Multiplication - calculate in rectangles

How many windows does this house have? You can quickly see it has six windows: 2 rows, with 3 windows in each row. This house is larger. How many windows does it have? 5 plus 5 plus 5, that’s … 15 windows.

This took you slightly longer to count, right? And then there is this tall building with 1,2 3 … 8 floors, and 4 windows on each floor. In all, there are: 4 plus 4 plus 4 plus 4 plus 4 plus 4 plus 4 plus 4 … which equals 32 windows. This time it took even longer to count all the windows, didn’t it? How about this?

Twelve floors with nine windows on each. Now it starts to become a pain to count. It takes time, and it’s easy to forget a window half way through, when you’re fed up with counting and start to get distracted. What a relief, there is another way! Look at this house again.

Three floors, five windows on each floor. We just calculated 5+5+5. We added five three times. So: 5+5+5 is 15. 5, three times, is 15.

We say: 3 times 5 is 15. When we do this we use a certain kind of arithmetic: times, or multiplication. We multiply 3 by 5. 3 times 5 equals 15. We note times with this sign.

The multiplication sign. Let’s calculate the windows on the other houses using multiplication, too. 8 floors with 4 windows on each floor. A minute ago, we counted 4+4+4+4+4+4+4+4, that is we added 4, 8 times. We can multiply instead: There are 4 times 8 windows on the wall, and this equals 32.

So, instead of adding 4 to 4 several times, we only do one single calculation: a multiplication. 8 times 4 equals 32. Instead of counting 5 plus 5 plus 5 we do one calculation: a multiplication. 3 times 5 equals 15. Do you see the pattern?

Multiplying is the same thing as adding the same number several times. Multiplication is a way to calculate a repeated addition. Take another look at the windows on the walls. There are two rows with three windows. It becomes a rectangle, with 2 times 3 windows, 6 windows.

Here: 5 rows with 3 windows in each. Altogether 5 times 3 windows. This is a rectangle with 15 windows. And this wall has a rectangle with 8 times 4, which equals 32, windows. You can think of multiplication as a description of a rectangle.

One side of the rectangle is one of the numbers, one factor, in the multiplication. The other side of the rectangle is the other number, the other factor, in the multiplication. And the whole rectangle, one factor times another factor, is a product. This goes for all multiplications. 5 times 4 is a rectangle.

6 times 7 is a rectangle. … and this wall - do you remember the large one we saw a minute ago? - has 12 floors with 9 floors placed in a rectangle. How many windows in total? 12 times 9. Multiplying is like repeating an addition with the same number. Multiplying is taking one factor times another factor.

The result is a product. A product can be seen as a rectangle, where one factor is one side, and one factor the other side.