# How Long Multiplication Works

You will now learn how to multiply large numbers with each other. Some call this method “long multiplication”.

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Rule

 $\text{FACTOR}\cdot \text{FACTOR}=\text{PRODUCT}$

When you are multiplying, the numbers have different names. The numbers that are multiplied with each other are called factors, and the answer to the multiplication is called a product.

Example 1

Find the product of the factors 6 and 7.

 $6\cdot 7=42$

Rule

$\begin{array}{llll}\hfill \text{NUMBER}\cdot 0& =0\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \text{NUMBER}\cdot 1& =\text{NUMBER}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $\text{NUMBER}\cdot 0=0\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\text{NUMBER}\cdot 1=\text{NUMBER}$

When you multiply a number with $0$, the product will always be $0$. When you multiply a number with $1$, the product will always be the number itself.

Example 2

### Multiplyingwith0and1

 $9562\cdot 0=0\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}31\cdot 1=31$

You have previously learned how to multiply. A method for multiplying larger numbers requires a lot of steps, so I will try to explain what happens rather than go step by step. Please study the examples carefully afterwards!

To make it as simple as possible, put the smallest factor to the right of the multiplication sign. Start with the last digit in the factor to the right, and multiply it with each digit in the factor on the left, starting with the digit closest to the multiplication sign. That means you multiply with the digit in the ones place first, then the number in the tens place, and so on. While doing this, you will often get numbers larger than $9$. When that happens, put the number of ones underneath the line, and transfer the number of tens to the next digit you will multiply with. When you multiply with that digit, remember to add those transferred tens to the answer.

When you start with the next digit in the factor to the right, you do the same thing, except you write the answers you get one line down and one space in. Finally, you can add all the numbers under the line together according to the column method.

Example 3

### Multiplying a Number with One Digit Number

Calculate $27\cdot 5$, $347\cdot 8$ and $2435\cdot 3$.

Example 4

### Multiplying a Number with a Two Digit Number

Calculate $23\cdot 35$, $207\cdot 18$ and $8763\cdot 45$.

Example 5

### Multiplying Larger Numbers

Calculate $753\cdot 391$ and $6043\cdot 840$.