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A fraction represents a part of a whole or, more generally, any number of equal parts.

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The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. The Egyptians used Egyptian fractions c. 1000 BC. About 4000 years ago, Egyptians divided with fractions using slightly different methods. They used least common multiples with unit fractions. Their methods gave the same answer as modern methods.
The Greeks used unit fractions and continued fractions. Followers of the Greek philosopher Pythagoras (c. 530 BC) discovered that the square root of two cannot be expressed as a fraction of integers.

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The numerator indicates how many sections of the fraction are represented. It is placed in the upper part of the whole.
The denominator indicates how many parts the whole has been divided into. It is placed in the lower part of the fraction.

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A mixed fraction is a mixture of a whole and a proper fraction.

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Proper fractions are the fractions in which the numerator is less than its denominator. It is often smaller than the whole. Example: 5/7, 3/8, 2/5, etc.

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Fractions with numerator as 1 are known as unit fractions. Example: 1/4, 1/7, 1/9, etc.

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An improper fraction is the type of fraction in which the numerator is more than or equal to its denominator. It is always the same or greater than the whole. Example: 4/3, 5/2, 8/5, etc.