MULTIPLYING FRACTIONS BY WHOLE NUMBERS

In this section, you will learn, how to multiply a fraction by a whole number. 

To multiply a proper or improper fraction by a whole number, first, we have to multiply the whole number with by numerator of the fraction, keeping the denominator same.

For example, 

⋅ 3/5  =  (2 ⋅ 3)/5  =  6/5

⋅ 7/11  =  (3 ⋅ 7)/11  =  21/11

To multiply a mixed fraction by a whole number, first convert the mixed fraction to an improper fraction and proceed as explained above.

For example, 

⋅ 3⁴⁄₇   =  4 ⋅ 25/7

4 ⋅ 3⁴⁄₇  =  (4 ⋅ 25)/7

4 ⋅ 3⁴⁄₇  =  100/7

4 ⋅ 3⁴⁄₇  =  14²⁄₇

Example 1 :

Find the value of :

⋅ 1/7

Solution :

4 ⋅ 1/7  =  (4 ⋅ 1)/7

4 ⋅ 1/7  =  4/7

Example 2 :

Find the value of :

1/4 of 2

Solution :

1/4 of 2  =  1/4 ⋅ 2

1/4 of 2  =  1/4  11/5

1/4 of 2  =  (1 ⋅ 11)/(4 ⋅ 5)

1/4 of 2  =  11/20

Example 3 :

In a group of 60 students 3/10 of the students like to study Science, 3/5 of the students to study Math.

(i) How many students like to study Science ?

(ii) How many students like to study Math ?

Solution :

(i)  Out of 60 students, 3/10 of the students like to study Math.

Then, the number of students who like to study Science is

=  3/10 of 60

=  3/10 ⋅ 60

=  (3 ⋅ 60)/10

=  (3 ⋅ 6)/1

=  18/1

=  18

(ii)  Out of 60 students, 3/5 of the students like to study Math.

Thus, the number of students who like to study Math is

=  3/5 of 60

=  3/5 ⋅ 60

=  (3 ⋅ 60)/5

=  (3 ⋅ 12)/1

=  36/1

= 36

Example 4 :

A car runs 20 miles using 1 liter of petrol. How much distance will it cover using 2 3/4 liters of petrol ?

Solution :

Distance covered in 1 liter of petrol is 20 miles.

Then, the distance covered using 2 3/4 liters of petrol is 

=  2¾ ⋅ 20 miles

=  11/4 ⋅ 20 miles

=  (11 ⋅ 20)/4 miles

= (11 ⋅ 5)/1 miles

=  55/1 miles

=  55 miles

So, the car can cover 55 miles of distance using 2 3/4 liters of petrol.

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