Long Multiplication Anyone Can Understand

Four Methods of Long Multiplication for One Sum

Ever struggled with your children’s math homework?

Need to help your children learn math concepts with ease?

Every week I am met by parents who suffer with Math especially multiplication. This is the easy guide to long multiplication.



It is a little-known fact that the only timetables you need to master are 1’s, 2’s, 3’s, 5’s and 10’s. Once you or your child have learnt these five you can do any of your timetables. Let me show you.

If the sum we are working out is 6 x 7 =

Thinking about the five timetables we know, what two numbers make up the first number in the sum. 6 in this case.

You would be right to say 1 and 5 or 3 and 3

Let us start by taking 1 and 5

1 x 7 = 7
5 x 7 = 35

If we add the two answers together 7 + 35 we get the answer 42 (6 x 7 = 42)

If we then look at 3 and 3 we can do it exactly the same way.

3 x 7 = 21
3 x 7 = 21

If we add the two numbers together 21 + 21 = 42

One more example for clarification lets look at the sum 8 x 9 =

The two numbers that make 8 from our timetable list are 3 and 5

3 x 9 = 27
5 x 9 = 45

If we add the two answers together 27 + 45 = 72 (8 x 9 = 71)

Long Multiplication

There are four methods for working out long multiplication.

Box Multiplication Method

Let us take the sum 25 x 42 =

The numbers, in this case, are split into ten’s and units. Each of these numbers is put into a box.

We then times each box together

20 x 40 = 800 (Easy method for this 2 x 4 = 8 / There are 2 zero’s in the question so there has to be 2 in the answer so 8 becomes 800)

So let us now finish the sum
20 x 40 = 800
5 x 40 = 200
20 x 2 = 40
5 x 2 = 10

We then add all the boxes and answers together

800 + 200 + 40 + 10 = 1050

25 x 42 = 1050

Diagonal Multiplication Method

The hardest part of this method is drawing it out correctly. Again the numbers are drawn in boxes but this time each box is divided in two with a diagonal. The numbers are also placed separately rather than in tens and units.

You once again then times the boxes across

2 x 4 = 08 (the zero eight represents no ten’s and 8 units)
2 x 2 = 04
5 x 4 = 20
5 x 2 = 10

This time though you add the numbers down the diagonal starting from the right-hand side. If an answer is bigger than 9 then you need to carry the numbers to the next column like you would on any sum.

Traditional Multiplication Method

Japanese Multiplication Method

This method has been shown several times on social media. As with everything teaching I don’t know it enough to show someone else. I will let the experts explain it.

This is a complete contrast to other posts I have published. The idea came to me in the middle of the night. If you would like more of this type of post please leave me a comment letting me know what you would like a guide on next. Thank you for reading.

View at Medium.com

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