Multiplying a 4-digit number by a 1 or 2-digit number

In a nutshell

Multiplying four-digit numbers by one- and two-digit numbers require short and long multiplication, as they are too long to be worked out mentally.

Written multiplication methods

The long and short multiplication methods are written methods where columns are used to set out multiplication calculations.

Multiplying a four-digit number by a one-digit number

When multiplying a four-digit number by a one-digit number, short multiplication is used. The calculation is set out as usual and multiplication by the number happens from right to left in columns.

Example 1

What is $1352\times6$ ?

Set out the calculation.

$\begin{array}{cccc}&\text{Th} & \text{H} & \text{T} & \text{O} \\& 1& 3 & 5 & 2 \\\times & & && 6 \\ \hline&&&& \\ \hline&&&&\end{array}$ 

Multiply each digit of the four-digit number by six.

$2\times6=12\\5\times6=30\\3\times6=18\\1\times6=1$ 

Place each answer in the correct column, carrying and adding where necessary.

$\begin{array}{cccc}&\text{Th} & \text{H} & \text{T} & \text{O} \\& 1& 3 & 5 & 2 \\\times & & && 6 \\ \hline&8&1&1& 2\\ \hline&^2&^3&^1&\end{array}$

$1352\times6=\underline{8112}$

Multiplying a four-digit number by a two-digit number

Multiplying by a two-digit number is almost the same - the only difference is that the two digit number has to be partitioned into tens and units. This method is known as long multiplication.

PROCEDURE

1.	Set out the calculation: Write your numbers one below the other, in columns where tens and ones line up. Draw a multiplication symbol on the left.
2.	Partition the two-digit number into tens and units and multiply each separately.
3.	Adjust zeros accordingly.
4.	Add the answers together.

Example 2

What is $1784\times27$ ?

Set out the calculation.

$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &2& 7 \\ \hline& &&&& \\+& &&&& \\ \hline& &&&& \end{array}$ 

Partition $27$ into tens and ones.

$27=20+7$

First multiply by the ones.

$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &2& \underline7 \\ \hline& ^11&^52&^54&^28&8 \\+& &&&& \\ \hline& &&&& \end{array}$ 

Then multiply by the tens.

Treat $20$ as $2$ , then add a zero in the first column.

$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& &&&&0 \\ \hline& &&&& \end{array}$ 

Continue multiplying by $2$ .

$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& ^13&^15&6&8&0 \\ \hline& &&&& \end{array}$

Add the results.

$\begin{array}{ccccc}&\text{Tth}&\text{Th} & \text{H} & \text{T} & \text{O} \\& &1 & 7& 8& 4 \\\times & & & &\underline2& 7 \\ \hline& ^11&^52&^54&^28&8 \\+& ^13&^15&6&8&0 \\ \hline& 4&^18&^11&6&8 \end{array}$