**Chapter Notes and Summary**

• **Fraction : **A fraction is a number representing a part of a whole. whole may be a single object or a group of** **objects. It is defined as Fraction** **Numerator** **Denominator** **=** **N** **D** **,** **where D ≠ 0.•

**Fractions on Number Line :**Every fraction has a point associated with it on number line. For this, we will

**need to divide gap of 0 to 1 into as many equal parts as in denominator of that fraction.**

**In order to represent 3/5 on a number line, we divide length between 0 and 1 into 5 equal parts and show three**

**parts as 3/5.**

**The point A represents number 3/5.**

**A fraction whose numerator is less than its denominator is called a proper fraction. Each**

Types of fractions :

(i) Proper fraction :

Types of fractions :

(i) Proper fraction :

**proper fraction is less than 1. e.g.,**

**1**

**3**

**7**

**8**

**5**

**11**

**, , etc.**

**A fraction whose numerator is greater than or equal to its denominator is called an**

(ii) Improper fraction :

(ii) Improper fraction :

**improper fraction**

**e.g.,**

**5**

**3**

**, ,**

**11**

**7**

**9**

**9**

**etc.**

**i.e., Improper fraction =**

**(Whole Number × Denominator) + Numerator**

**Denominator**

**A combination of a whole number and a proper fraction is called a mixed fraction.**

(iii) Mixed fraction :

(iii) Mixed fraction :

**e.g.,**

**3**

**4**

**5**

**, 2**

**1**

**3**

**i.e., Mixed fraction = Quotient**

**Remainder**

**Divisor**

**Two or more fractions representing same part of a whole are called equivalent**

(iv) Equivalent fraction :

(iv) Equivalent fraction :

**fraction.**

**To get a fraction equivalent to a given fraction we multiply or divide numerator and denominator of given fraction by same non-zero number.**

e.g., 3 4 3 2 4 2 6 8 Note :

e.g., 3 4 3 2 4 2 6 8 Note :

**•**

**Simplest form of a fraction :**A fraction is said to be in simplest form if HCF of its numerator and

**denominator is 1. e.g., consider**

**36**

**24**

**.**

**Fractions having same denominator are called like fraction.**

(v) Like fractions :

(v) Like fractions :

**e.g.,**

**1**

**15**

**2**

**15**

**3**

**15**

**, ,**

**etc.**

**Fractions having different denominators are called unlike fractions.**

(vi) Unlike fractions :

(vi) Unlike fractions :

**e.g.,**

**1**

**2**

**3**

**4**

**5**

**7**

**, ,**

**etc.**

**•**

**Addition of fractions :**

(i) For like fractions :Sum of like fractions =

(i) For like fractions :

**Sum of their numerator**

**Common denominator**

**Change given fractions into equivalent like fractions and then add.**

(ii) For unlike fractions :

(ii) For unlike fractions :

**•**

**Subtraction of fractions :**

(i) For like fractions :Difference of like fractions =

(i) For like fractions :

**Difference of their numerators**

**Common denominator**

**Change given fraction into equivalent like fractions and then subtract.**

(ii) For unlike fractions :

(ii) For unlike fractions :

**A whole number + A fraction General method : Let a b and c b be two given fractions :**

A mixed fraction =

A mixed fraction =

**1. Cross multiply as shown :**

a

**b**

**c**

**b**

**and find cross products ad and bc.**

**(i) If ad > bc, then**

2.

2.

**a>**

**b**

**c<**

**d**

**(ii) If ad < bc, then**

**a<**

**b**

**c>**

**d**

(iii) If ad = bc, then

**a**

**=**b

**c=**

**d**