What is multiplication?
Multiplying 5 by 3 is the same as saying 5 times 3 or writing 5 x 3.
It means that we need five lots of three.
Here is a grid showing 5 lots of 3 alien eggs:
If you count the eggs, there are 15, so 5 lots of three equals 15. We can write it down like this:
5 x 3 = 15
We can look at the same lot of alien eggs and split them up differently:
Now there are 3 rows each with five eggs in. There are still 15 eggs in total, so ‘5 lots of 3’ and ‘3 lots of 5’ both equal 15.
With multiplication, the order in which you multiply the numbers doesn’t matter – you get the same result.
You may have been taught different techniques for multiplying numbers than the ones we look at here, you must use the one you feel most comfortable with. The following methods are the ones we use and you should be able to understand them even if you use a different one.
When multiplying a big number by a single digit number like 321 x 4, you must lay out the sum in columns with the big number on top of the little one, and the digits in the correct columns:
Now you take each digit in the big number one at a time, and times it by the small number. When the answer is more than 10 you carry over the 1 just like in addition.
1 x 4 is 4 so we can fill that in.
2 x 4 is 8 so we can fill that in.
3 x 4 is 12 so we fill in this in but remember that the ‘1’ gets carried over to the next column – if there were more digits in the sum the one would sit below the answer box and would get added on, like in addition.
Lets work through this multiplication sum: 143 x 25
Long multiplication requires a slightly different approach to short multiplication. But really all that we are going to do is multiply 143 by 5 and then multiply 143 by 20 and add the answers together.
Lets lay our sum out in columns, making sure the digits are in the correct places. We lay out long multiplications like this:
We start off multiplying each digit in the top number by 5 and we ignore the ‘2’ in ’25’ for now.
Now we multiply each digit in the top number by 20 ignoring the ‘5’ in ’25’.
Now we must add together our two answers to get our final answer:
You can use some tricks to help you answer questions when they are suitable. We take a look in another lesson at how when multiplying by 10, 100 or 1000 you can just add the same number of zeroes as are in the number you are multiplying by.
Another trick is to break down the multiplication. If the sum is 40 x 12, you can first do 4 x 12 and then move the decimal place by however many zeroes there are in 40, in this case one place:
4 x 12 = 48
Add one zero = 480
Lets look at this agin for the sum 700 x 7
7 x 7 = 49
Add 2 zeroes = 4900