Skill: Identify patterns in multiplication tables

A multiplication table has patterns you can use to find an unknown fact.

• If one factor increases by $1$, the product increases by the other factor.
• Multiplying by $1$ keeps a number the same, and multiplying by $0$ gives $0$.
• Factors can switch places without changing the product: $(6 \times 7 = 7 \times 6)$.

Example: Find $(6 \times 7)$.

1. Start with a fact you know:

$$6 \times 5 = 30$$

2. The second factor changes from $5$ to $7$. That is an increase of $2$.

3. Each new group has $6$, so add two groups of $6$:

$$30 + 6 + 6 = 42$$

4. Therefore,

$$6 \times 7 = 42$$

You can check the related fact because the factors can switch places:

$$7 \times 6 = 42$$