## 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.