Types of Fractions: Definition, Types, Examples

Types of Fractions: It’s a fragment of a larger quantity, where the larger quantity can be any number, a specific value, or an item. Proper/Improper Fractions, Mixed Fractions, Equivalent Fractions, and Like/Unlike fractions are the six types of fractions in mathematics. The numerator and denominator are the two parts of a Fraction.
Every quantity we encounter daily cannot be an exact whole number. As a result, we’ll have to deal with fractions, portions of a whole, and parts of a whole. Fractions are the terms used to describe the parts of a whole object. When a pizza is divided into four slices, each piece is 1/4 of the whole. Read the complete article to grasp better the types of fractions, including proper fractions examples, equivalent fractions examples, and like fractions examples.

Definition of Fraction

The term ‘fraction’ represents a numerical quantity part of a whole object. We can understand fractions with an example. Suppose we have a large cake and we cut the cake into 8 equal slices. Then each portion of the slice is only 1/8th of the total quantity of cake. Here, 1/8 is a fraction.

The top part of the fraction is called the numerator, and the bottom part is the denominator. 1 is the numerator in this example, and 8 is the denominator. We do not always deal with whole objects in our day-to-day life. Sometimes, we have to deal with parts or portions of whole objects. To quantify them, we need fractions.

Parts of a Fraction

Check out the image below:

1. 1. Numerator: The top half of a fraction that represents the number of parts you have. In the above example, 5 is the numerator.

1. 1. Denominator: The bottom half of a fraction that represents the number into which the whole object is divided. In the above example, 8 is the denominator.

As shown in the image above, the whole fraction is read as ‘5 by 8’. Likewise, ¼ is read as ‘1 by 4’, and ¾ is read as ‘3 by 4’.

Example of Fraction

Now that we know what fractions are and the different parts of a fraction let’s see how many types of fractions are there. Based on the numerators and denominators, fractions are classified into the following types:

1. Proper Fractions

Proper Fraction Definition: When Numerator<Denominator, i.e. when the numerator of a fraction is less than the denominator, the fraction is called a proper fraction. Have a look at the proper fraction example below.

2. Improper Fractions

Improper Fraction Definition: When Numerator > Denominator, i.e. when the numerator is greater than the denominator, the fraction is called an improper fraction.

Note that you can represent any natural number as an improper fraction as the denominator is always 1. Also, all improper fractions are either equal to or greater than 1.

3. Mixed Fractions

Mixed Fraction Definition: A fraction comprising a natural number and a fraction is called a mixed fraction.

You can convert a mixed fraction into an improper fraction and vice versa. A mixed fraction is always greater than 1.

4. Like Fractions

Like Fraction Definition: Fractions that have the same denominators are like fractions. For example, the fractions 2/7, 3/7, 5/7, and 6/7 all have the same denominator – 7. Hence, these are like fractions.

Simplification of like fractions is easy. For example, if you want to add the above four fractions, all you have to do is add the numerators. The denominator will remain the same. Have a look at the like fraction example below.

So, (2/7) + (3/7) + (5/7) + (6/7) = (2 + 3 + 5 + 6)/7 = 16/7.

5. Unlike Fractions

Unlike Fraction Definition: Fractions that have different denominators are unlike fractions. For example, the fractions 2/3 and 1/4 have different denominators. So, they are unlike fractions.

Simplifications involving unlike fractions are not as straightforward as like fractions.

Addition Of Unlike Fractions

For example, to add the above two unlike fractions, first, we have to convert them to like fractions. The steps involved are:

• Calculate the LCM of the two denominators 3 and 4.
• LCM of 3 & 4 = 12. This LCM will be the denominator of both the fractions.
• Calculate the equivalent value of the first fraction (2/3). To do this, divide the LCM calculated in the previous step (12) by the denominator of the first fraction (3). So, 12 ÷ 3 = 4. Now, multiply 4 by the numerator (2), which gives 8. Therefore, the first fraction becomes 8/12.
• Likewise, calculate the equivalent value of the second fraction (1/4). To do this, divide the LCM calculated in the first step (12) by the second fraction’s denominator (4). So, 12 ÷ 4 = 3. Now, multiply 3 by the numerator (1), which gives 3. Therefore, the second fraction becomes 3/12. Now, both the fractions have the same numerator, i.e. 12.
• Now, add the two like fractions in a similar manner as shown in the previous section. So, (8/12) + (3/12) = (8 + 3)/12 = 11/12. So, (2/3) + (1/4) = 11/12.

6. Equivalent Fractions

Equivalent Fraction Definition: Fractions that give the same value are called equivalent fractions upon simplification. Have a look at the Equivalent fraction example -1/2 and 50/100 are equal to 0.5. Hence, these are equivalent fractions.

7. Unit Fractions

A fraction whose numerator is one and the denominator is a positive integer is called a unit fraction. Examples of unit fractions are 1/2. 1.5, 2/8, etc.

FAQs on Types of Fractions