# 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.

## 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.

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

$=\dfrac{6+1}{3}$

$=\dfrac{7}{3}$

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

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

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

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

$=2+\dfrac{1}{5}=2\dfrac{1}{5}$

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).

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