Fractions are a way of expressing parts of a whole. We can understand this by looking at the figure below:
The complete circle is the whole. In this example, it has been divided into a total of 4 parts. So to express the whole circle as a fraction, we would need all 4 parts: 4/4. If we wanted to express half of the circle as a fraction, we would need only 2 of the 4 parts: 2/4. The reciprocal of a fraction is simply the fraction turned upside down. I.e. the numerator becomes the denominator and vice versa.
To understand fractions, we should try and look at the big picture. 7/8 does not mean anything until we understand that 7/8 is 7 parts of something that has been divided into 8 parts.
For the lessons that follow, we will need to know the parts of a fraction and how they relate to each other. We can see that fractions can be written in numerous ways:
So using 7/8 as an example, we see that 7 is the numerator (the number being divided or the number of parts being taken from the whole) and 8 is the denominator (the number doing the dividing or the number of parts in total).
To find the reciprocal of a given fraction, we re-write it so that the denominator is the numerator and vice versa. So if we are given 4/9 and asked for its reciprocal, the answer would be 9/4.