Skill: Use partial products

To use partial products, break one factor into its place-value parts. Multiply each part by the other factor, then add the products.

Example: Find $324 \times 6$.

1. Decompose $324$ by place value:

$$324=300+20+4$$

2. Multiply $6$ by each part:

$$6\times300=1{,}800$$ $$6\times20=120$$ $$6\times4=24$$

These are the partial products. Each one keeps the place value of its part.

3. Add the partial products:

$$1{,}800+120+24=1{,}944$$

Therefore,

$$324\times6=1{,}944$$

The distributive property explains this process:

$$6(300+20+4)=(6\times300)+(6\times20)+(6\times4)$$

An area model would show three sections with areas $1{,}800$, $120$, and $24$. The total area is $1{,}944$, so the partial products add to the total product.