NCERT Solution class 7 Mathematics EXERCISE- 2.3
CHAPTER – 2
EXERCISE – 2.3
Q1. Find:
(i) ¼ of
(a) ¼
SOLUTION:-
= 1/16
(B) 3/5
SOLUTION:-
= 3/20
(C) 4/3
SOLUTION:-
= 4/12
(ii) 1/7 of
(a) 2/9
SOLUTION:-
2/63
(B) 6/5
SOLUTION:-
= 6/35
(C) 3/10
SOLUTION:-
= 3/70
Q2. Multiply and reduce to lowest form
(i) 2/3 x 8/3
SOLUTION:-
=16/9
(ii) 2/7 x 7/9
SOLUTION:-
= 2/9
(iii) 3/8 x 6/4
SOLUTION:-
= 18/32
= 9/16
(iv) 9/5 x 3/5
SOLUTION:-
= 27/25
(v) 1/3 x 15/8
SOLUTION:-
= 15/24
= 5/8
(vi) 11/2 x 3/10
SOLUTION:-
= 33/20
(vii) 4/5 x 12/7
SOLUTION:-
= 49/35
Q3. Multiply the following fractions:
(i) 2/5 x 21/4
SOLUTION:-
= 42/20
= 6/5
(ii) 32/5 x 7/9
SOLUTION:-
= 224/45
(iii) 3/2 x 16/3
SOLUTION:-
= 48/6
= 8
(iv) 5/6 x 17/7
SOLUTION:-
= 85/42
(v) 17/5 x 4/7
SOLUTION:-
= 68/35
(vi) 13/5 x 3
= 39/5
(vii) 25/7 x 3/5
SOLUTION:-
= 75/35
= 15/7
Q4. Which is greater :
(i) 2/7 of ¾ or 3/5 of 5/8
SOLUTION:-
We have,
= (2/7) x (3/4) and (3/5) x (5/8)
By the rule multiplication of fraction,
Product of fraction = ( product of numerator / product of denominator)
Then,
= (2/7) x (3/4)
= (2 x3) / (7×4)
= (1x 3) /(7×2)
= (3/14) [i]
And,
= (3/5) x (5/8)
= (3/5) / (5×8)
= (3 x 1) / (1×8)
= (3/8) [ii]
Now , convert [i] and [ii] into like fraction
LCM of 14 and 8 is 56
Now let us change each of the given fraction into an equivalent fraction having 56 as the denominator
[(3/14) x (4/4)] = (12/56)
[(3/8) x (7/7)] = (21/56)
Clearly
(12/56) < (21/56)
Hence,
(3/14) < ( 3/8)
(ii) (1/2) of (6/7) or (2/3) of (3/7)
SOLUTION:-
We have,
= (1/2) x (6/7) and (2/3) x (3/7)
By the rule of multiplication of fraction
Product of fraction = (product of numerator) / (product of denominator)
Then,
= (1/2) x (6/7)
= (1 x 6) / (2 x 7)
= (1 x 3 )/(1 x 7)
= (3/7) [i]
And,
= (2/3) x (3/7)
= (2 x 3 ) / (3 x 7)
= ( 2 x 1) / (1 x 7)
= (2/7) [ii]
By comparing [i] and [ii]
Clearly,
(3/7) > (2/7)
Q5. Saili plants 4 sampling , in a row , in her garden. The distance between two adjacent sampling is ¾ m. Find the distance between the first and last sapling .
SOLUTION:-
From the question , it is the given that,
The distance between two adjacent sapling = ¾ m.
Numbers of saplings planted by saili in a row = 4
Then, numbers of gap in sapling = ¾ x 4
= 3
The distance between the first and last saplings = 3 x ¾
= (9/4) m
=2 ¼ m
Hence, the distance between and the last saplings is 2 ¼ m.
Q6. Lipika reads a book for 1 ¾ hours every day. She reads the entire book in 6 days .
How many hours in all were required by her to read the book ?
SOLUTION:-
From the given question ,it is given that,
Lipika reads the book for = 1¾ hours every day = 7/4 hours
Numbers of day she took to read the entire book = 6 days
Total numbers of hours required by her to complete the book = (7/4) x 6
= (7/2) x 3
= 21/2
= 10 ½ hours.
Hence, the total numbers of hours required by her to complete the book is 10 ½ hours.
Q7. A car runs 16km using 1 liter of petrol . How much distance will it cover using 2¾ liters of petrol.
SOLUTION:-
From the question , It is given that,
The total numbers of distance travelled by a car in 1 liter of petrol = 16km
Then,
Total quantity of petrol = 2¾ = 11/4 liters
Total numbers of distance travelled by car in 11/4 liters of petrol = (11/4) x 16
= 11 x4
= 44km
Total numbers of distance travelled by car in 11/4 liters of petrol is 44km.
Q8. (A) (i) Provide the numbers in the box [] such that 2/3 x [] = 10/30.
SOLUTION:-
Let the required numbers be x,
Then,
= (2/3) x (x) = (10/30)
By cross multiplication ,
= x= (10/30) x (3/2)
= x= (10 x3 )/ (30 x 2)
= x= ( 5 x 1) / (10 x 1)
=x = 5/10
The required number in the box is (5/20)
(ii) The simplest form of the numbers obtained in [] is
SOLUTION:-
The numbers in the box is 5/10
Then,
The simplest form of 5/10 is ½
(b) (i) provide the number in the box [], such that (3/5) x [] = (24/75)
SOLUTION:-
Let the required number be x,
Then,
= (3/5) x (x) = (24/75)
By cross multiplication,
= x= (24/75) x (5/3)
=x= (24×5)/(75x 3)
= x= (8 x 1 ) / (15 x 1)
=x= 8/15
The required number in the box is (8/15)
(ii) The simplest form of the number obtained in [] is
SOLUTION:-
The number in the box is 8/15
Then,
The simplest form of 8/15 is 8/15