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NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Exercise 2.1

Q1: Which of the drawings (a) to (d) show: 

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans:
(i) 2 × (1/5) represents the addition of 2 figures, each represents 1 shaded part out of the given 5 equal parts.
∴ 2 × (1/5) is represented by fig (d).
(ii) 2 × ½ represents the addition of 2 figures, each represents 1 shaded part out of the given 2 equal parts.
∴ 2 × ½ is represented by fig (b).
(iii) 3 × (2/3) represents the addition of 3 figures, each representing 2 shaded parts out of the given 3 equal parts.
∴ 3 × (2/3) is represented by fig (a).
(iii) 3 × ¼ represents the addition of 3 figures, each represents 1 shaded part out of the given 4 equal parts.
∴ 3 × ¼ is represented by fig (c).

Q2: Some pictures (a) to (c) are given below. Tell which of them show:

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans:

(i) 3 × (1/5) represents the addition of 3 figures, each represents 1 shaded part out of the given 5 equal parts and (3/5) represents 3 shaded parts out of 5 equal parts.
∴ 3 × (1/5) = (3/5) is represented by fig (c).
(ii) 2 × (1/3) represents the addition of 2 figures, each represents 1 shaded part out of the given 3 equal parts and (2/3) represents 2 shaded parts out of 3 equal parts.
∴ 2 × (1/3) = (2/3) is represented by fig (a).
(iii) 3 × (3/4) represents the addition of 3 figures, each represents 3 shaded part out of the given 4 equal parts and 2 ¼ represents 2 fully and 1 figure having 1 part as shaded out of 4 equal parts.
∴ 3 × (3/4) = 2 ¼ is represented by fig (b)


Q3: Multiply and reduce to lowest form and convert into a mixed fraction: 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (7/1) × (3/5)
= (7 × 3)/ (1 × 5)
= (21/5)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (4/1) × (1/3)
= (4 × 1)/ (1 × 3)
= (4/3)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (2/1) × (6/7)
= (2 × 6)/ (1 × 7)
= (12/7)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iv) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (5/1) × (2/9)
= (5 × 2)/ (1 × 9)
= (10/9)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (2/3) × (4/1)
= (2 × 4)/ (3 × 1)
= (8/3)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (5/2) × (6/1)
= (5 × 6)/ (2 × 1)
= (30/2)
= 15

(vii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (11/1) × (4/7)
= (11 × 4)/ (1 × 7)
= (44/7)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(viii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (20/1) × (4/5)
= (20 × 4)/ (1 × 5)
= (80/5)
= 16

(ix) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (13/1) × (1/3)
= (13 × 1)/ (1 × 3)
= (13/3)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(x) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (15/1) × (3/5)
= (15 × 3)/ (1 × 5)
= (45/5)
= 9


Q4: Shade:

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: (i) From the question,
We may observe that there are 12 circles in the given box. So, we have to shade ½ of the circles in the box.
∴ 12 × ½ = 12/2
 = 6
So we have to shade any 6 circles in the box.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) From the question,
We may observe that there are 9 triangles in the given box. So, we have to shade 2/3 of the triangles in the box.
∴ 9 × (2/3) = 18/3
 = 6
So we have to shade any 6 triangles in the box.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii) From the question,
We may observe that there are 15 squares in the given box. So, we have to shade 3/5 of the squares in the box.
∴ 15 × (3/5) = 45/5
 = 9
So we have to shade any 9 squares in the box.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Q5: Find: 
(a) 1/2 of (i) 24 (ii) 46
Ans: (i) 24
We have,
= ½ × 24
= 24/2
= 12

