Skill: Use partial products to multiply

To multiply using partial products, break one factor into its place-value parts, multiply each part, and then add the products.

Example: Find $(347 \times 26)$.

1. Decompose $(26)$

The $2$ is in the tens place, so it means $(20)$:

$$26=20+6$$

2. Multiply by each part

$$347\times 20=6{,}940$$ $$347\times 6=2{,}082$$

These are the partial products. Each one shows the product from one place-value part of $(26)$.

3. Add the partial products

Align the numbers by place value:

$$\begin{array}{r} 6{,}940\\ + 2{,}082\\ \hline 9{,}022 \end{array}$$

Therefore,

$$\boxed{347\times 26=9{,}022}$$

This works because of the distributive property:

$$347\times 26 =347\times(20+6) =(347\times20)+(347\times6).$$

The digits in $(26)$ are not treated separately as just $2$ and $6$; the $2$ represents $(20)$ because it is in the tens place.