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1.1 F) Multiplication – Grid Method
1.1 F) Multiplication – Grid Method
There are two main methods to multiply numbers that are fairly large. These are the grid method and the column method. This section will look at the grid method and the next section will look at the column method. I would recommend having a go at both of the methods. After you have had a go, choose one method to remember and forget about the other one.
The Grid Method
The grid method involves splitting each of the numbers that we are multiplying into each of their place values. After we have split the numbers up into their place values, we then multiply the rows and the columns. The final step is to add all of the numbers that are inside the grid.
This will all make a lot more sense after we have a look through a few examples.
The grid method involves splitting each of the numbers that we are multiplying into each of their place values. After we have split the numbers up into their place values, we then multiply the rows and the columns. The final step is to add all of the numbers that are inside the grid.
This will all make a lot more sense after we have a look through a few examples.
Example 1
Complete the calculation below:
Complete the calculation below:
The first step in this question is to split these two numbers up into their place values. For 28, we split it up into 20 and 8. For 34, we split it up into 30 and 4. The grid becomes:
We now multiply the row and the columns.
For the top left, we are multiplying 20 by 30. The best way to multiply these two numbers is to multiply the numbers without the zeros (we ignore the zeros) and then add the zeros at the end. When we ignore the zeros, we are multiplying 2 by 3, which gives us 6. We ignored 2 zeros (1 from each of the numbers), therefore we need to add two zeros onto our answer. This means that 20 multiplied by 30 is 600.
For the top left, we are multiplying 20 by 30. The best way to multiply these two numbers is to multiply the numbers without the zeros (we ignore the zeros) and then add the zeros at the end. When we ignore the zeros, we are multiplying 2 by 3, which gives us 6. We ignored 2 zeros (1 from each of the numbers), therefore we need to add two zeros onto our answer. This means that 20 multiplied by 30 is 600.
I am now going to complete the top right box, which is 20 multiplied by 4. The first step is to ignore the zeros and multiply the numbers; we therefore multiply 2 by 4 and this gives 8. We ignored 1 zero, which we need to add to the end of our answer. Therefore, 20 multiplied by 4 is 80.
The bottom left box is 8 multiplied by 30, so we do 8 multiplied by 3, which gives us 24. We then add the zero that we ignored, which gives us 240.
The final calculation is 8 multiplied by 4, which is 32.
We now have all of the values in the grid and this brings us onto the final step, which is to add all of the multiplied results from the grid; for our grid, we are adding all of the orange numbers. You may find it easier to add the numbers in the column, especially if we have written the numbers nicely whereby the place values are lined up.
We now add the two columns together.
The answer for this question is 952.
Example 2 – Large Numbers
The gird method works better when we are dealing with large numbers or very small numbers (decimals). Example 2 will be looking at the gird method with large numbers and example 3 will be looking at the grid method with decimals.
Complete the calculation below:
The gird method works better when we are dealing with large numbers or very small numbers (decimals). Example 2 will be looking at the gird method with large numbers and example 3 will be looking at the grid method with decimals.
Complete the calculation below:
The first step is to split the two numbers up into place values. 736 become 700, 30 and 6. 59 becomes 50 and 9. The first step is to multiply all of the rows and the columns (the video goes through all of this in more detail). The completed table is shown below.
We now add all of the multiplied numbers together. I am going to add each of the columns and then add the outcomes together. The added columns are shown below.
We then add the numbers at the end of each of columns together.
The answer to this calculation is 43,424.
Example 3 – Decimals
We are now going to have an example that will be looking at decimals.
Complete the calculation below:
We are now going to have an example that will be looking at decimals.
Complete the calculation below:
The first step in answering this question is to split the two numbers up into place values. The 8.6 become 8 and 0.6. The 9.4 becomes 9 and 0.4.
We now multiply across. The value in the top left box is calculated by multiplying 8 by 9, which gives 72.
The top right box is calculated by multiplying 8 by 0.4. The best way to do this is to imagine that we are multiplying 8 by 4 (rather than 0.4), which is 32. We then need to divide our answer by 10 because we should have multiplied by 0.4 and not 4. This means that our answer is 3.2.
The bottom left box is found by multiplying 0.6 by 9. We multiply 6 by 9, which is 54, and then divide our answer by 10 (because we should be multiplying by 0.6 and not 6) and this gives us 5.4.
The last box is the bottom right box, which is found by multiplying 0.6 by 0.4. We ignore one decimal place for each number (which is two in total) and multiply 6 by 4, which is 24. As we ignored two decimal places, we need to divide our answer by 100/ move the decimal place two places to the left, which results in our answer becoming 0.24.
We now add all of the numbers in the 4 boxes that we worked out. I am going to add the columns together and then add the results. The added columns are shown below.
We now add the results of the two columns. The working is shown below.
The answer to 8.6 x 9.4 is 80.84.