(ii) 46
We have,
= ½ × 46
= 46/2
= 23

(b) 2/3 of (i) 18 (ii) 27

Ans: (i) 18
We have,
= 2/3 × 18
= 2 × 6
= 12

(ii) 27
We have,
= 2/3 × 27
= 2 × 9
= 18

(c) 3/4 of  (i) 16 (ii) 36

Ans: (i) 16
We have,
= ¾ × 16
= 3 × 4
= 12

(ii) 36
We have
= ¾ × 36
= 3 × 9
= 27

(d) 4/5 of (i) 20 (ii) 35

Ans: (i) 20
We have,
= 4/5 × 20
= 4 × 4
= 16

(ii) 35
We have,
= 4/5 × 35
= 4 × 7
= 28


Q6: Multiply and express as a mixed fraction: 
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 26/5
Now,= 3 × (26/5)
= 78/5
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
= 6 ¾ = 27/4
Now,
= 5 × (27/4)
= 135/4
= 33 ¾ 

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
= 2 ¼ = 9/4
Now,
= 7 × (9/4)
= 63/4
= 15 ¾ 

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 19/3
Now,
= 4 × (19/3)
= 76/3
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
= 3 ¼ = 13/4
Now,
= (13/4) × 6
= (13/2) × 3
= 39/2
= 19 ½ 

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: First convert the given mixed fraction into improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1) = 17/5
Now,
= (17/5) × 8
= 136/5
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q7: Find:
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: (i) First convert the given mixed fraction into an improper fraction.
= 2 ¾ = 11/4
Now,
= ½ × 11/4
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= ½ × (11/4)
= (1 × 11)/ (2 × 4)
= (11/8)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) First convert the given mixed fraction into improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 38/9
Now,
= ½ × (38/9)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= ½ × (38/9)
= (1 × 38)/ (2 × 9)
= (38/18)
= 19/9
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: (i) First convert the given mixed fraction into an improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1) = 23/6
Now,
= (5/8) × (23/6)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (5/8) × (23/6)
= (5 × 23)/ (8 × 6)
= (115/48)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) First convert the given mixed fraction into improper fraction.
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1) = 29/3
Now,
= (5/8) × (29/3)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
= (5/8) × (29/3)
= (5 × 29)/ (8 × 3)
= (145/24)
= NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Q8: Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed 2/5 of the water. Pratap consumed the remaining water. 
(i) How much water did Vidya drink? 
(ii) What fraction of the total quantity of water did Pratap drink? 
Ans: (i) From the question, it is given that,
Amount of water in the water bottle = 5 liters
Amount of water consumed by Vidya = 2/5 of 5 liters
= (2/5) × 5
= 2 liters
So, the total amount of water drank by Vidya is 2 liters

(ii) From the question, it is given that,
Amount of water in the water bottle = 5 liters
Then,
Amount of water consumed by Pratap = (1 – water consumed by Vidya)
= (1 – (2/5))
= (5-2)/5
= 3/5
∴ Total amount of water consumed by Pratap = 3/5 of 5 liters
 = (3/5) × 5
 = 3 liters
So, the total amount of water drank by Pratap is 3 liters

Exercise 2.2

Fractions and Decimals Fractions and Decimals 

Q1: 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: 
By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
(i)
 (a) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(b) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(c) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii)
 (a)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(b) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(c) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q2: Multiply and reduce to lowest form (if possible): 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans:
(i) First, convert the given mixed fraction into an improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 8/3,

By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii) By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iv) By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v) By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi) By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vii) By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Multiplying FractionMultiplying FractionQ3: Multiply the following fractions: 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: 
(i) First convert the given mixed fraction into improper fraction.
= 5 ¼ = 21/4
Now,
= (2/5) × (21/4)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) First, convert the given mixed fraction into an improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 32/5Now,= (32/5) × (7/9)

By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then, 
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii) First, convert the given mixed fraction into an improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 16/3
Now,
= (3/2) × (16/3)
By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv) First convert the given mixed fraction into an improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 17/7
Now,
= (5/6) × (17/7)
By the rule Multiplication of fractions,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v) First convert the given mixed fraction into improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 17/5
Now,
= (17/5) × (4/7)

