Maths GCSE Revision - Lesson #1
This lesson from the ‘Number’ section of GCSE Maths is all about Number Types and BODMAS (transcript below video).
Let's get started with this first part of the course, which is all about different types of number.
Firstly, you need to know what an integer is. Integers are whole numbers, and these can be positive or negative, including zero. So, if we just jot down some examples. We could have minus five, zero, seventeen, two hundred and fifty, and so on.
Next, you need to know that all numbers are split into two different types. The first of these is rational numbers, and rational numbers can always be written as a fraction. For example, four can be written as four over one, one fifth can be written as zero point two, and a third can be written as zero point three recurring. So rational numbers can always be written as a fraction and this includes repeating decimals.
Irrational numbers however cannot be written as a fraction. These include things like certain square roots, root two and root three, and also the number pi, for example. These go on forever and they are non-repeating (they don't have a repeating pattern), and these are known as irrational numbers.
This section is titled BODMAS, and this is something that you use when your given an equation, and you're not sure which part of the equation you should calculate first. It stands for, brackets, orders (which includes any indices like squaring and square rooting), division, multiplication, addition and subtraction. The easiest thing to do here is to just go through an example. So let’s say you have to calculate three plus twenty-four, times two, minus twelve. With BODMAS you have to start from left to right, and this tells you what you should do first. We've got multiplication, addition and subtraction in this equation, and you can see that multiplication comes first. That means we want to do this part of the equation first, twenty-four times two, which gives you forty-eight. Next, we've got addition, so this is the next part of the equation we want to do. We're going to want to do three plus forty-eight, and that gives us fifty-one. Finally, we can do the last part which is subtraction. Fifty-one minus twelve gives you an answer of thirty-nine.
Let's just go through one more example. This one's slightly more complicated. Here you can see we've got some brackets and we also have a power. If you look at BODMAS, brackets come first. We want to do this first so that means we can ignore the square power for the time being, and we just look at what's inside the bracket. Inside the bracket we've got a multiplication. We also have a subtraction but because multiplication comes first in BODMAS we do that first. We're going to do the five multiplied by two, which is ten, and you still have the close bracket and the square. Now we finish off what's inside the bracket, using the subtraction. So, we do twenty-five minus ten, and that gives us fifteen. Now everything within the bracket has been done, we are left with fifteen squared. Fifteen squared will give us our final answer, which will be fifteen times fifteen, and we end up with two hundred twenty-five.
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