A Complete Guide to Fractions & Their Types!

Have you ever wondered why one slice of pizza from a total of 6 slices is called 1/6 and why half a lemon is called ½? All these questions come to a halt when you study the concept of fractions during your school time. It is one of the most underrated topics in mathematics and yet easy to understand and implement.

In the following paragraphs, we will discuss all the technicalities associated with fractions; like their types, meaning, examples, and simplifying fractions. All this will help you get a clearer idea of fractions.

What does a fraction mean?

• The word fraction simply means how many parts of a whole we have. You can recognize a fraction by the slash (/) between the two numbers. A fraction has a top number, the numerator, along with a bottom number, the denominator.
• For example 2 – Numerator

7   – Denominator

Types of fractions:

1. Proper fractions: Any fraction that has a small numerator & a large denominator is called a proper fraction. For example- ½, 4/9, 3/5, etc
2. Improper fractions: All the fractions which have a large numerator and smaller denominator are called improper fractions. For example- 10/2, 5/1, 15/6, etc.
3. Mixed fractions: Such fractions are made up of a combination of an integer & a proper fraction. For example- ₃³which is solved by multiplying the

2 the denominator by the integer and then adding their answer into the numerator. So, in this case, it will be 2×3= 6, 6+3=9. The answer will be 9/2.

4. Like fractions: All the fractions which are similar after simplification are called like fractions, as their result is always the same. For example- ½ & 2/4.
5. Unlike fractions: Every fraction which is not similar after simplification is called an, unlike fraction. For example- 2/3 and 5/8.
6. Equivalent fractions: Those fractions which have the same answer after simplification are called equal fractions. For example- 2/3 & 4/6. When we solve 4/6, it comes out to be 2/3 as 2×2=4&2×3=6

How to convert an improper fraction into a mixed fraction?

A fraction formed from an improper fraction can also be decomposed and expressed as a mixed number. For this, simply divide the numerator by the denominator. The result becomes the whole number, while the remainder becomes the numerator of the new fraction.

If there is no remainder, then there is no fraction, simply a whole number is the result. This is because the denominator of the new fraction is the same as the denominator of the original fraction.

For example- 7/3 will become ₂¹ with 1 being the remainder and 2 is left.

3

How to convert mixed fractions into improper fractions?

The whole number can be divided by the denominator, then the denominator is added to the numerator, which becomes the numerator of the improper fraction. The original denominator becomes the purported denominator of the improper fraction.

For example, 42/6, can be converted to a mixed number by adding 4×6 and 24 + 2. So,4 2/6 becomes 26/6.

Properties of fractions:

• Associative property: Addition- a+(b+c)=(a+b)+c, multiplication- a×(b×c)= (a×b)×c
• Commutative property: Addition- a+b=b+a, Multiplication- a×b=b×c
• Identity: Addition- a+0=a, Multiplication- a×1=a
• Inverse: Addition- a+(-a)=0, Multiplication- a×(1/a)=1
• Distributive property: a×(b+c)=(a×b) + (a×c)

How can fractions be taught by giving real-life examples?

• Review the calendar and ask students how each day represents a fraction of the total days in that month. A few fractions related to the month can be explained just by looking at the calendar (2/30 represents 2 of 30 of the 30 days in that month) and used to answer fraction questions.
• Tell the students that a foot-long ruler has 10 equal sections, or inches. Then, have them use a ruler to measure items in the classroom. Make sure they round the measurements to the nearest inch. Then show them how to add the inches together.

Fractions can also be converted into decimal numbers through very simple steps of division, for understanding it more clearly, take help from Cuemath experts who will assist you in better understanding the concept.