Hello Learners, Good Day.

Today we are going to learn about Fractions. We are starting from basics like what is Fraction? How many types of fractions are there with many examples and practice questions? Hope it will help you to understand the fractions in a better manner.

Let’s Dive in…

**Complete Tutorials on Fraction**

Part 1: Addition of Fraction

Part 2: Subtraction of Fractions

Part 3: Multiplication of Fractions

## What is Fraction?

### Definition 1

Fraction can be defined as a rational number in the form of a/b where b cannot be zero. In a fraction a/b a is known as numerator and b as denominator.

For example : – 3/6 is a fraction, where 3 (the upper part) is numerator and 6

(the lower part) is the denominator.

### Definition 2

In other words, we can say that Fractions show a part of the whole.

Suppose you want to divide a number into four parts, then it can be written as x/4. So the fraction x/4, defines 3/4th of the number x. Hence 3/4 is the fraction, which means three in four equal parts. The fraction can be read off as three-fourth or 3/4.

## Parts Of Fractions

The fractions consist of two parts: –

**Numerator**: Numerator can be defined as the upper part of the fraction. In simple words, it indicates how many sections of the fraction are selected.

**Denominator**: Denominator can be defined as the lower or bottom part of the fraction. It represents the total parts in which the fraction is divided.

For Example: If 2/5 is a fraction, then 2 is the numerator and 5 is the denominator.

## Types Of Fractions

Based on the System of Numerator and Denominator these are the different types of **Fractions in Mathematics**. They are:

- Proper fractions
- Improper fractions
- Mixed fractions
- Like fractions
- Unlike fractions
- Equivalent fractions
- Unit Fraction

### 1. Proper Fractions

Proper fractions are the fractions where the numerator is less than the denominator.

For example: – 4/9 is a proper fraction as the numerator is less than the denominator (numerator < denominator).

### 2. Improper Fractions

Improper fractions are fractions where the numerator is greater than the denominator.

For example: – 11/9 is an improper fraction as the numerator is greater than the denominator (numerator >denominator).

### 3. Mixed Fractions

As the name itself suggests mixed, mixed fractions are a mixture of a proper fraction and an integer or whole number.

For example, 31/3, where 3 is the whole number or integer and 1/3 is the proper fraction.

We will later study how we can convert it into simple form (mixed to simple fractions & simple to mixed fractions).

Must Read : Remember Multiplication Tables of Any Number Using Mental Mathematics

### 4. Like Fractions

Like fractions can be defined as fractions having the same denominator.

For example: – 11/5, ⅗ or ⅞, 13/8 etc.

### 5. Unlike Fractions

Unlike fractions can be defined as fractions having different denominators.

For example: – ½ and ⅕ or 3/7 and 4/9.

### 6. Equivalent Fractions

Equivalent fractions are the fractions that give an equal value after simplification. In simple words, we can say that two fractions are equivalent to each other when they give equal values to each other.

For example: – 6/10 and 3/5 are equivalent fractions.

We can get equivalent fractions by: –

- By Multiplying both the numerator and the denominator of the fraction by the same number.
- By Dividing both the numerator and the denominator of the fraction by the same number.

Also Read : How to find HCF in 10 seconds

### 7. Unit Fractions

What is Unit Fraction?

A fraction is a unit fraction when the numerator is equal to 1. Let’s understand that.

- One half of the whole number= ½
- One-third of the whole number= ⅓
- One-fourth of the whole number= ¼
- One-fifth of the whole number= ⅕

### How Can We Simplify Fractions?

We can simplify the fractions by the following steps: –

- Firstly, write down the factors of both the numerator and denominator.
- Now, find the largest factor that is common for both the numerator and denominator.
- Divide both the numerator and the denominator by the GCF(greatest common factor from the second step)to get the reduced fraction.

Must Read: Sum of cubes of n natural numbers

### Understand with Examples:

Now, let us understand the concept with an example to find the simplest fraction: –

**Example 1: 12/48**

**Step 1** = Factors of 12 are 1, 2, 4, 6, and 12.

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

**Step 2 =** The greatest common factor for 12 and 48 will be 12.

GCF (12, 48) = 12.

**Step 3** = Now, divide both the numerator and denominator by 12, we will get

12/48 = (12/12) / (48/12) = 1/4.

**Step 4 =** The simplest form of the fraction 12/48 is 1/4.

**Example 2: ****3/36**

**Step 1 =** Factors of 3 are 1, 3.

Factors of 36 are 1, 2, 3, 4, 6,12, 36..

**Step 2 =** The greatest common factor for 3 and 36 will be 3 itself.

GCF (3, 36) = 3.

**Step 3 =** Now, divide both the numerator and denominator by 3, we will get

3/36 = (3/3) / (36/3) = 1/12.

**Step 4 =** The simplest form of the fraction 3/36 is 1/12.

**Example 3: 15/90**

**Step 1** = Factors of 15 are 1, 3, 5, 15.

Factors of 90 are 1,2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

**Step 2 =** The greatest common factor for 15 and 90 will be 15.

GCF (15, 90) = 15.

**Step 3 =** Now, divide both the numerator and denominator by 15, we will get

15/90 = (15/15) / (90/16) = 1/6.

Step 4 = The simplest form of the fraction 15/90 is 1/6.

**Example 4: 14/80**

**Step 1 =** Factors of 14 are 1, 2, 7, and 14.

Factors of 80 are 1, 2, 4, 5, 8,10, 16, 20, 40 and 80.

**Step 2 =** The greatest common factor for 14 and 80 will be 2.

GCF (14, 80) = 2.

**Step 3 =** Now, divide both the numerator and denominator by 2, we will get

14/80 = (14/2) / (80/2) = 7/40.

**Step 4 =** The simplest form of the fraction 14/80 is 7/40.

### Practice Questions:

- 12/60
- 42/90
- 15/125
- 8/112
- 112/780

## Quizzes:

**Question 1: What is the equivalent of 6/12?**

**Options**

- ⅓
- ⅖
- ½ ( c
**orrect answer )** - ¼

**Question 2 :** Which of the Following is an Improper Fraction?

**Options**

- 2/4
- 11/5
- 3/6
**( correct answer )** - 4/9

**Question 3 :** which of the following is like Fractions?

**Options**

- ⅔ and 6/5
- ⅗ and ⅘ Correct answer
- 2/7 and 4/9
- 6/5 and ⅞

**Question 4** : Which of the following is the simplest form of 3/12?

Options

- 2/4
- ⅕
- ⅓
- ¼
**( correct answer )**