Skill: Use the associative property of multiplication

The associative property of multiplication lets you change the grouping of three factors without changing the product:

$$(a \times b) \times c = a \times (b \times c)$$

Use it to group factors that are easier to multiply.

Example: Find $4 \times 25 \times 2$.

1. Group the first two factors:

$$(4 \times 25) \times 2$$

2. Multiply inside the parentheses:

$$100 \times 2 = 200$$

3. Regroup the factors so the easier pair is together:

$$4 \times (25 \times 2)$$

4. Multiply inside the parentheses first:

$$4 \times 50 = 200$$

Both groupings give the same product:

$$(4 \times 25) \times 2 = 4 \times (25 \times 2) = 200$$

The grouping changed, but the order of the factors did not. The factors stayed $4$, $25$, and $2$ in the same order.