CLASS 7TH | UNIT 1: NUMBER SYSTEM | FRACTIONS (INCLUDING PROBLEMS) | REVISION NOTES

Introduction: Fractions

The word fraction derives from the Latin word “Fractus” meaning broken. It represents a part of a whole, consisting of a number of equal parts out of a whole.
E.g : slices of a pizza.

Representation of Fractions

A fraction is represented by 2 numbers on top of each other, separated by a line. The number on top is the numerator and the number below is the denominator. Example :34  which basically means 3 parts out of 4 equal divisions.

Fractions on the Number Line

In order to represent a fraction on a number line, we divide the line segment between two whole numbers into n equal parts, where n is the denominator.
Example: To represent 1/5 or 3/5, we divide the line between 0 and 1 in 5 equal parts. Then the numerator gives the number of divisions to mark.

Multiplication of Fractions

Multiplication of Fractions

Multiplication of a fraction by a whole number :
Example 1: 7×(1/3) = 7/3
Example 2 : 5×(7/45) = 35/45, Dividing numerator and denominator by 5, we get 7/9

Multiplication of a fraction by a fraction is basically product of numerators/product of denominators

Example 1: (3/5) × (12/13) = 36/65
Example 2 : Multiplication of mixed fractions

First convert mixed fractions to improper fractions and then multiply
143×87

Fraction as an Operator ‘Of’

The ‘of’ operator basically implies multiplication.

Example: 1/6 of 18 = (1/6)×18 = 18/6 = 3
or, 1/2 of 11 = (1/2) × 11 = 11/2 

Division of Fractions

Reciprocal of a Fraction

Reciprocal of any number n is written as1n
Reciprocal of a fraction is obtained by interchanging the numerator and denominator.
Example: Reciprocal of 2/5 is 5/2
Although zero divided by any number means zero itself, we cannot find reciprocals for them, as a number divided by 0 is undefined.
Example : Reciprocal of 0/7 ≠ 7/0

Division of Fractions

Division of a whole number by a fraction : we multiply the whole number with the reciprocal of the fraction.
Example: 63÷(7/5) = 63×(5/7) = 9×5 = 45

Division of a fraction by a whole number: we multiply the fraction with the reciprocal of the whole number.
Example: (8/11)÷4 = (8/11)×(1/4) = 2/11

Division of a fraction by another fraction : We multiply the dividend with the reciprocal of the divisor.
Example: (2/7) ÷ (5/21) = (2/7) × (21/5) = 6/5

Types of Fractions

Types of Fractions

Proper fractions represent a part of a whole. The numerator is smaller than the denominator.
Example: 1/4, 7/9, 50/51. Proper fractions are greater than 0 and less than 1

Improper fractions have a numerator that is greater than or equal to the denominator.
Example: 45/6, 6/5. Improper fractions are greater than 1 or equal to 1.

Mixed fractions are a combination of a whole number and a proper fraction.
Example: 43/5 can be written as .

Conversion of fractions : An improper fraction can be represented as mixed fraction and  a mixed fraction can represented as improper.
In the above case, if you multiply the denominator 5 with the whole number 8 add the numerator 3 to it, you get back 435

Like fractions : Fractions with the same denominator are called like fractions.
Example: 5/7, 3/7. Here we can compare them as (5/7) > (3/7)

Unlike fractions : Fractions with different denominators are called unlike fractions.
Example: 5/3, 9/2. To compare them, we find the L.C.M of the denominator.
Here the L.C.M is 6 So, (5/3)×(2/2) , (9/2)×(3/3)
⇒ 10/6, 27/6
⇒ 27/6 > 10/7