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Multiplication of Fraction - Fraction as an Operator 'Of'

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Fraction as an operator 'of':

Look at these similar squares

Each shaded portion represents `1/2` of 1.

So, the three shaded portions represent `1/2` of 3.

Combine the 3 shaded parts.

It represents `1 1/2 "i.e.," 3/2`.

So, `1/2  "of"  3  "is"  3/2`. 

Also, `1/2 xx 3 = 3/2.`

Thus, `1/2 "of"  3 = 1/2 × 3 = 3/2`.

So we see that 'of' represents multiplication.

Example

What is `1/2` of 10?

`1/2` of 10

= `1/2 xx 10`

= `(1 xx 10)/2`

= `10/2`

= 5.

Example

What is `2/5` of 20?

`2/5` of 20

= `2/5 xx 20`

= `(2 xx 20)/5`

= `40/5`

= 8.

Example

What is `2/3` of 60.

`2/3` of 60

= `2/3 xx 60` 

= `(2 xx 60)/3`

= `(120)/3`

= 40.

Example

In a class of 40 students `1/5` of the total number of students like to study English, 25 of the total number like to study Mathematics and the remaining students like to study Science.
(i) How many students like to study English?
(ii) How many students like to study Mathematics?
(iii) What fraction of the total number of students like to study Science?

Total number of students in the class = 40.

(i) Of these `1/5` of the total number of students like to study English.

Thus, the number of students who like to study English = `1/5` of 40

= `1/5 xx 40` = 8 students.

(ii) `2/5 "of"  40 = 2/5 xx 40 = (2 xx 40)/5 = 80/5` = 16 Students.

(iii) The number of students who like English and Mathematics = 8 + 16 = 24.
Thus, the number of students who like Science = 40 – 24 = 16.
Thus, the required fraction is `16/40`.

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