Long Multiplication | Grid Method | Maths Made Easy

# Long Multiplication and Grid Method

Level 1-3

## 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 prefer long multiplication, so we will look at both.

0 votes, 0 avg
378
Created on By ALex

Long Multiplication Quiz

Try the MME Long Multiplication quiz.

1 / 4

Calculate $33 \times 517$, without using a calculator.

2 / 4

Calculate $99 \times 69$, without using a calculator.

3 / 4

Calculate $87 \times 765$, without using a calculator.

4 / 4

Calculate $321 \times 123$, without using a calculator.

The average score is 68%

0%
KS3 Level 1-3

## Test your skills with online exams on the MME Revision Platform

##### 5 Question Types

Our platform contains 5 question types: simple, multiple choice, multiple answers, fraction and image based questions. More question types are coming soon.

##### Video Solutions

Premium users have access to Video Solutions for every single exam question. Our expert Maths tutors explain all parts of the question and answer in detail. Follow along and improve your grades.

##### Written Solutions

Get written solutions for every single exam question, detailing exactly how to approach and answer each one, no matter the difficulty or topic.

##### Track your progress

Every exam attempt is stored against your unique student profile, meaning you can view all previous exam and question attempts to track your progress over time.

KS3 Level 1-3

## Method 1: Long Multiplication (Column) 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: Next, the second digit is the tens digit, for this 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 by every digit from the top number, writing the results underneath the last step from right to left.

Step 4: Add up the final numbers using the column addition method, writing the results under another line.

From this we can see:

$281 \times 23 = 6463$

KS3 Level 1-3
KS3 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.

Step 3: We add up all the answers from the grid to get our final answer.

$14000+800+700+210+40+12=15762$

KS3 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,

$281 \times 23 = 6463$

KS3 Level 1-3

## GCSE Maths Revision Cards

(252 Reviews) £8.99

### 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,

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

### Worksheets and Exam Questions

#### (NEW) Long Multiplication - Exam Style Questions - MME

Level 1-3 New Official MME

### Learning resources you may be interested in

We have a range of learning resources to compliment our website content perfectly. Check them out below.