RD Sharma Solutions: Operations on Whole Numbers (Exercise 4.3)

 Page 1


 
 
 
 
 
 
Exercise 4.3                                                                      page: 4.14 
1. Fill in the blanks to make each of the following a true statement: 
(i) 785 × 0 = ….. 
(ii) 4567 × 1 = ….. 
(iii) 475 × 129 = 129 × ….. 
(iv) ….. × 8975 = 8975 × 1243 
(v) 10 × 100 × …. = 10000 
(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5 
(vii) 12 × 45 = 12 × 50 – 12 × ….. 
(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5 
(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66 
(x) 49 × 66 + 49 × 34 = 49 × (….. + …..) 
Solution: 
 
(i) 785 × 0 = 0 
 
(ii) 4567 × 1 = 4567 based on multiplicative identity 
 
(iii) 475 × 129 = 129 × 475 based on commutativity 
 
(iv) 1243 × 8975 = 8975 × 1243 based on commutativity 
 
(v) 10 × 100 × 10 = 10000 
 
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5 
 
(vii) 12 × 45 = 12 × 50 – 12 × 5 
 
(viii) 78 × 89 = 78 × 100 – 78 × 16 + 78 × 5 
 
(ix) 66 × 85 = 66 × 90 – 66 × 4 – 66 
 
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34) 
 
2. Determine each of the following products by suitable rearrangements: 
(i) 2 × 1497 × 50 
(ii) 4 × 358 × 25 
(iii) 495 × 625 × 16 
(iv) 625 × 20 × 8 × 50 
Solution: 
 
(i) 2 × 1497 × 50 
It can be written as 
2 × 1497 × 50 = (2 × 50) × 1497 
                        = 100 × 1497  
                        = 149700 
  
(ii) 4 × 358 × 25 
It can be written as 
Page 2


 
 
 
 
 
 
Exercise 4.3                                                                      page: 4.14 
1. Fill in the blanks to make each of the following a true statement: 
(i) 785 × 0 = ….. 
(ii) 4567 × 1 = ….. 
(iii) 475 × 129 = 129 × ….. 
(iv) ….. × 8975 = 8975 × 1243 
(v) 10 × 100 × …. = 10000 
(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5 
(vii) 12 × 45 = 12 × 50 – 12 × ….. 
(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5 
(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66 
(x) 49 × 66 + 49 × 34 = 49 × (….. + …..) 
Solution: 
 
(i) 785 × 0 = 0 
 
(ii) 4567 × 1 = 4567 based on multiplicative identity 
 
(iii) 475 × 129 = 129 × 475 based on commutativity 
 
(iv) 1243 × 8975 = 8975 × 1243 based on commutativity 
 
(v) 10 × 100 × 10 = 10000 
 
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5 
 
(vii) 12 × 45 = 12 × 50 – 12 × 5 
 
(viii) 78 × 89 = 78 × 100 – 78 × 16 + 78 × 5 
 
(ix) 66 × 85 = 66 × 90 – 66 × 4 – 66 
 
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34) 
 
2. Determine each of the following products by suitable rearrangements: 
(i) 2 × 1497 × 50 
(ii) 4 × 358 × 25 
(iii) 495 × 625 × 16 
(iv) 625 × 20 × 8 × 50 
Solution: 
 
(i) 2 × 1497 × 50 
It can be written as 
2 × 1497 × 50 = (2 × 50) × 1497 
                        = 100 × 1497  
                        = 149700 
  
(ii) 4 × 358 × 25 
It can be written as 
 
 
 
 
 
 
4 × 358 × 25 = (4 × 25) × 358 
                       = 100 × 358 
                       = 35800 
 
(iii) 495 × 625 × 16 
It can be written as 
495 × 625 × 16 = (625 × 16) × 495 
                          = 10000 × 495 
                          = 4950000 
 
(iv) 625 × 20 × 8 × 50 
It can be written as 
625 × 20 × 8 × 50 = (625 × 8) × (20 × 50) 
                              = 5000 × 1000 
                              = 5000000 
 
