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

Multiplying a whole number of up to four digits by a one-digit number involves decomposing by place value and combining partial products, with the distributive property explaining regrouping when a product exceeds a place-value unit. Place-value models, equations, and the standard algorithm represent the same relationship; the scope is limited to whole numbers and does not include decimal factors, fractions, or two- or more-digit multipliers.

Detailed Explanation: 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.

Learn by doing: Multiply a multi-digit number by a 1-digit number

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Multiplication - Whole Number 4 x 1 - Columns

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