Last modified on July 11th, 2024

chapter outline

 

Types of Fractions

Fractions are classified into different types based on their numerators and denominators.  

Proper Fraction

A fraction in which the numerator is less than its denominator is called a proper fraction. Its value is always less than 1.

${\dfrac{2}{3}}$, ${\dfrac{4}{5}}$, and ${\dfrac{2}{7}}$ are a few examples of proper fractions.

Proper Fraction

Improper Fraction

An improper fraction is a fraction in which the numerator is greater than or equal to its denominator. The value of a proper fraction is always greater than or equal to 1.

${\dfrac{3}{2}}$, ${\dfrac{5}{4}}$, ${\dfrac{7}{2}}$, and ${\dfrac{9}{9}}$ are a few examples of improper fractions.

Improper Fraction

Mixed Fraction

A mixed fraction consists of a whole number and a proper fraction. Thus, they are always greater than 1.

${1\dfrac{2}{3}}$ and ${2\dfrac{3}{5}}$ are some examples of mixed fractions.

Mixed Number

Like Fractions

Fractions with the same denominators are called like fractions. 

${\dfrac{2}{3}}$, ${\dfrac{5}{3}}$, ${\dfrac{7}{3}}$, and ${\dfrac{8}{3}}$ are a few like fractions.

Like Fractions

Simplifying such fractions is easy, as the denominators of all the fractions are the same. 

For example,

${\dfrac{2}{3}+\dfrac{5}{3}-\dfrac{7}{3}+\dfrac{8}{3}}$

= ${\dfrac{2+5-7+8}{3}}$

= ${\dfrac{8}{3}}$

Unlike Fractions

Fractions with different denominators are known as unlike fractions.

${\dfrac{2}{3}}$, ${\dfrac{7}{5}}$, and ${\dfrac{7}{9}}$ are a few unlike fractions.

Unlike Fractions

Simplifying such fractions involves factorizing the denominators before carrying out addition and subtraction.  

For example,

${\dfrac{2}{3}+\dfrac{7}{5}}$

= ${\dfrac{2\times 5+7\times 3}{3\times 5}}$

= ${\dfrac{31}{15}}$

While multiplying, we first multiply the numerators and then the denominators. 

For example,

${\dfrac{2}{3}\times \dfrac{7}{5}}$

= ${\dfrac{2\times 7}{3\times 5}}$

= ${\dfrac{14}{15}}$

In division, we multiply the dividend by the reciprocal of the divisor.

${\dfrac{2}{3}\div \dfrac{7}{5}}$

= ${\dfrac{2}{3}\times \dfrac{5}{7}}$

= ${\dfrac{2\times 5}{3\times 7}}$

= ${\dfrac{10}{21}}$

Equivalent Fractions

Equivalent fractions represent the same value after being simplified or reduced. To get equivalent fractions, we can multiply or divide the numerator and denominator of the given fraction by the same number.

For example, 

${\dfrac{2}{3}}$ and ${\dfrac{6}{9}}$ are equivalent fractions.

Equivalent Fractions

Unit Fractions

Unit fractions are the fractions whose numerators are 1.

For example,

${\dfrac{1}{3}}$ and ${\dfrac{1}{9}}$ are unit fractions.

Unit Fraction

Here, we summarize the different types of fractions.

Solved Examples

From the following fractions, identify the types of fractions as proper, improper, or mixed:
${\dfrac{1}{15}}$, ${1\dfrac{3}{8}}$, ${\dfrac{9}{3}}$, ${\dfrac{1}{7}}$, ${\dfrac{5}{5}}$, ${\dfrac{7}{3}}$

Solution:

Here,
Proper fractions: ${\dfrac{1}{15}}$, ${\dfrac{1}{7}}$
Improper fractions: ${\dfrac{9}{3}}$, ${\dfrac{5}{5}}$, ${\dfrac{7}{3}}$
Mixed fraction: ${1\dfrac{3}{8}}$

Identify the like fractions:
${\dfrac{1}{5}}$, ${1\dfrac{3}{5}}$, ${\dfrac{9}{2}}$, ${\dfrac{2}{7}}$, ${\dfrac{3}{2}}$, ${\dfrac{10}{7}}$, ${\dfrac{10}{5}}$

Solution:

Here,
${\dfrac{1}{5}}$, ${1\dfrac{3}{5}}$, and ${\dfrac{10}{5}}$ are like fractions.
${\dfrac{9}{2}}$ and ${\dfrac{3}{2}}$ are like fractions.
${\dfrac{2}{7}}$ and ${\dfrac{10}{7}}$ are like fractions.

Write two equivalent fractions of ${\dfrac{12}{15}}$

Solution:

Here, ${\dfrac{12\div 3}{15\div 3}=\dfrac{4}{5}}$
${\dfrac{12\times 2}{15\times 2}=\dfrac{24}{30}}$
Thus, ${\dfrac{4}{5}}$ and ${\dfrac{24}{30}}$ are two equivalent fractions of ${\dfrac{12}{15}}$

Last modified on July 11th, 2024