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3 times 4 is the same as saying 3 multiplied by 4. It is important to be familiar with both terms. This method makes large calculations with addition easier!

A multiplication consists of a factor, a dot and another factor. When you multiply, you answer the question: What do you get if you have a number added with itself a given number of times?

Rule

### EssentialWordsandPhrases

 $\text{FACTOR}\cdot \text{FACTOR}$

Multiplication can be visualized like this: Picture the number $4$. If you add $4$ to itself several times, you will get a row of $4$’s and pluses following each other, like this:

 $4+4+4+4+4+4+4+4$

Above, you can see that $4$ is added to itself eight times. Writing it like this can be tiresome in the long run. Imagine if you have to plus $4$ with itself a hundred times. Then you would have to write the number $4$ one hundred times, with a plus between every single number. It would look like this:

$\begin{array}{llll}\hfill & \phantom{+}4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & +4+4+4+4+4+4+4+4+4+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ As this is a very tiring and inefficient way to do it, we have found another method. A much smarter method, which will save us a lot of time. The method I’m talking about is multiplication. The answer to the big addition expression above is $400$. Try to see if you can calculate it yourself. Now you are going to learn how to do this in an easier way, namely by multiplying. We begin with an example:

Example 1

Let’s say that you are wondering what the answer to $4$ added to itself ten times is. Up until now, you would have written:

 $4+4+4+4+4+4+4+4+4+4$

Instead of writing $4$ ten times after each other with the plus sign in between, you can write that you want $4$, ten times. You simplify the expression, like this:

 $10\cdot 4=40$

But then another important question appears. How can you know the answer to the expression ten times four just like that? The answer is simple. The small multiplication table gives you the answer to this, and ninety nine other multiplications.

With the small multiplication table, and some other techniques, you will be able to answer many other calculations - calculations you will need to know both in your everyday life, but also in mathematics at school. As you can see, you save a lot of time by learning how to multiply.

How can you write

 $2+2+2+2+2+2+2+2+2$

in a simpler way, and what is the answer?

The answer and the simplification is written like this:

$\begin{array}{llll}\hfill & 2+2+2+2+2+2+2+2+2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =9\cdot 2=18\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $2+2+2+2+2+2+2+2+2=9\cdot 2=18$