NCERT Solutions: Fractions & Decimals- 2 Notes | Study Mathematics (Maths) Class 7 - Class 7

Exercise 2.3 

Example for Multiplying Fractions

Ques 1: Find: 
(i) 1/4 of (a) 1/4 (b) 3/5 (c) 4/3
(ii) 1/7 of (a) 2/9 (b) 6/5 (c) 3/10
Ans: 
(i) (a)
(b)  
(c)  

(ii) (a)  
(b)  
(c)  

Ques 2: Multiply and reduce to lowest form (if possible): 
(i)
(ii)  
(iii)
(iv)
(v)
(vi)
(vii)

Ans:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)

Ques 3: Multiply the following fractions: 

(i)
(ii)  
(iii)
(iv)  
(v)  
(vi)  
(vii)  
Ans: 
(i)
(ii)
(iii)  
(iv)  
(v)  
(vi)
(vii)  

Ques 4: Which is greater: 
(i)
(ii)
Ans: 
(i)
⇒  
⇒  
⇒  

(ii)
⇒
⇒
⇒


Ques 5: Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last sapling. 
Ans: The distance between two adjacent saplings = 3/4 m
Saili planted 4 saplings in a row, then number of gap in saplings = 3

Therefore,
The distance between the first and the last saplings  
Thus the distance between the first and the last saplings is

Ques 6: Lipika reads a book forhours everyday. She reads the entire book in 6 days. How many hours in ail were required by her to read the book?
Ans: Time taken by Lipika to read a book = hours
She reads entire book in 6 days.
Now, total hours taken by her to read the entire book  
Thus, 10 hours were required by her to read the book.  

Ques 7: A car runs 16 km using 1 litre of petrol. How much distance will it cover using  of petrol?
Ans: In 1 litre of pertrol, car covers the distance = 16 km
In litres of petrol, car covers the distance =  

Thus, the car will cover 44 km distance.

Ques 8: (a) (i) Provide the number in the box
(ii) The simplest form of the number obtained in
(b) (i) Provide the number in the box
(ii) The simplest form of the number obtained in
Ans: 

(ii) The simplest form

(ii) The simplest form

Exercise 2.4 
Question 1:
Find: 
(i)
(ii)  
(iii)  
(iii)  
(iv)  
(v)  
Ans: 
(i)
(ii)  
(iii)  
(iv)  
(v)  
(vi)  

Ques 2: Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fraction, improper fractions and whole numbers. 
(i) 3/7 
(ii) 5/
(iii) 9/7
(iv) 6/5
(v) 12/7
(vi) 1/8
(vii) 1/11
Ans: 
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)

Question 3: 
Find: 
(i)
(ii)
(iii)
(iv)
(vi)
(vi)
Ans: 
(i)
(ii)  
(iii)  
(iv)
(v)
(vi)  

Ques 4: 
Find: 
(i)
(ii)  
(iii)  
(iv)  
(v)  
(vi)  
(vii)  
(viii)  
Ans 4: 
(i)
(ii)  
(iii)  
(iv)
(v)  
(vi)  
(vii)  
(viii)

Exercise 2.5 
Ques 1: Which is greater: 
(i) 0.5 or 0.05 
(ii) 0.7or 0.5 
(iii) 7 or 0.7
(iv) 1.37 or 1.49 
(v)  3.03 or 2.30 
(vi) 0.8 or 0.88
Ans: 
(i)  0.5 > 0.05    
(ii)  0.7 > 0.5
(iii) 7 >0.7
(iv) 1.37 <1.49
(v)  2.03 < 2.30
(vi) 0.8 <0.88

Ques 2: Express as rupees using decimals: 
(i) 7 paise 
(ii) 7 rupees 7 paise 
(iii) 77 rupees 77 paise 
(iv) 50 paise 
(v) 235 paise 
Ans: 
∵
∴
(i)
(ii)
(iii)
(iv)
(v)

Ques 3: (i) Express 5 cm in metre and kilometer. 
(ii) Express 35 mm in cm, m and km. 
Ans: 
(i) Express 5 cm in meter and kilometer.
∵ 100 cm = 1 meter
∴ 1 cm = 1/100 meter
⇒ 5 cm = 5/100 = 0.05 meter
Now,
∴ 1000 meters = 1 kilometers
∴ 1 meters = 1/1000 kilometer
⇒ 0.05 meter = 0.05/1000 = 0.00005 kilometer
(ii) Express 35 mm in cm, m and km.
∵ 10 mm = 1 cm
∴ 1 mm  = 1/10 cm
⇒ 35 mm = 35/100 = 3.5 cm
Now, ∵ 100 cm = 1 meter
∴ 1 cm = 1/100 meter
⇒ 3.5 cm  = 3.5/100 = 0.035 meter
Again,
∵ 1000 meters = 1 kilometers
∴ 1 meter = 1/1000 kilometers
⇒ 0.035 meter = 0.035/1000 = 0.000035 kilometer

Ques 4:  Express in kg. 
(i) 200 g 
(ii) 3470 g 
(iii) 4 kg 8 g 
Ans: 
Let us consider, 1000 g = 1 kg

⇒
(i) 
(ii) 
(iii)  4kg 8 g = = 5 kg + 0.008 kg = 4.005 kg

Ques 5: Write the following decimal numbers in the expanded form: 
(i) 20.03 
(ii) 2.03 
(iii) 200.03 
(iv) 2.034 
Ans: 
(i)
(ii)  
(iii)  
(iv)  

Ques 6: Write the place value of 2 in the following decimal numbers: 
(i) 2.56 
(ii) 21.37 
(iii) 10.25 
(iv) 9.42
(v) 63.352
Ans: 
(i) Place value of 2 in 2.56 = 2 x 1 = 2 ones
(ii)  Place value of 2 in 21.37 = 2 x 10 = 2 tens
(iii) Place value of 2 in 10.25
(iv) Place value of 2 in 9.42
(v) Place value of 2 in 63.352

Ques 7: Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much? 

Ans: 

Distance travelled by Dinesh when he went from place A to place B = 7.5 km and from place B to C = 12.7 km.
Total distance covered by Dinesh = AB + BC
= 7.5 + 12.7
= 20.2 km
Total distance covered by Ayub = AD + DC
= 9.3 + 11.8
= 21.1 km
On comparing the total distance of Ayub and Dinesh,
21.1 km > 20.2 km
Therefore, Ayub covered more distance by 21.1 – 20.2 = 0.9 km = 900 m

Ques 8: Shyam bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits? 
Ans: Total weight of fruits bought by Shyam = 5 kg 300 g + 3 kg 250 g = 8 kg 550 g
Total weight of fruits bought by Sarala = 4 kg 800 g + 4 kg 150 g = 8 kg 950 g
On comparing the quantity of fruits, 8 kg 550 g < 8 kg 950 g
Therefore, Sarala bought more fruits.

Ques: How much less is 28 km than 42.6 km? 
Ans: We have to find the difference of 42.6 km and 28 km.
Difference = 42.6 – 28.0 = 14.6 km
Therefore 14.6 km less is 28 km than 42.6 km.