# Types of Fractions – Definition with Examples

## Definition of Fractions

Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects. Fraction is a component or sector of a given quantity taken from the whole, which might be a number, a specified value, or an item.

A fraction represents a part of the whole or group of objects.In a fraction, numerator (top number) and denominator (bottom number) are separated by a horizontal bar known as the fractional bar. The denominator represents the number of equal parts the whole is divided into or total number of objects in a group. The numerator represents the number of parts of the whole or the number of objects from the group is taken.

Let us better understand fractions with the help of an example. A chocolate bar is divided into four equal parts. Each part of the whole bar represents $\frac{1}{4}$ , which depicts 1 out of 4 equal parts. The fraction ¼ is read as ‘1 by 4’.

## Types of Fractions

Fractions are differentiated on the basis of the numerators and the denominators. Fractions are classified into the following types:

1. Unit Fractions: Fractions with numerator 1 are called unit fractions.
1. Proper Fractions: Fractions in which the numerator is less than the denominator are called proper fractions. A proper fraction is less than 1
1. Improper Fractions: Fractions in which the numerator is more than or equal to the denominator are called improper fractions. An improper fraction is greater than 1.
1. Mixed Fractions: Mixed fractions consist of a whole number and a proper fraction. Since mixed fractions are combinations of whole numbers and a fraction, mixed fractions are always greater than 1.
1. Like Fractions:

Fractions with the same denominators are called like fractions.

1. Unlike Fractions

Fractions with different denominators are called unlike fractions.

1. Equivalent fractions: Fractions that represent the same value after being simplified are called equivalent fractions. To get equivalent fractions we can multiply or divide both the numerator and the denominator of the given fraction by the same number.

## Solved Examples

1. John coaches the baseball league team. There are 10 players on the team. Four of them bat left-handed. What fraction of the players are right-handed?

Solution:

Number of right handed players = 10 − 4 = 6

6 out of the 10 players are right-handed, so six-tenths or $\frac{6}{10}$ of the players are right-handed.

1. State true or false.

$\frac{4}{9}$ is an improper fraction

Solution:

False. The fraction $\frac{4}{9}$ has numerator 4 and denominator 9. Since the numerator is less than the denominator, $\frac{4}{9}$ is a proper fraction. A fraction with numerator more than or equal to the denominator is an improper fraction.

1. Find the value for x.

$\frac{7}{9}$ = $\frac{x}{36}$

Solution:

$\frac{7}{9}$ and  $\frac{x}{36}$ are equivalent fractions.

So, $\frac{x}{36}$ = $\frac{7}{9}$ = $\frac{7 ✕ 4}{9 ✕ 4}$ = $\frac{28}{36}$

Therefore, x must be 28.

1. What is the simplest form of $\frac{30}{45}$?

Solution:

Greatest common factor of 30 and 45 is 15. Divide both the numerator and the denominator by 15 we get

$\frac{30}{45}$ = $\frac{30 \div 15}{45 \div15}$ = $\frac{2}{3}$

Since 2 and 3 do not have a common factor, $\frac{2}{3}$ is in the simplest form.

## Practice Problems

1

### Which of the following is a fraction equivalent to $\frac{2}{5}$?

$\frac{2}{10}$
$\frac{6}{10}$
$\frac{4}{10}$
$\frac{5}{10}$
CorrectIncorrect
Correct answer is: $\frac{4}{10}$
$\frac{2}{5} = \frac{2 \times2}{5 \times2} = \frac{4}{10}$
2

### Which of the following has 11 as numerator?

$\frac{11}{17}$
11$\frac{1}{7}$
$\frac{14}{11}$
$\frac{1}{11}$
CorrectIncorrect
Correct answer is: $\frac{11}{17}$
$\frac{11}{17}$ has numerator 11 and denominator 17
3

### Fill in the blank. $\frac{1}{4}$, $\frac{2}{8}$, $\frac{3}{12}$, $\frac{4}{16}$ are _______

unit fraction
like fraction
improper fraction
equivalent fraction
CorrectIncorrect
$\frac{1}{4}$ = $\frac{2}{8}$ = $\frac{3}{12}$ = $\frac{4}{16}$
4

### Which of the following is unit fraction?

1$\frac{2}{5}$
$\frac{9}{1}$
$\frac{1}{8}$
$\frac{4}{2}$
CorrectIncorrect
Correct answer is: $\frac{1}{8}$
The numerator of unit fraction is 1.