3. Using distributivity of multiplication over addition of whole numbers, find each of the following 
products: 
(i) 736 × 103 
(ii) 258 × 1008  
(iii) 258 × 1008 
Solution: 
 
(i) 736 × 103 
It can be written as 
= 736 × (100 + 3) 
By using distributivity of multiplication over addition of whole numbers 
= (736 × 100) + (736 × 3) 
On further calculation 
= 73600 + 2208  
We get 
= 75808 
 
(ii) 258 × 1008  
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
We get 
= 260064 
 
(iii) 258 × 1008 
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
Page 3


 
 
 
 
 
 
Exercise 4.3                                                                      page: 4.14 
1. Fill in the blanks to make each of the following a true statement: 
(i) 785 × 0 = ….. 
(ii) 4567 × 1 = ….. 
(iii) 475 × 129 = 129 × ….. 
(iv) ….. × 8975 = 8975 × 1243 
(v) 10 × 100 × …. = 10000 
(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5 
(vii) 12 × 45 = 12 × 50 – 12 × ….. 
(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5 
(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66 
(x) 49 × 66 + 49 × 34 = 49 × (….. + …..) 
Solution: 
 
(i) 785 × 0 = 0 
 
(ii) 4567 × 1 = 4567 based on multiplicative identity 
 
(iii) 475 × 129 = 129 × 475 based on commutativity 
 
(iv) 1243 × 8975 = 8975 × 1243 based on commutativity 
 
(v) 10 × 100 × 10 = 10000 
 
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5 
 
(vii) 12 × 45 = 12 × 50 – 12 × 5 
 
(viii) 78 × 89 = 78 × 100 – 78 × 16 + 78 × 5 
 
(ix) 66 × 85 = 66 × 90 – 66 × 4 – 66 
 
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34) 
 
2. Determine each of the following products by suitable rearrangements: 
(i) 2 × 1497 × 50 
(ii) 4 × 358 × 25 
(iii) 495 × 625 × 16 
(iv) 625 × 20 × 8 × 50 
Solution: 
 
(i) 2 × 1497 × 50 
It can be written as 
2 × 1497 × 50 = (2 × 50) × 1497 
                        = 100 × 1497  
                        = 149700 
  
(ii) 4 × 358 × 25 
It can be written as 
 
 
 
 
 
 
4 × 358 × 25 = (4 × 25) × 358 
                       = 100 × 358 
                       = 35800 
 
(iii) 495 × 625 × 16 
It can be written as 
495 × 625 × 16 = (625 × 16) × 495 
                          = 10000 × 495 
                          = 4950000 
 
(iv) 625 × 20 × 8 × 50 
It can be written as 
625 × 20 × 8 × 50 = (625 × 8) × (20 × 50) 
                              = 5000 × 1000 
                              = 5000000 
 
3. Using distributivity of multiplication over addition of whole numbers, find each of the following 
products: 
(i) 736 × 103 
(ii) 258 × 1008  
(iii) 258 × 1008 
Solution: 
 
(i) 736 × 103 
It can be written as 
= 736 × (100 + 3) 
By using distributivity of multiplication over addition of whole numbers 
= (736 × 100) + (736 × 3) 
On further calculation 
= 73600 + 2208  
We get 
= 75808 
 
(ii) 258 × 1008  
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
We get 
= 260064 
 
(iii) 258 × 1008 
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
 
 
 
 
 
 
We get 
= 260064 
 
4. Find each of the following products: 
(i) 736 × 93 
(ii) 816 × 745 
(iii) 2032 × 613 
Solution: 
 
(i) 736 × 93 
It can be written as 
= 736 × (100 – 7) 
By using distributivity of multiplication over subtraction of whole numbers 
= (736 × 100) - (736 × 7) 
On further calculation 
= 73600 – 5152 
We get 
= 68448 
 
