd when one is left over. Every even number is a double: $8 = 4 + 4$.
Why it works
Why does only the ones digit matter? A ten is 5 pairs, so every ten pairs up with nothing left over. In 34, the 3 tens make 15 pairs. Only the 4 ones are left to pair, and 4 ones make 2 pairs. So 34 is even.
Worked example: Is 13 even or odd?
Is 13 even or odd?
- Make pairs: 6 pairs and 1 more.
- $13 = 6 + 6 + 1$.
- One is left over, so 13 is odd.
Answer: odd
Worked example: Is 58 even or odd?
Is 58 even or odd?
- The 5 tens make 25 pairs. Don’t let the 5 fool you.
- The ones digit is 8: 4 pairs, none left over.
- So 58 is even.
Answer: even
Worked example: Is 0 even or odd?
Is 0 even or odd?
- Zero things: nothing is left over.
- $0 = 0 + 0$, a double.
- Counting by 2s goes 0, 2, 4, 6, … so 0 is even.
Answer: even
Key idea
Even numbers make pairs with none left over and end in 0, 2, 4, 6 or 8. Odd numbers have one left over and end in 1, 3, 5, 7 or 9.
Common mistake
Looking at the wrong digit: “52 is odd because 5 is odd.” The tens always pair up, so only the ones digit counts: 52 is even. Another mix-up is thinking 0 is neither. Zero is even, because $0 = 0 + 0$ and nothing is left over.
Grown-up tip: Pair up socks, shoes or crackers and ask, “Is there one without a partner?”