By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi) First convert the given mixed fraction into improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 13/5
Now,
= (13/5) × (3/1)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vii) First convert the given mixed fraction into improper fraction.
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 25/7
Now,
= (25/7) × (3/5)
By the rule Multiplication of fraction,
Product of fraction = (product of numerator)/ (product of denominator)
Then,  
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q4: Which is greater: 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q5: 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
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
Therefore,
The distance between the first and the last saplings NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
Thus the distance between the first and the last saplings is NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q6: Lipika reads a book forNCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)hours every day. She reads the entire book in 6 days. How many hours in ail were required by her to read the book?
Ans: Time is taken by Lipika to read a book = NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)hours
She reads the entire book in 6 days.
Now, the total hours are taken by her to read the entire book NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
Thus, 10 hours were required by her to read the book. NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q7: A car runs 16 km using 1 litre of petrol. How much distance will it cover using  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)of petrol?

Ans: In 1 litre of petrol, car covers the distance = 16 km
In NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)litres of petrol, car covers the distance =  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
Thus, the car will cover 44 km distance.

Q8: (a) 
(i) Provide the number in the box 
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) The simplest form of the number obtained in NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(b)
 (i) Provide the number in the box
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) The simplest form of the number obtained in NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans:
 (a)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) The simplest form NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(b)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) The simplest form NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Exercise 2.3 

Q1:
Find: 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: 
(i) We have,
= 12 × reciprocal of ¾

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii) We have,
= 14 × reciprocal of (5/6)

  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii) We have,
= 8× reciprocal of (7/3)
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iv) We have,
= 4 × reciprocal of (8/3)

 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v) While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 7/3
Then,
= 3 ÷ (7/3)
= 3 × reciprocal of (7/3)

  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi) While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 25/7
Then,
= 5 ÷ (25/7)
= 5 × reciprocal of (25/7)   
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q2: Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) 3/7
Ans: Reciprocal of (3/7) is (7/3) [∵ ((3/7) × (7/3)) = 1]
So, it is an improper fraction.
Improper fraction is that fraction in which numerator is greater than its denominator.
(ii) 5/8
Ans: Reciprocal of (5/8) is (8/5) [∵ ((5/8) × (8/5)) = 1]
So, it is an improper fraction.
Improper fraction is that fraction in which numerator is greater than its denominator.
(iii) 9/7
Ans: Reciprocal of (9/7) is (7/9) [∵ ((9/7) × (7/9)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.
(iv) 6/5
Ans: Reciprocal of (6/5) is (5/6) [∵ ((6/5) × (5/6)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.
(v) 12/7
Ans: Reciprocal of (12/7) is (7/12) [∵ ((12/7) × (7/12)) = 1]
So, it is a proper fraction.
A proper fraction is that fraction in which denominator is greater than the numerator of the fraction.
(vi) 1/8
Ans: Reciprocal of (1/8) is (8/1) or 8 [∵ ((1/8) × (8/1)) = 1]
So, it is a whole number.
Whole numbers are collection of all positive integers including 0.
(vii) 1/11
Ans: Reciprocal of (1/11) is (11/1) or 11 [∵ ((1/11) × (11/1)) = 1]
So, it is a whole number.
Whole numbers are collection of all positive integers including 0.


Q3: Find: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: 
(i) We have,
= (7/3) × reciprocal of 2
= (7/3) × (1/2)
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) We have,
= (4/9) × reciprocal of 5
= (4/9) × (1/5)
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii) We have,
= (6/13) × reciprocal of 7
= (6/13) × (1/7)
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iv) First convert the mixed fraction into improper fraction. We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 13/3 Then,
= (13/3) × reciprocal of 3

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v) First convert the mixed fraction into improper fraction.
We have,
= 3 ½ = 7/2
Then,
= (7/2) × reciprocal of 4

 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi) First convert the mixed fraction into improper fraction.
We have,

=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 31/7
Then,
= (31/7) × reciprocal of 7

  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q4:  Find 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(ii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(iv)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(v)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vi)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(vii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

