A fraction is a portion of a larger amount. It is any portion of a whole sum that has been divided into equal parts. A fraction has two parts: a numerator and a denominator. A fraction is expressed as 𝑎𝑏,𝑎ab, a, and 𝑏b which are all whole numbers and 𝑏b cannot be 0. The various fractional operations include addition, subtraction, multiplication, and division.

Operating whole numbers, natural numbers, and integers are different from operating fractions. Let’s examine the procedures for carrying out the various fractional math operations. For more information, keep reading!

## Definition of Fractions

A fraction is a mathematical value that illustrates the components of a whole.

In general, the whole can be any particular thing or value, and the fraction might be a piece of any quantity out of the total.

The fundamentals of fractions describe the top and bottom numbers in a fraction. The bottom number indicates the overall number of pieces, while the top number indicates the number of pieces chosen of a whole.

Fractions are essential to our daily lives. You will face fractions frequently in daily life. Whether we like to or not, we have to share that delicious pizza with our loved ones. Four slices for three persons. It will be more enjoyable and thrilling if you can easily learn and visualize fractions. For instance, if you divide an apple into two halves, each piece will represent a fraction (equivalent to 1/2).

## Classification of Fractions

Fractions are classified into many categories based on the characteristics of the numerator and denominator. As follows:

• Proper fractions and Improper fractions
• Mixed fractions
• Like fractions and Unlike fractions
• Equivalent fractions

### 1. Proper Fractions and Improper Fractions

When the numerator is less than the denominator, then it is called a proper fraction. For ex, 8/9 will be a correct fraction because “numerator < denominator,”

When the numerator is greater than the denominator, it is called the improper fraction. For instance, 9/8 is an improper fraction since “numerator > denominator.”

### 2. Mixed Fractions

A fraction that combines both whole and part fractions is referred to as a mixed fraction. A mixed fraction always has a value higher than one.

For example, 11/2, 23/4, 55/6 are the mixed fractions.

### 3. Like Fractions and Unlike Fractions

As the names suggest, like fractions are fractions that are similar or identical.

Take the fractions 1/2 and 2/4 as an example; they are similar because they can both be simplified mathematically to produce the same fraction.

Fractions that are not similar or unidentical are called unlike fractions.

For instance, fractions of 1/2 and 1/3 are different.

### 4. Equivalent Fractions

When both of the two fractions are the same after being simplified, the two fractions are said to be equivalent.

For example, 2/3 and 4/6 are equivalent fractions.

Since, 4/6 = (2×2)/(2×3) = 2/3

## Rules for Fraction Simplification

There are a few rules we need to be aware of before solving issues with fractions.

Rule #1: The denominators should be equal before doing any fractional addition or subtraction. As a result, using a common denominator makes adding and subtracting fractions possible.

Rule #2: When we multiply two fractions, the numerators and the denominators are multiplied as well. Simplify the fraction later.

Rule #3: When dividing two fractions, we must first determine the reciprocal of one fraction before multiplying it by the other to obtain the result.

When fractions share a common denominator, adding them is simple.

As an example, 2/3 + 8/3 = (2+8)/3 = 10/3

As a result, all we have to do is sum the numerators.

### Adding Fractions with Different Denominators

If the two fractions’ denominators differ, we must combine them by first determining their LCM before making their common denominator applicable to both fractions.

Example: 3/4 + 4/5

The two denominators are 4 and 5, hence, LCM of 4 and 5 = 20.

Therefore, by multiplying 3/4 by 5/5 and 4/5 by 4/4, we get;

15/20 + 16/20

= (15+16)/20

= 31/20

### Subtracting Fractions

The rules for addition and subtraction equally apply when subtracting two or more fractions. To subtract two fractions, the denominators need to be similar.

Example: 7/2 – 5/2 = (7-5)/2 = 2/2 = 1

### Subtracting with Different Denominators

If the two fractions have different denominators, we must combine them by first determining the LCM of the denominators and then making it the same for both fractions.

Example: 3/4 – 4/5

The two denominators are 4 and 5, hence, LCM of 4 and 5 = 20.

Therefore, by multiplying 3/4 by 5/5 and 4/5 by 4/4, we get;

15/20 – 16/20

= (15-16)/20

= -1/20

### Multiplication of Fractions

Rule number 2 states that when two fractions are multiplied, the numerators at the top and the denominators at the bottom are multiplied simultaneously.

The result of multiplying a/b and c/d if a/b and c/d are two different fractions is:(a/b) x (c/d) = (axc)/(bxd) = (ac/bd)

Example: Multiply 2/3 and 3/7.

(2/3) x (3/7) = (2×3)/(3×7) = 2/7

### Division of Fractions

To divide any two fractions, we must multiply the first fraction by the reciprocal of the second fraction, as stated in rule 3, from the previous section.

The division of a/b by c/d can be written as follows if a/b and c/d are two separate fractions: