**What are fractions and what are fractions composed of ?**

Fraction is defined as an element of quotient field. Fraction is composed of numerator and denominator. It can be represented as "p/q" here fraction variable 'p' denotes the value called as numerator and fraction variable 'q' denotes the value called as denominator and the denominator 'q' is not equal to zero.

Let us learn what are fractions composed of.

Thus the fractions are composed of following types,

- Simple fraction
- Proper fraction
- Improper fraction
- Complex fraction
- Mixed fraction

**Simple fraction:**

Simple fraction is a fraction, which is composed of both numerator and denominator as whole number.

**Examples:**

1/5, 2/7, 8/9

**Proper fraction:**

It is a fraction, which is composed of a numerator less than its denominator, and the value of that fraction is less than one.

**Examples:**

3/5, 1/8, 24/25

**Improper fraction:**

Improper fraction is a fraction, where the top number of fraction that the numerator is greater than or equal to its own denominator (bottom number) and the value of that fraction is greater than or equal to one.

**Examples:**

7/2, 8 /8, 45/23, 123/120

**Complex Fractions:**

If a fraction is composed of numerator and denominator as a fraction, it is called complex fraction.

The complex fraction is also called as a rational expression because it has a numerator and denominator with fraction. Otherwise, the overall fraction includes at least one fraction.

**What are mixed numbers or mixed fractions composed of:**

Mixed numbers is a fraction which is composed of one whole number part with a fraction part. It can be represented as x y/z.

**Examples:**

2 3/4, 1 5/7

**Example: 1**

**Step1:** The denominators are not same. So take LCD by cross-multiplying as follows,

5 / 5 + 7 / 2 = ((5 * 2) + (7 * 5))/ 10

= (10 + 35)/ 10

**Step2:** Add the numerators

= 45 / 10

**Step3:** Then reduce the above fraction

45/10 = 9 / 2

**Example: 2**

**Divide the complex fraction: 8/ (1/4)**

**Solution:**

= 8/ (1/4)

It indicates

= 8 / 1/4

Numerator can be written as fraction as follows,

8 as = 8/1

That is = 8/1 ÷ 1/4

From rule 2 it can be written as

= 8/1 * 4/1

Finally we get

= 32/1

**Example: 3**

**Write the simple fraction: 2 / 7 – 1 / 5**

**Step1:** The denominators are not same. So take LCD by cross-multiplying as follows.

2/7 – 1/5 = (10-7)/35

**Step2:** Next, subtract the numerator

2/7 – 1/5 = 3/35

**Step3:** the fraction is in simplified form. So no need to simplification:

= 3/35