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Understanding Fractions

Introduction

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.

Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Divisor/Denominator - the ‘bottom’ number of a fraction. It is the total number of parts.
Dividend/Numerator - the ‘top’ number of a fraction. It is the number of parts being taken from the whole.
Reciprocal - The reciprocal of a fraction is the fraction turned upside down.

Lesson

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.

Examples

Identify Numerator and Denominator (Example #1)

Identify the numerator and denominator of the following fraction
The numerator is the number on the top of the fraction, which is 1
The denominator is the number on the bottom of the fraction, which is 2

Identify Numerator and Denominator (Example #2)

Identify the numerator and denominator of the following fraction
The numerator is the number on the top of the fraction, which is 5
The denominator is the number on the bottom of the fraction, which is 9

Identify Numerator and Denominator (Example #3)

Identify the numerator and denominator of the following fraction
The numerator is the number on the top of the fraction, which is 6
The denominator is the number on the bottom of the fraction, which is 2

Identify Numerator and Denominator (Example #4)

Identify the numerator and denominator of the following fraction
The numerator is the number on the top of the fraction, which is 9
The denominator is the number on the bottom of the fraction, which is 4

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