# Fraction

#### Those Numbers which can be expressed in form of p/q where q≠0 are know as Fractions.

eg. 3/5, 5/7 etc

 Proper Fraction If in any fraction numerator of the fraction  is less than the denominator of the fraction, then the fraction is known as proper fraction. eg. 3/7 is a proper fraction Improper Fraction If in any fraction numerator of the fraction is greater than the denominator of the fraction, then the fraction is known as improper fraction. eg. 7/3 is improper fraction Mixed Fraction Those fraction which consists a whole number and proper fraction are known as mixed fractions. eg. 31/4 Decimal Fraction Those fractions whose denominators are 10 or its higher power are known as decimals. eg. 5/10=0.5 Like Fraction Fractions having the same denominators are called like fractions. eg. 2/7, 3/7,5/7 are like fractions Unlike Fraction Fractions having different denominators are called unlike fractions. eg. 2/5, 3/7 etc. Compound Fraction A fraction of fraction is called compound fraction. eg. 1/5 of 3/7 is a compound fraction. Complex Fraction A complex fraction is that fraction in which the numerator or denominator or both are fractions.  eg. (1/2+1/3)/(2/5+3/7)
Any fraction is said to be in its lowest form, if HCF of numerator & denominator is 1.
If numerator & denominator of a fraction are divided or multiplied by same number, then value of fraction remain unchanged.

### How to Compare Fractions:

To compare the fractions there are two ways:
1. Convert the fractions into equivalent decimals and compare them.
##### Example:
2. To compare the fractions, denominator of the two fractions should be same.  If the denominator is not same convert them into equivalent fractions of the same denominator by taking LCM of the denominators of the given fractions.

## Operations on Fractions

#### Case 1: Same Denominators

If denominators are same, Add the top numbers (the numerators), put the answer over the denominator.

#### Case 2: Different Denominators

If the denominator is not same convert them into equivalent fractions of the same denominator by taking LCM of the denominators of the given fractions. Add the top numbers (the numerators), put the answer over the denominator.

### 2. Subtraction of Fractions

#### Case 1: Same Denominators

If denominators are same, Add the top numbers (the numerators), put the answer over the denominator.

#### Case 2: Different Denominators

If the denominator is not same convert them into equivalent fractions of the same denominator by taking LCM of the denominators of the given fractions. Subtact the top numbers (the numerators), put the answer over the denominator.

### 3. Multiplication of Fractions

Simply multiply the top numbers and multiply the bottom numbers.

### 4. Division of Fractions

When you divide by a fraction, the first thing you do is "flip-n-multiply". That is, you take the second fraction, flip it upside-down ("find the reciprocal"), and multiply the first fraction by this flipped fraction.

## Questions Asked from this Chapter:

### Question Type 1: Based on Smallest and Largest Fraction

Example:
The least among the fractions 15/16, 19/20, 24/25, 34/35 is:
a) 34/35
b) 15/16
c) 19/20
d) 24/25
Solution:

### Example:

If one-third of one-fourth of a number is 15. then three-tenth of the number is:
a) 35
b) 36
c) 45
d) 54
Solution:

### Question Type 3: Based on Finding the Ascending & Descending Order of Numbers

Example:
Arrange the following fraction in descending order 2/3, 5/6, 11/15 and 7/8
Solution: