Even and Odd Numbers

For Elementary Students

What Are Even Numbers?

An even number can be split into two equal groups with nothing left over.

Think about it like this: If you have 8 apples and share them equally between you and a friend, you each get 4. No apples left over. That means 8 is even.

Even numbers always end in: 0, 2, 4, 6, or 8

Examples of even numbers:

• 2, 4, 6, 8, 10
• 12, 14, 16, 18, 20
• 100, 52, 34

What Are Odd Numbers?

An odd number cannot be split evenly into two groups — there's always one left over.

If you have 7 cookies and try to split them between two people, one person gets 4 and the other gets 3. That's not equal! That means 7 is odd.

Odd numbers always end in: 1, 3, 5, 7, or 9

Examples of odd numbers:

• 1, 3, 5, 7, 9
• 11, 13, 15, 17, 19
• 101, 43, 27

Quick Trick

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

• Is 56 even or odd? Look at the 6 → even
• Is 123 even or odd? Look at the 3 → odd
• Is 1,000 even or odd? Look at the 0 → even

Pairing Objects

Here's another way to think about it:

• Even: You can make pairs with nothing left over. 🍎🍎 🍎🍎 (4 apples = 2 pairs)
• Odd: You make pairs, but one is left alone. 🍎🍎 🍎🍎 🍎 (5 apples = 2 pairs + 1 extra)

For Junior High Students

Even and Odd in Math

An even number can be written as 2 × n (two times some whole number).

• 6 = 2 × 3 → even
• 10 = 2 × 5 → even
• 100 = 2 × 50 → even

An odd number can be written as 2 × n + 1 (two times a number, plus one).

• 7 = 2 × 3 + 1 → odd
• 11 = 2 × 5 + 1 → odd
• 99 = 2 × 49 + 1 → odd

Rules for Adding and Multiplying

When you combine even and odd numbers, there are patterns:

Why does odd + odd = even?

Think about it: one left over + one left over = two left over = makes a pair! So the result is even.

Real-Life Uses

• Teams: If you have an odd number of people, someone won't have a partner.
• Sharing: Even numbers split evenly; odd numbers don't.
• Number patterns: Many math tricks use even/odd properties.

Practice