What is Algebra?
In algebra letters are used to show missing numbers.
Algebra is easy when you understand exactly what it is. You can think of the letters as question marks or empty boxes.
For example an algebra sum might look like this:
3 + x = 12
The ‘x’ is just a missing number, it’s like an empty box waiting to be filled or a question mark whose value we need to find:
3 + ? = 12
In algebra letters such as ‘x’ or ‘a’ or ‘b’ are simply used to show this missing number. All you have to do is work out the missing number.
To work out the missing number in the sum: 3 + x = 12
Remember that ‘x’ is simply a number that we don’t know. We just need to ask ourselves, what can we add to 3 to get 12?
Because subtraction is the opposite of addition, we can rearrange the sum like this:
12 – 3 = x
x = 9
Remember that in algebra the letters are just missing numbers and in order to find out what they are we often need to rearrange the calculation.
In algebra there are some expressions used that you need to learn.
This means 4 times a. Instead of writing 4 x a, in algebra we often just write 4a.
This means a x b.
This means 1/2 x ‘a’, or simply half of ‘a’.
This means ‘y’ divided by 4.
This means ‘a’ squared, which is the same as ‘a x a’.
4(a + 3)
Brackets are useful in algebra to seperate a sum in to sections. You always work out the brackets first. 4(a + 3) means ‘4 lots of (a + 3)’.
If you have read about mixed calculations, you should know about BODMAS. It is useful in algebra too because often algrebra involves mixed calculations.
Because it is so important let’s go over it again quickly:
BODMAS stands for:
Brackets, Other, Division and Multiplication, Addition and Subtraction.
It tells you the order in which to work out your calculations.
It tells you to start with Brackets, then work out Other (this means things like square numbers and cube numbers), next do Division and Multiplication (work left to right), and then Addition and Subtraction (work left to right). So if you are faced with a calcultaion with several parts – remember BODMAS.
Why is BODMAS so important?
Look at the following calculation:
(7 + 7) – (1 + 2) + (5 + 5) = x
In order to work out the value of ‘x’ we must use BODMAS. It tells us to do the Brackets (BODMAS) first:
(7 + 7) = 14
(1 + 2) = 3
(5 + 5) = 10
Now we can put these value back in to the sum where the brackets were:
14 – 3 + 10 = x
Next we do the the addition and subtraction working as we find them from left to right:
14 – 3 = 11
11 + 10 = 21
x = 21
As we have seen, in algebra letters are used in place of unknown numbers.
Solving algebraic equations is all about finding the value of any unknown numbers.
Equations just mean that there is an equals sign.
3 + 1 = 4 is a simple equation.
When solving equations the equals sign is very helpful. It tells you that the values on the left of it equal the values on the right of it.
It is so important by now to understand that multiplication and division are opposites, and that addition and subtraction are opposites, because this will help you to rearrange and solve algebraic equations.
Lets take a look why this is so important to know.
Here is a simple equation:
3 + 4 = 7
It can be rearranged to look like this:
3 = 7 – 4
Do you see what we did? We moved the + 4 from the left side and changed it to – 4 on the right side. We can do this because subtraction is the opposite of addition so the equation is still correct we have just moved it around. This becomes very helpful when looking at equations involving algebra.
Lets introduce algebra in to the equation:
x + 4 = 7
The same rules apply, we can use the opposite operation to rearrange the equation. We can move the ‘+ 4’ over to the other side making it ‘- 4’, like this:
x = 7 – 4
This is much easier to solve!
7 – 4 = 3
x = 3
Here is a trickier equation:
3a + 3 = 12
We want to know the value of a, so we want to rearrange the equation to get ‘a’ on it’s own – because we want to be able to say a = ‘something’. And to do this we need to simplify and change the equation we are given.
Look at the ‘+ 3’ bit on the left side of the equation. If we are adding 3 on one side, lets move it over to the other side and make it ‘- 3’:
3a = 12 – 3
We can now work out ’12 – 3′ on the right side of the equation and get to:
3a = 9
This is great, we have rearranged the equation and we are getting closer to ‘a’ being left on its own. Now remember that 3a is the same as ‘3 x a’ so the equation is really:
3 x a = 9
If 3 times ‘a’ equals 9, we can move the multiplication over to the other side and turn it in to a division:
a = 9 ÷ 3
a = 3