## Learn fractions of various types:

### 1. Proper Fractions:

Fractions in which the numerators are less than the denominators are called proper fractions.

**Examples:**

*½, 2/3, 4/7.*

NOTE: The value of proper fractions is always less than 1.

### 2. Improper Fractions:

Fractions in which the numerators are greater than the denominators are called improper fractions.

**Examples:**

*3/2, 7/5, 102/57.*

**NOTE:** The value of improper fractions is always greater than 1.

### 3. Mixed Fractions:

Fractions that contain both a whole number and a fraction are called Mixed Fractions.

**Examples:**

*2⅓, 4⅗, 9⅝ are all mixed fractions.*

In the mixed fraction:

- 2⅓, the whole number is 2, while the fraction is ⅓, and
- 4⅗, the whole number is 4, while the fractions is ⅗, and
- 9⅝, the whole number is 9, while the fraction is ⅝.

### 4. Decimal Fractions:

Fractions in which the denominators are either 10 or positive integral powers of 10 are called Decimal Fractions.

**Examples:**

*3/10, 7/100, 10/1000*

### 5. Vulgar Fractions:

Fractions in which the denominators are not 10 or powers of 10 are called Vulgar Fractions.

**Examples:**

*3/8, 4/9, 5/31, 23/59 and so on.*

### 6. Simple Fractions:

Fractions in which both the numerator and denominators are whole numbers are called Simple Fractions.

**Examples:**

*7/11, 25/39, 62/131 and so on.*

### 7. Complex Fractions.

Fractions in which either the numerator or the denominator or both are fractions are called Complex Fractions.

**Examples:**

*7/⅝, 9/⅗ and so on.*

In the complex fraction 7/⅝, the numerator is 7 and the denominator is ⅝, and in the complex fraction 9/⅗, the numerator is 9 and the denominator is ⅗.

### 8. Equivalent Fractions:

Fractions that have the same value on simplifying are called Equivalent Fractions.

**Example:**

*2/3, 4/6, 20/30.*

Fraction* 4/6 = 2/3 and 20/30 = 2/3.*

So, the three fractions *2/3, 4/6, 20/30* are same in value and the value is 2/3.

**Tip:** To find equivalent fractions of a given fraction, multiply a same value to both numerator and denominator of the given fraction.

**Example:**

A few equivalent fractions of the fraction 3/5 are:

*(3 × 4)/ (5 × 4) = 12/20,*

*(3 × 7)/ (5× 7) = 21/35*

### 9. Like Fractions:

Fractions in which the denominators are same are called Like Fractions.

**Examples:**

*3/7, 5/7, 11/7.*

### 10. Unlike Fractions:

Fractions in which the denominators are different are called Unlike Fractions.

**Examples:** *¾, 8/9, 11/15.*