Skill: Use the commutative property of multiplication

The commutative property of multiplication means you can switch the order of the factors without changing the product:

$$a \times b=b \times a$$

For example, find the product of $3 \times 4$.

1. Think of $3 \times 4$ as an array with 3 rows of 4:

$$\begin{array}{cccc} \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet & \bullet \end{array}$$

2. Count the objects. There are $12$, so:

$$3 \times 4=12$$

3. Rotate the array. It now has 4 rows of 3:

$$\begin{array}{ccc} \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet\\ \bullet & \bullet & \bullet \end{array}$$

4. The number of objects is still $12$, so:

$$4 \times 3=12$$

Therefore:

$$3 \times 4=4 \times 3=12$$

The commutative property changes the order of the factors, not the factors themselves.