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Types of Fractions

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**Fraction **

A fraction is number representing a part of a whole. The whole can be a group of objects or a single object.

For example, $\frac{\text{3}}{\text{10}}$ is a fraction and read as three-tenth. In the fraction, the top number is called the numerator whereas the bottom number is called the denominator. In the fraction $\frac{\text{3}}{\text{10}}$, 3 is the numerator and 10 is the denominator.

In the above figure, the shaded portion is represented by $\frac{\text{2}}{\text{6}}$.

**Representation of fractions on the number line **

A fraction can be represented on the number line. Every fraction has a corresponding point on the number line.

For example,

Consider a fraction $\frac{\text{1}}{\text{2}}$.

$\frac{\text{1}}{\text{2}}$ is greater than 0, but less than 1.

Divide the space between 0 and 1 into two equal parts. We can show one part as the fraction $\frac{\text{1}}{\text{2}}$.

Consider another fraction $\frac{\text{1}}{\text{5}}$.

$\frac{\text{1}}{\text{5}}$ is greater than 0, but less than 1.

Divide the space between 0 and 1 into five equal parts.

We can show the first part as $\frac{\text{1}}{\text{5}}$, the second as $\frac{\text{2}}{\text{5}}$ and the third as $\frac{\text{3}}{\text{5}}$, the fourth as $\frac{\text{4}}{\text{5}}$ and the fifth part as $\frac{\text{5}}{\text{5}}$ = 1.

**Types of fractions
Proper fraction**

Fractions in which the numerator is less than the denominator are called proper fractions. In a proper fraction, the number in the denominator shows the number of parts into which the whole is divided, while the number in the numerator shows the number of parts that have been taken.

e.g. $\frac{\text{4}}{\text{20}}$,$\frac{\text{3}}{\text{20}}$,$\frac{\text{10}}{\text{20}}$

Fractions in which the numerator is equal to or bigger than the denominator are called improper fractions.

e.g. $\frac{\text{4}}{\text{3}}$, $\frac{\text{13}}{\text{8}}$, $\frac{\text{7}}{\text{7}}$

A combination of a whole number and a proper fraction is called a mixed fraction. It is the combination of a whole and a part.

e.g. 3$\frac{\text{1}}{\text{2}}$, 4$\frac{\text{2}}{\text{5}}$

An improper fraction can be expressed as a mixed fraction by dividing the numerator by the denominator of the improper fraction to obtain the quotient and the remainder. Then the mixed fraction will be Quotient $\frac{\text{Reminder}}{\text{Divisor}}$.

A mixed fraction can be written in the form of an improper fraction by writing it in the following way

**Like fractions**

Fractions with the same denominator are said to be like fractions.

e.g. $\frac{\text{4}}{\text{15}}$, $\frac{\text{6}}{\text{15}}$, $\frac{\text{8}}{\text{15}}$

**Unlike fractions**

Fractions with the different denominators are called unlike fractions.

e.g. $\frac{\text{3}}{\text{15}}$, $\frac{\text{3}}{\text{20}}$, $\frac{\text{9}}{\text{28}}$$$__ __

**Equivalent fractions**

Fractions that represent the same part of a whole are said to be equivalent fractions.

e.g. $\frac{\text{1}}{\text{2}}$ = $\frac{\text{2}}{\text{4}}$ = $\frac{\text{3}}{\text{6}}$ = $\frac{\text{4}}{\text{8}}$ = $\frac{\text{5}}{\text{10}}$------

To find an equivalent fraction of a given fraction either multiply both the numerator and the denominator of the given fraction by the same number other than zero or divide by their common factor other than 1, if any.

**Simplest form of a fraction**

A fraction is said to be in its simplest form or in its lowest terms if its numerator and denominator have no common factor except one. The simplest form of a given fraction can also be found by dividing its numerator and denominator by its highest common factor (HCF).

**Fraction **

A fraction is number representing a part of a whole. The whole can be a group of objects or a single object.

For example, $\frac{\text{3}}{\text{10}}$ is a fraction and read as three-tenth. In the fraction, the top number is called the numerator whereas the bottom number is called the denominator. In the fraction $\frac{\text{3}}{\text{10}}$, 3 is the numerator and 10 is the denominator.

In the above figure, the shaded portion is represented by $\frac{\text{2}}{\text{6}}$.

**Representation of fractions on the number line **

A fraction can be represented on the number line. Every fraction has a corresponding point on the number line.

For example,

Consider a fraction $\frac{\text{1}}{\text{2}}$.

$\frac{\text{1}}{\text{2}}$ is greater than 0, but less than 1.

Divide the space between 0 and 1 into two equal parts. We can show one part as the fraction $\frac{\text{1}}{\text{2}}$.

Consider another fraction $\frac{\text{1}}{\text{5}}$.

$\frac{\text{1}}{\text{5}}$ is greater than 0, but less than 1.

Divide the space between 0 and 1 into five equal parts.

We can show the first part as $\frac{\text{1}}{\text{5}}$, the second as $\frac{\text{2}}{\text{5}}$ and the third as $\frac{\text{3}}{\text{5}}$, the fourth as $\frac{\text{4}}{\text{5}}$ and the fifth part as $\frac{\text{5}}{\text{5}}$ = 1.

**Types of fractions
Proper fraction**

Fractions in which the numerator is less than the denominator are called proper fractions. In a proper fraction, the number in the denominator shows the number of parts into which the whole is divided, while the number in the numerator shows the number of parts that have been taken.

e.g. $\frac{\text{4}}{\text{20}}$,$\frac{\text{3}}{\text{20}}$,$\frac{\text{10}}{\text{20}}$

Fractions in which the numerator is equal to or bigger than the denominator are called improper fractions.

e.g. $\frac{\text{4}}{\text{3}}$, $\frac{\text{13}}{\text{8}}$, $\frac{\text{7}}{\text{7}}$

A combination of a whole number and a proper fraction is called a mixed fraction. It is the combination of a whole and a part.

e.g. 3$\frac{\text{1}}{\text{2}}$, 4$\frac{\text{2}}{\text{5}}$

An improper fraction can be expressed as a mixed fraction by dividing the numerator by the denominator of the improper fraction to obtain the quotient and the remainder. Then the mixed fraction will be Quotient $\frac{\text{Reminder}}{\text{Divisor}}$.

A mixed fraction can be written in the form of an improper fraction by writing it in the following way

**Like fractions**

Fractions with the same denominator are said to be like fractions.

e.g. $\frac{\text{4}}{\text{15}}$, $\frac{\text{6}}{\text{15}}$, $\frac{\text{8}}{\text{15}}$

**Unlike fractions**

Fractions with the different denominators are called unlike fractions.

e.g. $\frac{\text{3}}{\text{15}}$, $\frac{\text{3}}{\text{20}}$, $\frac{\text{9}}{\text{28}}$$$__ __

**Equivalent fractions**

Fractions that represent the same part of a whole are said to be equivalent fractions.

e.g. $\frac{\text{1}}{\text{2}}$ = $\frac{\text{2}}{\text{4}}$ = $\frac{\text{3}}{\text{6}}$ = $\frac{\text{4}}{\text{8}}$ = $\frac{\text{5}}{\text{10}}$------

To find an equivalent fraction of a given fraction either multiply both the numerator and the denominator of the given fraction by the same number other than zero or divide by their common factor other than 1, if any.

**Simplest form of a fraction**

A fraction is said to be in its simplest form or in its lowest terms if its numerator and denominator have no common factor except one. The simplest form of a given fraction can also be found by dividing its numerator and denominator by its highest common factor (HCF).