Multiplication Grid, The Grid Method of Multiplication and Multiplying Decimals using the Grid Method

Video 1– Mul­ti­pli­ca­tion Using the Grid Method (whole numbers).

I think this is about the best video I’ve seen to explain mul­ti­pli­ca­tion using the grid method (see video 2, below, for mul­ti­ply­ing dec­i­mals using the grid method):-

Video 2– Mul­ti­ply­ing Dec­i­mals Using the Grid Method

This video builds on the above video to show how you can also mul­ti­ply with dec­i­mals using the grid method:-

I think those videos are well explained and easy to fol­low. I know some peo­ple like to see all the detailed work­ings in front of them, so here is another exam­ple with all the detailed work­ings also shown below:

Video 3 — Mul­ti­pli­ca­tion Using the Grid Method– Another Example

Fol­low this video to show the basics of grid mul­ti­pli­ca­tion and read below how you can use the same method (with a lit­tle trick) to mul­ti­ply using decimals.

Exam­ple of how to use the Grid Method to Mul­ti­ply with Decimals

I decided to inves­ti­gate the grid method of mul­ti­pli­ca­tion because my son, in his first year of sec­ondary school (Year 7), came home with his first bit of maths home­work. The home­work included the fol­low­ing multiplication:-

7.23 x 6.3

My son is ok at Maths, in fact he’s quite good, he was one of only a few at his pri­mary school that achieved “Level 6″. How­ever, he was really strug­gling with this ques­tion. He was using the grid method of mul­ti­pli­ca­tion. The grid method was never used when I was at school but now it’s com­monly used as a step­ping stone to the tra­di­tional method of long multiplication.

The Grid Method of Multiplication

The grid method can only really be explained by using an example.

So let’s use:-

16 x 23

First you draw up grid. In this exam­ple which is mul­ti­ply­ing a two digit by a two digit num­ber, we need 2 columns and two rows. Next we split the num­bers into tens and dig­its. So 16 becomes 10 and 6 and 23 becomes 20 and 3 and enter as below. Then mul­ti­ply out (refer the grid below) 20 x 10 = 200, 20 x 6 = 120, 3 x 10 = 30 and 3 x 6 =18. Then add up each col­umn 200 + 30 = 230 and 120 + 18 = 138. Finally (see the sum beneath the grid) just add 230 +138 = 368.

Multiplication Grid Example

 

 

 

 

 

 

 

 

 

 

 

 

I can see the advan­tages of using the grid method. It is highly visual, con­trast how dif­fi­cult it was to fol­low my writ­ten expla­na­tion com­pared to how easy it was to just look at the actual grid! The other advan­tage is that it clearly sep­a­rates tens and units (and hun­dreds and thou­sands etc. for larger num­bers). In my view this helps chil­dren to under­stand how it works.

Mul­ti­ply­ing Dec­i­mals Using The Grid Method

As my son now realises, you have to be care­ful when you use the grid method to mul­ti­ply dec­i­mals. As I men­tioned above he had to solve this mul­ti­pli­ca­tion question:-

7.23 x 6.3

This was roughly how he set out his grid to answer this ques­tion (THIS IS AN EXAMPLE OF HOW NOT TO DO IT!):-

Multipliaction Grid with Decimals- How NOT to do it

 

 

 

 

 

 

 

 

 

The cells in the grid above are cor­rect. My son, using pen and paper and the typ­i­cally less than neat pre­sen­ta­tion skills of an eleven year old, man­aged to get the dec­i­mal point in the wrong place in more than one of the cells. The trick here is to elim­i­nate the dec­i­mal point when you use the grid and use a sim­ple rule to intro­duce it back after you’ve used the grid. So we have:

7.23 x 6.3

Step 1 — Elim­i­nate the dec­i­mal points;

7.23 x 6.3 becomes 723 x 63

Step 2 — Use the grid method;

Grid Method for Multiplying Decimals

Step 3: Rein­tro­duce the dec­i­mal point using this sim­ple method.

Count the num­ber of dig­its in the orig­i­nal ques­tion that are after the dec­i­mal point and then alter the answer from the grid so that there are that num­ber of dig­its after the dec­i­mal place. Hmmm… that’s not easy to put into words! Best look at our example:-

The orig­i­nal ques­tion was 7.23 (2 dig­its after the dec­i­mal place) x 6.3 (1 digit after the dec­i­mal place), so in this case there are 3 dig­its after the dec­i­mal place. So we need to take our answer from the grid:- 45549 and alter it so that there are 3 dig­its after the dec­i­mal place = 45.549

Grid Method Multiplying Decimals

 

 

 

 

 

 

 

 

 

 

Final Answer 7.23 x 6.3 = 45.549

This entry was posted in 6. How to Multiply Using the Grid Method, 7. How to Multiply with Decimals Using the Grid Method. Bookmark the permalink.

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