Multiply multi-digit numbers using the standard algorithm

Multiplication of multi-digit whole numbers is understood as combining partial products for each digit’s place-value unit, with products shifted according to ones, tens, hundreds, and beyond, and regrouping when necessary. The standard algorithm represents these relationships efficiently for factors such as a four-digit number multiplied by a two-digit number; this scope excludes decimal or fractional factors and more generalized symbolic treatments.

Detailed Explanation: 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.

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Multiplication - Whole Number 3 x 2 - Columns

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Multiply multi-digit numbers using the standard algorithm

Detailed Explanation: Multiply multi-digit numbers using the standard algorithm

Learn by doing: Multiply multi-digit numbers using the standard algorithm

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Multiplication - Whole Number 3 x 2 - Columns