Two Equal Addends

If a number pairs up evenly, you can also split it into two equal groups.

Write it as an equation

14 makes 7 pairs, and it also splits into 7 and 7. So 14 = 7 + 7.

These are your doubles

Every even number is a double. That is the same fact family from Chapter 1.

Odd numbers cannot

There is no whole number that doubles to 9. That is what makes 9 odd.

Every even number splits in half

Because an even number pairs up completely, you can always split it into two equal groups: 14 is 7 + 7, 20 is 10 + 10, 6 is 3 + 3. This is exactly the doubles work from Chapter 1, running backwards.

Odd numbers cannot

Try to split 15 into two equal whole groups and you get 7 and 8 — close, but not equal. There is no whole number that doubles to 15. That impossibility is what "odd" means, and it is why odd and even matter beyond just naming numbers.

Why this matters when sharing

Sharing 12 sweets fairly between two people works perfectly: 6 each. Sharing 13 does not — someone gets more, or one is left over. Knowing whether a number is odd or even tells you in advance whether a fair share is possible.