Fractions

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word 'fractio' which means 'to break'.

What are Fractions?

Fractions, in Mathematics, are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

For example in the figure,

• the bottom circle is divided into $4$ equal parts. Each part can be be expressed as ${\frac {1}{4}}$
• another circle in the bottom is divided into $8$ equal parts. Each part can be be expressed as ${\frac {1}{8}}$

Parts of a Fraction

All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fraction bar.

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  Fractions
  The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.
• The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.

Types of Fractions

Based on the numerator and denominator, which are parts of a fraction, there are different types of fractions as listed below:

Proper Fraction

Proper fractions are the fractions in which the numerator is less than its denominator. For example, ${\frac {4}{7}},{\frac {3}{5}},{\frac {1}{8}}$ are proper fractions.

Improper Fraction

An improper fraction is the type of fraction in which the numerator is greater than its denominator. For example,${\frac {7}{4}},{\frac {5}{3}},{\frac {8}{5}}$ are improper fractions.

Unit Fraction

Fractions in which the numerator is 1 are known as unit fractions. For example, ${\frac {1}{4}},{\frac {1}{3}},{\frac {1}{5}}$ are unit fractions.

Mixed Fraction

A mixed fraction is a mixture of a whole number and a proper fraction. For example, $5{\frac {1}{2}}$ where $5$ is the whole number and ${\frac {1}{2}}$ is the proper fraction, or, $2{\frac {1}{3}},7{\frac {9}{11}}$.

Equivalent Fraction

Equivalent fractions are the fractions that represent the same value after they are simplified. To get equivalent fractions of any given fraction:

• We can multiply both the numerator and the denominator of the given fraction by the same number.
• We can divide both the numerator and the denominator of the given fraction by the same number.

Example: Find the two fractions that are equivalent to ${\frac {4}{7}}$.

Solution:

Equivalent Fraction 1: Let us multiply the numerator and the denominator with the same number $2$.

This means, ${\frac {4}{7}}={\frac {4\times 2}{7\times 2}}={\frac {8}{14}}$

Equivalent Fraction 2: Let us multiply the numerator and the denominator with the same number 3.

This means, ${\frac {4}{7}}={\frac {4\times 3}{7\times 3}}={\frac {12}{21}}$

Therefore, ${\frac {4}{7}},{\frac {8}{14}},{\frac {12}{21}}$ are equivalent fractions.

Like and Unlike Fractions

Like fractions are the fractions that have the same denominators. For example, ${\frac {4}{7}},{\frac {2}{7}},{\frac {1}{7}}$ are like fractions.

Unlike fractions are the fractions which have different denominators. For example, ${\frac {4}{7}},{\frac {9}{14}},{\frac {13}{21}}$ are unlike fractions.