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,
2 ⋅ 3/5 = (2 ⋅ 3)/5 = 6/5
3 ⋅ 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,
4 ⋅ 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 :
4 ⋅ 1/7
Solution :
4 ⋅ 1/7 = (4 ⋅ 1)/7
4 ⋅ 1/7 = 4/7
Example 2 :
Find the value of :
1/4 of 2⅕
Solution :
1/4 of 2⅕ = 1/4 ⋅ 2⅕
1/4 of 2⅕ = 1/4 ⋅ 11/5
1/4 of 2⅕ = (1 ⋅ 11)/(4 ⋅ 5)
1/4 of 2⅕ = 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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