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Area of Right Regular Pyramid Adding/Subtracting Decimals Percentages Introduction Volume of a Cone Laws of Indices Comparing Fractions Irrational NumbersHow to do Long Multiplication

The page on __ Short Multiplication__, showed
examples of multiplication sums such as:

Learning how to do Long Multiplication isn't really much more difficult than learning multiplication
with shorter sums.

It's just a process that takes a bit longer to do, hence the name.

Long Multiplication Examples

18 × 12

This is a small basic example, but the same approach can be used for larger multiplication sums also.

Set up the sum as a usual multiplication sum.

First step is to multiply the **1** and the **8** on the top row, by the **2** below.

As if it was just the **2** in the sum.

Next thing to do is to multiply the **1** and **8** on the top row by the **1** below.

But remembering that this **1** is in the "TENS" column.

As such, a **0** needs to first be placed in the units answer column first, to account for
this.

Now, the  2 separate results from each multiplication are added together, and the result of this addition is the answer to the whole multiplication sum.

So:

294 × 23

Now adding the **2** results together:

464 × 314

464

464

With the **3** on the bottom line, we're multiplying by "HUNDREDS".

So two **0**'s are placed in the answer section first, before multiplying the
top row by **3**:

464

Now this time there are  3 multiplication results to add together:

1856

+ 4640

464 × 314 = 145696

Shorter Approach

As one becomes more confident with long multiplication, they may feel comfortable using vertical multiplication, laying out the sums in one part, with the multiplication results laid out below in rows, then added together.

34 × 128

128

512

34 × 128 = 4352

This approach usually looks a bit neater, requiring less writing.

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