Long Multiplication | Grid Method | Maths Made Easy

# Long Multiplication and Grid Method

Level 1 Level 2 Level 3

## Long Multiplication and Grid Method

The 2 multiplication methods we will see are the long multiplication (column) method and the grid method. The grid method is taught by many schools in the UK but there are many that still prefer long multiplication, so we will look at both.

## Method 1: Long Multiplication Method

Step 1: Write the two numbers we are multiplying on top of each other, usually with the bigger one on top. We write the values so that the $1$s, $10$s, $100$s and so on all line up in the correct column.

Step 2: Multiply the last digit from the bottom number with every digit from the top number, writing the results underneath from right to left, and carrying forward when values go above $10$

$3\times1 = 3$, $3\times8=24$, $3\times2 = 6$

Step 3: If the bottom number has a tens digit, we write a $0$ underneath the last step’s working so that everything is shifted one space to the left. We then multiply this digit (second from the right) by every digit from the top number, writing the results underneath the last step from right to left, and carrying forward when values go above $10$

Step 4: If the bottom number has a hundreds digit, we write two $0$‘s below the last step’s working and repeat the above steps, and so on (in this example it’s not the case).

Step 5: The numbers under the top line we now add up using the column addition method to get our final answer.

Level 1-3

## Method 2: The Grid Method

Step 1: Split each number into $1$s, $10$s, $100$s and so on, and write each component of one number along the top of a grid, and each component of the other number down the left-hand side.

$\textcolor{red}{2}\textcolor{blue}{1}\textcolor{limegreen}{3} \times \textcolor{maroon}{7}\textcolor{purple}{4}$

Step 2: Fill all the squares of the grid by multiplying each part of one number by each part of the other.

$\begin{array}{r}\begin{array}{r}14000\\800\\700\\210\\40\\+\,\,\,\,\,\,12\\\hline15762\end{array}\end{array}$

Level 1-3

## Example: The Grid Method

Work out $23\times 281$, without using a calculator.

[3 marks]

Split each number into $1$s, $10$s, $100$s and so on, writing each component of one number along the top of the grid, and each component of the other number down the left-hand side. Then, fill all the squares of the grid by multiplying each bit of one number by each bit of the other number.

Then, by whichever method you prefer, add together all the answers in the grid.

$4000+1600+600+240+20+3=6463$

So,

$281 \times 23 = 6463$

Level 1-3

### Example Questions

For this multiplication we will use the long multiplication method, multiplying $619$ first by $5$ then by $40$

$\begin{array}{r}619\\\times45\\\hline3095\\24760\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}3095\\+24760\\\hline27855\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $52$ first by $1$ then by $30$

$\begin{array}{r}\begin{array}{r}52\\\times31\\\hline52\\1560\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}52\\+1560\\\hline1612\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $760$ first by $4$ then by $20$

$\begin{array}{r}\begin{array}{r}760\\\times24\\\hline3040\\15200\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}3040\\+15200\\\hline18240\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $364$ first by $2$ then by $50$

$\begin{array}{r}\begin{array}{r}364\\\times52\\\hline728\\18200\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}728\\+18200\\\hline18928\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $185$ first by $8$ then by $30$

$\begin{array}{r}\begin{array}{r}185\\\times38\\\hline1480\\5550\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}1480\\+5550\\\hline7030\end{array}\end{array}$

Level 1-3

Level 1-3

GCSE MATHS

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