Introduction to Algebra

We have started a new unit this term. This unit will be on Algebra. When people here the word Algebra they often get quite nervous and think it changes everything in maths, making it heaps harder. This is not the case. Algebra still obeys all of the same laws that standard maths follows. The only difference is we are using symbols to represent information, instead of number like we have previously. The reason we use symbols is because sometimes values or information can change. If we look at the number 4 for example, this can only ever represent one value (4 units). However, if we use symbols, they can be used to represent any value we want. An example could be;

If we want to find the total number of people at the school, we can set up an equation like so;

Total number of people = a + b + c + d

where a = the number of students at school today, b = the number of teachers at school today, c = the number of support staff at school today (i.e. cleaners, office staff, etc), and d = the number of visitors at school today (i.e. parents, builders, etc). 

The values for a, b, c, and d can all change every day, depending on how many people are at school at any particular time.  This means that the equation we have above will work every single day, no matter what. 

Now when we are dealing with algebra, it is important to understand some key words. These are in the table below. Make sure you familiarise yourself with these words. 

Now, when we work with Algebra there are a few little tricks you need to remember. The first is that when we write say "4x" this really means "4 lots of whatever x is representing" or "4 multiplied by x". We don't put in the multiplication symbol. 

Also, we rarely will write "1w" or "1g" or "1z" because what we are really saying is "1 lot of whatever symbol we choose", which in the end is just that symbol. So instead of writing "1w" we would just write "w", and the same with "1g" being just "g", or "1z" being just "z". 

Now for some examples.

If we have a certain number, a, write an expression for the following; 

• This certain number (a) increased by 7:

To do this, think of what we would do with any normal number if we wanted to increase it by 7. We would simply take this number and add 7. We use the same idea with this question here. So to increase this certain unknown number (a) by 7 we would simply add 7 to a, so an expression for this would simply be:

a + 7

• This certain number (a) decreased by 21:

Again, think of what we would do to a normal number if we were decreasing it by 21. We would simply take 21 away from the number. We use the same idea with this question here. So to decrease this certain unknown number (a) by 21 we would simply take 21 from a, so an expression for this would simply be:

a - 21

• 4 lots of this certain number (a):

Again, we think of what we would do with a normal number, which would be to multiply 4 by this number. We do this with our certain unknown number (a). We would get the expression:

4 x a

Which we know we write as:

4a

• Increase a certain number (a) by 5 then decrease the result by 7:

This is a two stage problem. First we would increase a by 5 and get the expression:

a + 5

Next, we need to decrease this by 7, or subtract 7 from this. This gives us:

a + 5 - 7

Which we can simplify (i.e. solve 5 - 7) and write as:

a - 2

Hopefully this gives you an introduction into what algebra is and the basics of how we use it. I have uploaded a worksheet on this into the "Worksheets" tab. Work through this sheet, checking your answers as you go. 

If you do have any questions on this, feel free to comment on this post, or email or chat to me in person.