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.
Types of fractions :
(i) Proper fraction : A fraction whose numerator is less than its denominator is called a proper fraction. Each proper fraction is less than 1. e.g., 1 3 7 8 5 11 , , etc.
(ii) Improper fraction : A fraction whose numerator is greater than or equal to its denominator is called an improper fraction e.g., 5 3 , , 11 7 9 9 etc.
i.e., Improper fraction =
(Whole Number × Denominator) + Numerator Denominator
(iii) Mixed fraction : A combination of a whole number and a proper fraction is called a mixed fraction.
e.g., 3 4 5 , 2 1 3 i.e., Mixed fraction = Quotient Remainder Divisor
(iv) Equivalent fraction : Two or more fractions representing same part of a whole are called equivalent fraction.
e.g., 3 4 3 2 4 2 6 8 Note : To get a fraction equivalent to a given fraction we multiply or divide numerator and denominator of given fraction by same non-zero number.
• 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 .
(v) Like fractions : Fractions having same denominator are called like fraction.
e.g., 1 15 2 15 3 15 , , etc.
(vi) Unlike fractions : Fractions having different denominators are called unlike fractions.
e.g., 1 2 3 4 5 7 , , etc.
• Addition of fractions :
(i) For like fractions : Sum of like fractions = Sum of their numerator Common denominator
(ii) For unlike fractions : Change given fractions into equivalent like fractions and then add.
• Subtraction of fractions :
(i) For like fractions : Difference of like fractions = Difference of their numerators Common denominator
(ii) For unlike fractions : Change given fraction into equivalent like fractions and then subtract.
A mixed fraction = A whole number + A fraction General method : Let a b and c b be two given fractions :
1. Cross multiply as shown :
a b c b and find cross products ad and bc.
2. (i) If ad > bc, then a> b c< d
(ii) If ad < bc, then a< b c> d
(iii) If ad = bc, then a =b c= d
Chapter Notes and Summary