(viii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Ans: 
(i) We have,
= (2/5) × reciprocal of ½
= (2/5) × (2/1)
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) We have,
= (4/9) × reciprocal of (2/3)
= (4/9) × (3/2)
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) We have,
= (3/7) × reciprocal of (8/7)
= (3/7) × (7/8)
  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv) First convert the mixed fraction into improper fraction.
We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 7/3
Then,
= (7/3) × reciprocal of (3/5)
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) First convert the mixed fraction into improper fraction.
We have,
= 3 ½ = 7/2
Then,
= (7/2) × reciprocal of (8/3)
= (7/2) × (3/8)

  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi) First convert the mixed fraction into improper fraction.
We have,
= 1 ½ = 3/2
Then,
= (2/5) × reciprocal of (3/2)

= (2/5) × (2/3)
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii) First convert the mixed fraction into improper fraction.
We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 16/5

=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 5/3Then,= (16/5) × reciprocal of (5/3)= (16/5) × (3/5)

  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(viii) First convert the mixed fraction into improper fraction.
We have,
=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 11/5

=NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)= 6/5
Then,
= (11/5) × reciprocal of (6/5)
= (11/5) × (5/6)
 NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Exercise 2.4 

NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

Q1: 
Find: 
(i) 0.2 x 6 
(ii) 8 x 4.6 
(iii) 2.71 x 5 
(iv) 20.1 x 4 
(v) 0.05 x 7 
(vi) 211.02 x 4 
(vii) 2 x 0.86 

Ans: 
(i) 0.2 x 6 = 1.2
(ii) 8 x 4.6 = 36.8
(iii) 2.71 x 5 = 13.55
(iv) 20.1 x 4 = 80.4
(v) 0.05 x 7 = 0.35
(vi) 211.02 x 4 = 844.08
(vii) 2 x 0.86 = 1.72


Q2: Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm. 
Ans: Given: Length of rectangle = 5.7 cm and
Breadth of rectangle = 3 cm
Area of rectangle = Length x Breadth = 5.7 x 3 = 17.1 cm2
Thus, the area of rectangle is 17.1 cm2.

Q3: Find: 
(i) 1.3 x 10 
(ii) 36.8 x 10 
(iii) 153.7 x 10 
(iv) 168.07 x 10 
(v) 31.1 x 100 
(vi) 156.1 x 100
(vii) 3.62 x 100 
(viii) 43.07 x 100 
(ix) 0.5 x 10
(x) 0.08 x 10 
(xi) 0.9 x 100 
(xii) 0.03 x 1000 
Ans:
(i) 1.3 x 10 = 13.0
(ii) 36.8 x 10 = 368.0
(iii) 153.7 x 10 = 1537.0
(iv) 168.07 x 10 = 1680.7
(v) 31.1 x 100 = 3110.0
(vi) 156.1 x 100 = 15610.0
(vii) 3.62 x 100 = 362.0
(viii) 43.07 x 100 = 4307.0
(ix) 0.5 x 10 = 5.0
(x) 0.08 x 10 = 0.80
(xi) 0.9 x 100 = 90.0
(xii) 0.03 x 1000 = 30.0

Q4: A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol? 
Ans: ∵ In one litre, a two-wheeler covers a distance = 55.3 km
∴ In 10 litres, a two- wheeler covers a distance = 55.3x10 = 553.0 km
Thus, 553 km distance will be covered by it in 10 litres of petrol.

Q5: Find: 
(i) 2.5 x 0.3 
(ii) 0.1 x 51.7 
(iii) 0.2 x 316.8 
(iv) 1.3 x 3.1 
(v) 0.5 x 0.05 
(vi) 11.2 x 0.15 
(vii) 1.07 x 0.02 
(viii) 10.05 x 1.05 
(ix) 101.01 x 0.01 
(x) 100.01 x 1.1 
Ans: 
(i) 2.5 x 0.3 = 0.75
(ii)  0.1 x 51.7 = 5.17
(iii) 0.2 x 316.8 = 63.36
(iv) 1.3 x 3.1=4.03
(v) 0.5 x 0.05 =0.025
(vi) 11.2 x 0.15 = 1.680
(vii) 1.07 x 0.02 = 0.0214
(viii) 10.05 x 1.05 = 10.5525
(ix) 101.01 x 0.01 = 1.0101
(x) 100.01 x1.1=110.11

