Skill: Multiply a multi-digit number by a 1-digit number

To multiply a multi-digit whole number by a one-digit number, multiply each place-value part, then combine the partial products.

Example: Find $2{,}347 \times 6$.

1. Break apart the number by place value

$$2{,}347=2{,}000+300+40+7$$

2. Multiply each part by $6$

$$\begin{aligned} 2{,}000\times 6&=12{,}000\\ 300\times 6&=1{,}800\\ 40\times 6&=240\\ 7\times 6&=42 \end{aligned}$$

3. Add the partial products

$$12{,}000+1{,}800+240+42=14{,}082$$

So,

$$\boxed{2{,}347\times 6=14{,}082}$$

You can also use the standard algorithm. Start multiplying from the ones place:

      2 3 4 7
  ×         6
  -----------

• $7\times6=42$: write $2$ in the ones place and regroup $4$ tens.
• $4\times6+4=28$: write $8$ in the tens place and regroup $2$ hundreds.
• $3\times6+2=20$: write $0$ in the hundreds place and regroup $2$ thousands.
• $2\times6+2=14$: write $14$ in the remaining places.

      2 3 4 7
  ×         6
  -----------
    1 4 0 8 2

The regrouped numbers represent extra groups of the next place value. This is why the standard algorithm gives the same answer as breaking the number apart.