Fractions:

Fractions are mathematical terms, which describe a part of a unit by denoting how many parts of a total number of equal size parts there are.

Let's say that you order a pizza and when it is delivered and you open the box, you find it sliced into 8 equal parts.

If you eat one slice, you will have one of eight equal size slices or one eighth, which is written as 1/8. The number above the slash is called the numerator and it signifies, in this specific case, how many slices of the pizza you have eaten.

The number below the slash is called the denominator and it expresses the total of the equal size parts of the whole (in this case the pizza).

Fractions can be added, subtracted, multiplied and divided just like integers and decimal numbers. There are certain tricks we have to learn first, though:

Fractions can be simplified:

Why? Because in the first fraction, 2/4, both the numerator (2) and the denominator (4) are divisible by 2.

and

and so we end up with a simplified fraction 1/2, which is equal to 2/4. As long as both the numerator and denominator are divisible by the same number, we can go ahead and divide them both, by that same number, to simplify that fraction. Why would we do it? Let's say that you find yourself with a fraction 175/200 in an equation. That does not look as a very easy number to work with, does it? However since the numerator (175) ends with 5 and the denominator (200) ends with 0, they are obviously both divisible by 5, We therefore divide both the numerator and denominator by 5 to get:

and

and we end up with a simplified fraction of 35/40.

Now we can see that both the numerator and denominator are still divisible by 5, so that we divide them both again by 5 to get:

and

and our even more simplified fraction becomes 7/8. That is certainly far easier to work with than 175/200, isn't it?

Remember, you can go ahead and simplify as long as you divide both the numerator and denominator by the same number!

This rule is actually something, which works in reverse, as well. This may sound a little difficult to accept, since we have just shown you how to simplify a fraction and hopefully convinced you of the necessity for this. You can also multiply the numerator and denominator by the same number!.

Why would you do this, if you - according to logic we have just accepted, will end up making the fraction more complicated or complex? We will explain when we get to the addition and subtraction of fractions.

Examples:

Answers: