# Fractions – Definition & Types

The word “fraction” is derived from the Latin word fractus, which means the number representing part of the whole or any number of parts. In layman language, a fraction is a number that describes the size of parts of a whole unit. These sizes can be one-half, three-quarters, and a third, etc.

A fraction is normally written in two parts, where the numerator is displayed above a line or before a slash whereas, the denominator is displayed below or before the line.

The terms numerator and denominator are also used in other fractions such as complex, compound, mixed and complex fractions.

## What are Fractions?

A fraction can be defined as a number that represents a whole number that has been divided into equal parts.

For example, if you have an orange and cut it into 4 equal slices, 1 of those slices is written: 1/4.

### What are Proper Fractions?

A proper fraction is a fraction in which the numerator is less than the denominator. In other words, a proper fraction is less than 1.

Examples of proper fractions are:

1/2, 2/3, 2/7, 4/7, 5/11, 15/26, 50/97, etc.

A fraction is said to be an improper fraction when its denominator is smaller than its numerator.

### What are improper fractions?

A fraction is said to be an improper fraction when its denominator is smaller than its numerator. This fraction is generated by the addition of a whole number and one proper fraction. The fractions 11/5, 23/9, 18/5, 3/2, 9/8, etc., are the fractions where the denominators are smaller than the numerators.

For example:

(i) 1 + 4/3 = 3/3 + 4/3 = (3 + 4)/3 = 7/3

(ii) 3 + 5/7 = (3 × 7)/7 + 5/7 = (21 + 5)/7 = 26/7

Similarly, fractions such as:13/5, 27/9, 5/3, 17/2, 9/7 are called improper fractions.

### What are Mixed Fractions?

A mixed fraction is a fraction in which a whole number and a proper fraction have been combined. Examples of mixed fractions are 11/3, 5 2 /3, 61/2, etc.

#### How to convert improper fraction to mixed fraction?

To convert an improper fraction into a mixed fraction, the numerator is divided by the denominator, and the quotient written as a whole number, and the remainder as the numerator.

Example 1

Convert 17/4 as a mixed fraction.

Solution

To solve this problem, these are the steps undertaken

• Divide the numerator by the denominator.
• The quotient is 4, and the remainder is 1.
• Combine the whole number 4 with the fraction 1/4
• 4 1/4 is the mixed fraction.

Example 2

Convert 14/9 to a mixed fraction.

Solution

• Begin by dividing the numerator by the denominator
• 14/9 = 1 and 5 as the remainder.
• Take 1 as the whole number and 5 as the numerator,
• Write down the fraction as: 14/9 = 1 5/9

Note: If during division, there is no remainder, then take the quotient as a whole number.

Example 3

Convert the fraction 20/5 to a mixed fraction.

Solution

• Divide the numerator by the denominator.
• 20/5 =4
• The quotient is 4, and there is no remainder. Therefore, take 4 as the answer.
• 20/5 = 4

#### How to convert mixed fractions as a proper fraction?

A mixed fraction can be expressed as a proper fraction. This I did by multiplying the fraction’s denominator with the whole number, and the product added to the numerator.

For example, to convert a mixed fraction 2 1/3 to an improper fraction, the following steps are followed:

• Multiply the denominator by the whole number.
• For this case, 2 is the whole number and 3 is the denominator,
• 2 x 3 = 6
• Add the product to the numerator
• 6 + 1 =7
• Now the numerator changes to 7 and the denominator remains 3.
• Write the result an improper fraction as 7/3.

Take another example, suppose we want to convert 52/3 to an improper fraction.

These are the steps:

• First of all, multiply the denominator by the whole number and add this product to the numerator.
• 3 x 5 = 15
• Add the numerator to the product
• 15 + 2 = 17
• Write fraction by taking 17 as the new numerator while 5 remaining as the denominator.
• The result is 17/5

### Practice Questions

1. True or False: $\dfrac{5}{6}$ is an example of a proper fraction.

2. True or False: $0.80$ is an example of a proper fraction.

3. What is the fraction represented by the shaded portions from the figure shown below?

4. Which of the following is not a proper fraction?

5. Which of the following is not an improper fraction?

6. Which of the following shows the mixed number equivalent to $\dfrac{12}{5}$?

7. Which of the following shows the mixed number equivalent to $\dfrac{93}{7}$?

8. Which of the following shows the fraction equivalent to $4 \dfrac{4}{5}$?

9. Which of the following shows the fraction equivalent to $6 \dfrac{2}{9}$?