Exercise 2.5 

Q1: Find: 
(i) 0.4 ÷ 2
(ii) 0.35 ÷ 5
(iii) 2.48 ÷ 4
(iv) 65.4 ÷ 6
(v)  651.2 ÷ 4
(v)  14.49 ÷ 7
(vii) 3.96 ÷ 4
(viii) 0.80 ÷ 5
Ans: 
(i) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(viii)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q2: Find: 
(i) 4.8 ÷ 10
(ii) 52.5 ÷ 10
(iii) 0.7 ÷ 10
(iv) 33.1 ÷ 10
(v) 272.23 ÷ 10
(vi) 0.56 ÷ 10
(vii) 3.97 ÷ 10
Ans: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q3: Find: 
(i) 2.7 ÷ 100
(ii)  0.3 ÷ 100
(iii) 0.78 ÷ 100
(iv) 432.6 ÷ 100
(v) 23.6 ÷ 100
(vi) 98.53 ÷ 100
Ans: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q4: Find: 
(i) 7.9 ÷ 1000 
(ii)  26.3 ÷ 1000 
(iii) 38.53 ÷ 1000
(iv) 128.9 ÷ 1000 
(v)  0.5 ÷ 1000
Ans: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q5: Find: 
(i) 7÷ 3.5 
(ii)  36 ÷ 0.2 
(iii)  3.25  ÷  0.5
(iv)  30.94 ÷ 0.7 
(v)  0.5 ÷ 0.25 
(vi)  7.75  ÷  0.25
(vii) 76.5 ÷ 0.15 
(viii)  37.8 ÷1.4 
(ix)  2.73  ÷  1.3
Ans: 
(i)NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iii) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(iv)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(v)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vi) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(vii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(viii)  NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
(ix) NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)


Q6: A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre petrol?
Ans:
∵ In 2.4 litres of petrol, distance covered by the vehicle = 43.2 km
∴ In 1 litre of petrol, distance covered by the vehicle = 43.2 ÷2.4
NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)
Thus, it covered 18 km distance in one litre of petrol.

The document NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1) is a part of the Class 7 Course Mathematics (Maths) Class 7.
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FAQs on NCERT Solutions for Class 7 Maths - Fractions and Decimals (Exercise 2.1)

1. What are fractions and how are they represented?
Ans. Fractions are a way to represent a part of a whole. They consist of two numbers: the numerator (the top number) and the denominator (the bottom number). The numerator indicates how many parts we have, while the denominator shows how many equal parts the whole is divided into. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator, meaning we have three parts out of four equal parts of a whole.
2. How do you convert a fraction to a decimal?
Ans. To convert a fraction to a decimal, you divide the numerator by the denominator. For example, to convert the fraction 1/4 to a decimal, you divide 1 by 4, which equals 0.25. This means that 1/4 is equivalent to 0.25 in decimal form.
3. What is the difference between proper and improper fractions?
Ans. A proper fraction is a fraction where the numerator is less than the denominator, such as 2/5. An improper fraction, on the other hand, has a numerator that is greater than or equal to the denominator, like 5/3 or 4/4. Improper fractions can also be expressed as mixed numbers, which combine a whole number and a proper fraction.
4. How can you add or subtract fractions?
Ans. To add or subtract fractions, you need a common denominator. If the denominators are the same, you simply add or subtract the numerators and keep the denominator the same. If the denominators are different, find the least common multiple (LCM) of the denominators, convert the fractions to have this common denominator, and then add or subtract the numerators.
5. What are some real-life applications of fractions and decimals?
Ans. Fractions and decimals are used in many real-life situations, such as cooking (measuring ingredients), shopping (calculating discounts), and construction (measuring lengths). For example, if a recipe calls for 1/2 cup of sugar, that is a fraction. Similarly, if an item costs $5.75, that is a decimal. Understanding how to work with fractions and decimals helps in making accurate calculations in everyday tasks.
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