Simple fractions and Compound fractions

Fractions are usually expressed as a ratio of two numbers. There are various types of fractions. In this article, we will learn about simple fractions and compound fractions.

Definition of Simple Fraction

A fraction is said to be a simple fraction if it is of the form a/b for some integers a and b (b ≠ 0). For example, 3/5, 5/3, 7/10, etc are simple fractions.

Here, the number a is called the numerator and b is called the denominator of the fraction a/b. Depending upon which are greater between the numbers a and b, there are two types of fractions:

  • Proper fraction: If a is smaller than b, then the fraction a/b is called a proper fraction. For example, 2/3 is a proper fraction.
  • Improper fraction: If a is bigger than b, then the fraction a/b is called an improper fraction. For example, 3/2 is an improper fraction.

Note that when a=b then the fraction a/b represents the number 1.


Definition of Compound Fraction

A fraction is called a compound fraction if it is a combination of a whole number and a proper fraction. compound fractions are also known as mixed fractions or mixed numbers.

Compound fraction examples: $3\dfrac{2}{5}$ is a compound fraction where the whole number 3 and the proper fraction 2/ 5 are involved. The numbers $1\dfrac{1}{2}, 7\dfrac{2}{3}$, etc are examples of mixed fractions.

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Properties of Simple and Compound Fractions

The following properties are satisfied by the simple and compound fractions.

  • An integer can be regarded as an example of a simple fraction.
  • All proper fractions are simple fractions.
  • A compound fraction is basically an improper fraction.
  • Compound fraction = whole number + proper fraction.
  • Any compound fraction can be converted into a simple fraction, which we learn below.


Convert Compound Fractions into Simple Fractions

How to convert a compound fraction to a simple fraction? The following steps have to be followed for the conversion of mixed fractions into simple fractions.

We know that a compound fraction has the form $a \dfrac{b}{c}$, where $a$ is the whole number part and b/c is the fractional part.

Step 1: At first, we multiply the whole number by the fraction’s denominator.

a × c 

Step 2: Add the above product to the fraction’s numerator.

b + a × c = b+ac

Step 3: Add the above product to the fraction’s numerator.

b + a × c = b+ac

Then $\dfrac{b+ac}{c}$ is the desired simple fraction converted from the compound given fraction. See that $a \dfrac{b}{c}$ $=a+\dfrac{b}{c}$. Thus we can conclude that a compound fraction is the sum of its whole number part and the fractional part.


Solved Problems of Simple and Compound Fractions

The following exercises on simple fractions and compound fractions will be solved here.

Question 1: Convert $2 \dfrac{1}{3}$ to a simple fraction.


$2 \dfrac{1}{3}$ $=2 + \dfrac{1}{3}$



Thus we have converted a mixed number to a simple fraction.

Question 2: Convert $\dfrac{11}{5}$ to a compound fraction.


$\dfrac{11}{5}$ $=\dfrac{10+1}{5}$



Here we convert a simple improper fraction to a compound fraction.

FAQs on Simple and Compound Fractions

Q1: What is a simple fraction?

Answer: A simple fraction is either a proper fraction or an improper fraction. Both 3/7 and 7/3 are simple fractions.

Q2: What is a compound fraction?

Answer: A compound fraction is a sum of a whole number and a proper fraction. For example, 9+1/2 is a compound fraction. It is sometimes called mixed fractions.

Q3: What type of fraction is 3/5?

Answer: As 3<5, so 3/5 is a proper fraction.

Q4: What type of fraction is 8 5/9?

Answer: See that 8 5/9 = 8+5/9. Thus 8 5/9 is an improper fraction (or compound fraction).