RD Sharma Class 7 Math 2nd Chapter Fractions Exercise 2.3 Solution

Exercise 2.3

 

1. Find the reciprocal of each of the following fractions and classify them as proper, improper and whole numbers

(i) 3/7

(ii) 5/8

(iii) 9/7

(iv) 6/5

(v) 12/7

(vi) 1/8

Solution:

(i)  3/7

7/3 = improper number

(ii)  5/8

8/5 = improper number

(iii)  9/7

7/9 = proper number

(iv) 6/5

5/6 = proper number

(v) 12/7

7/12 = proper number

(vi) 1/8

8 = whole number

2. Divide

(i) (3/8) by (5/9)

(ii) 3 (1/4) by (2/3)

(iii) (7/8) by 4 (1/2)

(iv) 6 (1/4) by 2 (3/5)

Solution:

 

(i) Given (3/8) by (5/9)

From the rule of division of fraction we know that (a/b) ÷(c/d) = (a/b) ×(d/c)

(3/8) / (5/9) = (3/8) ×(9/5)

= (3×9) / (8×5)

= (27/40)

(ii) Given 3 ( (1/4) by (2/3)

Converting 3 (1/4) to improper we get (13/4)

From the rule of division of fraction we know that (a/b) ÷ (c/d) = (a/b) ×(d/c)

(13/4) / (2/3) = (13/4) ×(3/2)

= (13×3) / (4×2)

= (39/8)

4 (2/7)

(iii) Given (7/8) by (1/2)

Converting 4 (1/2) to improper we get (9/2)

From the rule of division of fraction we know that (a/b) ÷(c/d) = (a/b) ×(d/c)

(7/8) (9/2) = (7/8) ×(2/9)

= (7×2) / (8×9)

= (14/72)

= (7/36)

(iv) Given 6 (1/4) by 2 (3/5)

Converting 6 (1/4) and 2 (3/5) to improper we get (25/4) and (13/5)

From the rule of division of fraction we know that (a/b) ÷(c/b) = (a/b) ×(d/c)

(25/4) / (13/5) = (5/13) ×(5/13)

= (25×5) / (4×13)

= (75/52)

= 2 (21/52)

3. Divide:

 

Solution:

4. Simplify:

 

(i) (3\10) ÷(10/3)

Solution:

Given (3/10) ÷ (10/3)]

= (3×3) / (10×10)

= (9/100)

(ii) 4 (3/5) ÷(4/5)

Solution:

Given 4 (3/5) ÷(4/5)

First convert the given mixed fractions into improper fraction

4 (3/5) = (23/5)]

(23/5) ÷(4/5) = (23×5) / (5×4)

= (23/4)

= 5 (3/4)

(iii) 5 (4/7) ÷1 (3/10)

Solution:

Given 5 (4/7) ÷1 (3/10)

First converting the given mixed fraction into improper fractions

(39/7) and (13/10)

(39/7) ÷(13/10)  = (39×10)/ (7×13)

= (390/91)

= (30/7)

= 4 (2/7)

(iv) 4÷2(2/5)

Solution:

Given 4 ÷ 2 (2/5)

First converting the given mixed fractions into improper

2 (2/5) = (12/5)

4 ÷(12/5) = (4×5)/ 12

= (20/12)

1 (1(2/3)

5. A wire of length 12 (1/2) m is cut into 10 pieces of equal length. Find the length of each piece.

 

Solution:

Given total length of the wire is = 21(1/2) = (25/2) m

It is cut into 10 pieces, so length of one piece is

= (25/2)/ 10

= (25/20)

= (5/4)

= 1 (1/4) m

6. The length of a rectangular plot of area 65(1/3) m2 is 12(1/4) m. What is the width of the plot?

 

Solution:

Given,

The length of a rectangular plot of area 65(1/3) m2 is 12(1/4) m.

7. By what number 6(2/9) be multiplied to get 4(4/9)?

 

Solution:

Let x be the number which needs to be multiplied by 6 (2/9) = (56/9)

X × (56/9) = 4 (4/9)

X × (56/9) = (40/9)

X = (40/9) ×(9/56)

X = (40/56)

X = (5/7)

8. The product of two number 25 (5/6). If one of the numbers is 6 (2/3), find the other.

 

Solution:

Given product of two number is 25 (5/6) = (155/6)

One of the numbers i9s 6 (2/3) = (20/3)

Let the other be x

(155/6) = x× (155/3)

X = (3/20) ×(155/6)

X = (31/8)

X = 3(7/8)

9. The cost of 6 (1/4) kg of apples is Rs. 400. At what rate per kg are the alpple being sold?

Solution:

Cost of total apples = Rs 400.

10. By selling oranges at the rate of Rs 5(1/4) per orange, a fruit seller get Rs 630. How many dozens of oranges does he sell?

 

Solution:

By selling oranges at the rate of Rs 5(1/4) per orange, a fruit seller get Rs 630.

5(1/4) = 2(1/4)

12 apples = 1 dozen

Therefore, 120 apples = 10 dozen

11. In mid-day meal scheme 3/10 litre of milk is given to each student of a primary school. If 30 litres of milk is distributed every-day in the school, how many students are there in the school?

 

Solution:

Given,

3/10 litre of milk is given to each student of a primary school.

30 litres of milk is distributed everyday in the school

Number of students given 3/10 litres of milk = 1

Number of students given 1 litre of milk = 10/3

Number of students given 30 litres of milk = 10/3 × 30 = 100 Students

12. In a charity show Rs 6496 were collected by selling some tickets. If the price of each ticket was Rs 50(3/4), how many tickets were sold?

 

Solution:

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