Skill: Multiply multi-digit numbers using the standard algorithm

To multiply a multi-digit number by a two-digit number, multiply by the ones digit first, then multiply by the tens digit. Finally, add the partial products.

Example: Find $3{,}248 \times 26$.

First, set up the numbers:

$$\begin{array}{r} 3{,}248\\ \times\ \ 26\\ \hline \end{array}$$

1. Multiply by the ones digit, $6$.

• $6 \times 8=48$. Write $8$ and regroup $4$.
• $6 \times 4=24$, plus $4=28$. Write $8$ and regroup $2$.
• $6 \times 2=12$, plus $2=14$. Write $4$ and regroup $1$.
• $6 \times 3=18$, plus $1=19$.

The first partial product is $19{,}488$:

$$\begin{array}{r} 3{,}248\\ \times\ \ 26\\ \hline 19{,}488 \end{array}$$

2. Multiply by the tens digit, $2$.

The $2$ represents $2$ tens, or $20$, so begin this row one place to the left. You can show this by writing a zero in the ones place.

• $2 \times 8=16$. Write $6$ and regroup $1$.
• $2 \times 4=8$, plus $1=9$.
• $2 \times 2=4$.
• $2 \times 3=6$.

This partial product is $64{,}960$:

$$\begin{array}{r} 3{,}248\\ \times\ \ 26\\ \hline 19{,}488\\ 64{,}960\\ \hline \end{array}$$

3. Add the partial products.

$$\begin{array}{r} 19{,}488\\ + 64{,}960\\ \hline 84{,}448 \end{array}$$

Therefore,

$$\boxed{3{,}248 \times 26=84{,}448}$$

Remember: multiply by the ones, multiply by the tens with a one-place shift, and then add.