# What is Proper Fraction?

## Proper Fraction

Fractions are one of the most significant terms used widely in Maths. Fractions simply represent the number of equal parts a whole is divided into. It is represented by a symbol “/”, such as x/y. Fraction came from the Latin word “Fractus” which means “broken”. There are numerous types of fractions such as proper fraction, improper fraction, like fraction, unlike fraction, and equivalent fraction. In this article, we will briefly discuss fractions, types of fractions, proper fraction definition, proper fraction examples, and some facts based on the proper fraction.

### What is a Fraction?

Fraction characterizes equal parts of a whole or a collection.

The Fraction of a whole- When the whole is divided into equal parts, each equal part of a whole is considered as a fraction.

Fraction even characterizes the parts of a set or a collection.

For example- There are 7 students in a classroom.

5 out of 7 are girls. So, the fraction of girls is four-fifth (4/5)

### Fraction Notation

A fraction has two parts

Numerator – The top digit of a fraction is the numerator of a fraction. It shows the number of parts we are considering as a whole.

Denominator – The bottom digit of a fraction is the denominator of a fraction. It shows the number of equal parts of a whole is divided into.

For example- ½

In the above example, 1 is considered as a numerator and 2 is considered as a denominator of a fraction

### What is a Proper Fraction?

A fraction in which the numerator (the upper value) is less than the denominator (the lower value) is known as the proper fraction. The value of a proper fraction after simplification is always less than 1.

### Proper Fraction Definition

A proper fraction is a fraction in which the numerator is always less than the denominator. For example- 2/3, 5/8 is a proper fraction.

Numerator < Denominator

### Proper Fraction Example

In all the above proper fraction examples, numerators on the top is less than the denominators at the bottom.

### Solved Example

Here are some proper fraction examples of addition and subtraction of different denominators.

1.     4/5 + 2/3

Solution: Here the denominators are different,

So we will find the LCM to make the denominators equal

LCM of 5 and 3 is 15

Accordingly,

4 x 3/ 5 x 3 = 12/15

2 x 5 / 3 x 5= 10/15

Now, we will add both numbers with similar denominators i.e.

= 12/15 + 10/15

= 22/15

2.   1/4 -1/5

Solution: Here the denominators are different

So we will find the LCM to make the denominators equal

LCM of 4 and 5 is 20

Accordingly,

1 x 5 /4 x 5 = 5/20

1 x 4 / 5 x 4 =4/20

= 5/20 -4/20

=1/ 20

### Fun Facts

• The word fraction is acquired from the Latin word ‘Fractus’ which implies  ‘broken’

• The fraction originated from the Egyptian era which is renowned as one of the oldest civilizations of the world. However, fractions are considered as numbers. They are actually used to compare whole numbers with one another.

### Quiz Time

1.  Which of the following is considered as a proper fraction?

1. 2/5

2. 8/7

3. 1/1

4. 10/9

2. Which of the following is an addition 7/12 and 3/12

1. 4/6

1. 21/12

2. 4/12

3. 5/6

3. What fraction of the numbers from 2 to 12 are prime numbers?

1. 1/11

2. 10/11

3.  5/11

4. 6/11

1. Explain the Properties of a Fraction ?

Some properties of the fraction are as follows:-

• Identical to the properties of real numbers and whole numbers, there are also some properties of the proper fraction.

• Commutative and associative properties retain for both fractional addition and multiplication

• The multiplicative inverse of x/y is y/x, where x and y should always be non- zero elements

• The identical element for fraction addition is 0 whereas the identity element for fractional multiplication is 1

• If two fractions have similar numerators then the fraction with smaller denominators will be greater. If x, y, and z are integers, and both y and z are nonzero

• If two fractions have similar denominators then the fraction with greater numerator will be greater. If x, y, and z are three integers, and z is not equal to zero.

2.   Define Fraction and Its Types.

The term Fraction represents the total number of parts to a whole. In other words, it states as the portion or section or division of any quantity. For example, a number is divided into 5 parts. Then it will be represented as x/5. Here x/5 defines 1/5th of a number x.

### Types of Fraction

Proper Fraction- Proper fractions are considered as those fractions in which the numerator is always less than the denominator. For example- 3/4 is a proper fraction.

Improper Fraction- Proper fractions are those fractions where the numerator is greater than the denominator. For example- 6/4 is a proper fraction.

Like Fractions- Like fractions are those fractions, which have similar denominators. For example- ½ 5/2 7/2, 9/2 are like fractions.

Unlike Fractions – Like fractions are those fractions, which have different denominators. For example- 1/5, 5/7 7/3, 9/4 are like fractions

Mixed Fraction- It is a combination of both natural numbers and a fraction is known as a mixed fraction. Mixed Fractions are generally improper fractions.