Long Multiplication | Grid Method | Maths Made Easy

Long Multiplication and Grid Method

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What you need to know

Long Multiplication and Grid Method

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

Note:The key to not making a mistake with long multiplication is to make sure you know your times tables and you write your workings neatly, ensuring your columns are always lined up correctly.

Long Multiplication

With long multiplication we write the two numbers we are multiplying on top of each other. We write the values so that the 1’s, 10’s, 100’s….. all line up in the correct column. Then we multiply each digit with every other digit, writing the results underneath and carrying forward when values go above 10. 

The Grid Method

The grid method involves splitting each number into 1s, 10s, 100s and so on, and writing each component of one number along the top of a grid, and each component of the other number down the left-hand side. Then, we fill all the squares of the grid by multiplying each bit of one number by each bit of the other as seen in the example below.

Example 1: Long Multiplication

Work out 23\times 281

To start, write the bigger number over the smaller one, making sure that the 1s are above each other, the 10s are above each other and so on.

 

Then, we want to multiply each component of 281 by the “3” part of 23 and write the results under the grey line. 1\times 3=3, so we write a 3 in the 1s column under the grey line. Then, 8\times 3=24, so we write the 4 in the 10s column and carry the two over to the 100s column. Then, 2\times3=6, but we carried over an extra 2, so we write 6+2=8 in the 100s hundreds column as shown. 

Now, we multiply each component of 281 by the “2” part of 23. The only difference is because the 2 represents a 20, everything is shifted one space to the left and a zero is put in the 1s column, before you then multiply in exactly the same way. 

The final step is to add your two answers using the column addition method as shown.

Example 2: The Grid Method

Work out 23\times 281

Split each number into 1s, 10s, 100s 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=6,463

Example Questions

For this multiplication we will use the long multiplication method, multipliying 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}31\\\times52\\\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}24\\\times760\\\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}24\\\times760\\\hline3040\\15200\end{array}\end{array}

 

Adding the results of each components multiplication,

 

\begin{array}{r}\begin{array}{r}724\\+18200\\\hline18924\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}38\\\times185\\\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}

 

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