Odd and even, multiplied
A hall has 7 rows of 9 chairs. Can everyone sit in pairs, with nobody left alone?
- 3 groups of 5 dots.
- Each group: 2 pairs, and 1 spare.
- Gather the 3 spares. Pair them up: 1 pair, and 1 left alone.
- 3 × 5 = 15. It has 1 left alone. It is odd.
The rule
No. 7 × 9 = 63 chairs, an odd number. So one person has no partner.
Even or odd is called parity. Odd plus odd is even. That rule is about adding, not multiplying.
A product is the answer to a multiplication. A product is even when at least one number is even. It is odd only when both numbers are odd.
3 × 4 = 12 pairs up completely. One group of 4 already pairs up on its own. 3 × 5 = 15 leaves one spare. Both 3 and 5 are odd.
Add one row: 8 × 9 = 72 chairs, an even number. Everyone pairs up.
A grid of 21 × 15 squares? Both are odd, so the number of squares is odd. A grid of 19 × 24? One is even, so the number of squares is even.
Set rows and columns. Does every dot get a partner?
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