Think about equal groups again. What if every plate is empty? What if there is only one plate?
Why it works
$4 \times 0$ means 4 groups with 0 in each. Four empty plates hold nothing, so the product is 0. $0 \times 5$ means 0 groups of 5: no plates at all, so again nothing. And $1 \times 7$ is one group of 7, which is just 7.
Key idea
Any number times 0 is 0. Any number times 1 is that same number.
Worked example: Times 0
Find $6 \times 0$.
- 6 groups of 0: six empty plates.
- $0 + 0 + 0 + 0 + 0 + 0 = 0$.
Answer: $0$
Worked example: Times 1
Find $1 \times 9$ and $9 \times 1$.
- $1 \times 9$ is one group of 9: that is 9.
- $9 \times 1$ is 9 groups with 1 in each: also 9.
Answer: $9$ both ways
Common mistake
Writing $6 \times 0 = 6$. That mixes up multiplying with adding. Adding 0 leaves a number the same: $6 + 0 = 6$. Multiplying by 0 means groups of nothing: $6 \times 0 = 0$. Check by picturing six empty plates.
| Fact | Means | Product |
|---|---|---|
| $5 + 0$ | 5, then nothing more | 5 |
| $5 \times 0$ | 5 groups of nothing | 0 |
| $5 \times 1$ | 5 groups of one | 5 |