In this section of the , we are going to take a look at algebra. By clicking on the buttons above you can investigate other algebraic subjects.
In algebra we don’t just talk about numbers, we also talk about symbols. ("Uh-oh!"). When we say that a packet of sugar weighs 0.5 grams, we could also write that that’s a load of rubbish! But the algebraic approach is to write that it weighs G grams and not tell anyone what G is equal to. Saying that a packet of sugar weighs 0.5 grams is making a particular statement, saying that it weighs G grams is making a general statement.

Our algebra comes to life by using algebraic symbols. The most common ones are x and y: they pop up all over the place. For example, let’s say that Tony needs to find out what the sum of two numbers is, but he doesn’t know what one of the numbers is. Let’s say that Tony does know that the first number is 83.

83 + an unknown number = …

We would write this down as:

83 + x = …

We can also multiply these unknown numbers by a known number, or even another unknown number as below:

2 X y
65 X x
x X y
2 X y X 65 X x

To make it more clear, in algebra we usually write 65 X x as 65x, so 2 X y becomes 2y and 2 X y X 65 X x becomes 2y X 65x.

Take a note here: All unknown numbers with the same symbol in a particular equation are the same in that particular equation.

To add algebraic terms, you just treat them like normal numbers, as long as they are the same types. Therefore, you can’t add 2x to 5y if you don’t know what x or y is. Like terms are terms that have the same letter. So 56x, 9x and –34x are all like terms. You can add them by adding the numbers up and putting the letter on the end. To add 4x and 5x, follow these easy steps:

4x + 5x Get rid of the x on each number

4 + 5 Add the numbers

Subtraction is pretty much the same, except that this time you subtract! To subtract 4x from 5x, follow these (a little bit harder) steps:

5x – 4x Get rid of the x on each number

5 - 4 Subtract the numbers

OK, now onto division – uh-oh! Lets say we want to do the following equation: . Firstly take off the unknowns. Doing this leaves us with 6 divided by 2 which gives 3. Now go back to the unknowns and divide them. The unknowns in this case are x and y and dividing these terms simply gives us ! In algebra, it is written . Now, as before, put this back onto the known value and you have the answer: .

So the process is:

1. Take off the unknowns
2. Divide the remaining known values
3. Go back and "divide" the unknowns
4. Put the result back onto the known values in the correct format.
5. Feel good!