When it comes to having a scrumptious pizza, we have often argued over the division of pizza so that everyone gets equally sized pieces. Dividing the whole object or material into equal parts is not just merely a fun activity but an essential concept of mathematics. Whenever we divide a portion into equal parts, it is called a Fraction. It is one of the most interesting topics of mathematics which is generally introduced around class 4th or 5th and finds its application in questions related to Maths for competitive exams. Being an inseparable topic of Maths syllabus, including scholastics and competitive exams, it becomes essential to develop a clear understanding of the concept. So, if you also want to know what is fraction and its types, then here’s a blog that will shed light on the same!
What is Fraction?
Whenever we cut a portion out of a whole and then represent it, it is called a fraction. It represents equal or sometimes unequal parts of a whole. It has 2 parts which are written as numerator and denominator. Out of the whole, the numerator represents the parts that are taken out whereas the denominator is a representation of the total number of parts that are made. The numerator is always written on top and the denominator is written at the bottom.
Example: 2/3, 5/10, 6/7, etc.
Though they represent the same concept, there are many types of fractions. Their concepts have been summarised below along with examples.
Types of Fraction
Fractions can be easily divided into various categories. Based on the ratio as well as numbers at denominator and numerator, one type can be distinguished from another. Listed below are some types along with their examples.
It is a number where the numerator is less than the denominator. For example: 6/10, 11/15, etc.
When the value of the numerator is higher than that of the denominator, it’s called an Improper Fraction. For example 10/5, 4/2, etc
It can be understood as a combination of natural numbers and fractions. It is basically an improper number attached to a natural number. For example, , etc
Numbers which have the same denominators are called Like Fractions. For example 4/7, 3/7, 5/7, etc. In comparison to the other types, the addition or subtraction in this type is easy.
Example: 4/7 + 3/7 + 5/7 = 12/7
The numbers which have different denominators are referred to as Unlike Fractions. For example 2/5, 1/6, 1/4, etc. As compared to the Like Fractions the addition or subtraction in this is a little difficult. Here, the digits in the denominator are different. So, you have to first factorise them and then add. The below-mentioned steps will help you understand the process-
- Let us assume that we have to add ½ and ⅓.
- In the primary step, we’ll find the LCM of 2 and 3 which comes out to be 6.
- Both, in numerator and denominator, we will multiply ½ by 3 and ⅓ by 2.
- Now, our new fractions are 3/6 and 2/6.
- Upon adding, we get, 3/6 + 2/6= ⅚.
Whenever two or more fractions have similar results after simplification, they show similar results. Such numbers are called Equivalent Fractions.
Example: 1/4, 4/16, etc
By now, you must have understood what is a fraction. However, just like any other concept of mathematics, these numbers also have some properties, learning which is essential to build a strong command over the topic. Have a look at the properties:
- The addition and multiplication of fractions can be done using the commutative and associative properties.
- The multiplicative inverse of ½ is 2/1, where the numbers in denominator and numerator must be non zero elements.
- The identity element of fractional multiplication is 1 and addition is 0.
- All the fractional numbers obey the distributive property of multiplication over the addition.
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