(ii) 816 × 745 
It can be written as 
= 816 × (750 – 5) 
By using distributivity of multiplication over subtraction of whole numbers 
= (816 × 750) - (816 × 5) 
On further calculation 
= 612000 – 4080 
We get 
= 607920 
 
(iii) 2032 × 613 
It can be written as 
= 2032 × (600 + 13) 
By using distributivity of multiplication over addition of whole numbers 
= (2032 × 600) + (2032 × 13) 
On further calculation 
= 1219200 + 26416 
We get 
= 1245616 
 
5. Find the values of each of the following using properties: 
(i) 493 × 8 + 493 × 2 
(ii) 24579 × 93 + 7 × 24579 
(iii) 1568 × 184 – 1568 × 84 
(iv) 15625 × 15625 – 15625 × 5625 
Solution: 
 
(i) 493 × 8 + 493 × 2 
It can be written as 
= 493 × (8 + 2) 
By using distributivity of multiplication over addition of whole numbers 
Page 4


 
 
 
 
 
 
Exercise 4.3                                                                      page: 4.14 
1. Fill in the blanks to make each of the following a true statement: 
(i) 785 × 0 = ….. 
(ii) 4567 × 1 = ….. 
(iii) 475 × 129 = 129 × ….. 
(iv) ….. × 8975 = 8975 × 1243 
(v) 10 × 100 × …. = 10000 
(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5 
(vii) 12 × 45 = 12 × 50 – 12 × ….. 
(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5 
(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66 
(x) 49 × 66 + 49 × 34 = 49 × (….. + …..) 
Solution: 
 
(i) 785 × 0 = 0 
 
(ii) 4567 × 1 = 4567 based on multiplicative identity 
 
(iii) 475 × 129 = 129 × 475 based on commutativity 
 
(iv) 1243 × 8975 = 8975 × 1243 based on commutativity 
 
(v) 10 × 100 × 10 = 10000 
 
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5 
 
(vii) 12 × 45 = 12 × 50 – 12 × 5 
 
(viii) 78 × 89 = 78 × 100 – 78 × 16 + 78 × 5 
 
(ix) 66 × 85 = 66 × 90 – 66 × 4 – 66 
 
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34) 
 
2. Determine each of the following products by suitable rearrangements: 
(i) 2 × 1497 × 50 
(ii) 4 × 358 × 25 
(iii) 495 × 625 × 16 
(iv) 625 × 20 × 8 × 50 
Solution: 
 
(i) 2 × 1497 × 50 
It can be written as 
2 × 1497 × 50 = (2 × 50) × 1497 
                        = 100 × 1497  
                        = 149700 
  
(ii) 4 × 358 × 25 
It can be written as 
 
 
 
 
 
 
4 × 358 × 25 = (4 × 25) × 358 
                       = 100 × 358 
                       = 35800 
 
(iii) 495 × 625 × 16 
It can be written as 
495 × 625 × 16 = (625 × 16) × 495 
                          = 10000 × 495 
                          = 4950000 
 
(iv) 625 × 20 × 8 × 50 
It can be written as 
625 × 20 × 8 × 50 = (625 × 8) × (20 × 50) 
                              = 5000 × 1000 
                              = 5000000 
 
3. Using distributivity of multiplication over addition of whole numbers, find each of the following 
products: 
(i) 736 × 103 
(ii) 258 × 1008  
(iii) 258 × 1008 
Solution: 
 
(i) 736 × 103 
It can be written as 
= 736 × (100 + 3) 
By using distributivity of multiplication over addition of whole numbers 
= (736 × 100) + (736 × 3) 
On further calculation 
= 73600 + 2208  
We get 
= 75808 
 
(ii) 258 × 1008  
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
We get 
= 260064 
 
(iii) 258 × 1008 
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
 
 
 
 
 
 
We get 
= 260064 
 
4. Find each of the following products: 
(i) 736 × 93 
(ii) 816 × 745 
(iii) 2032 × 613 
Solution: 
 
(i) 736 × 93 
It can be written as 
= 736 × (100 – 7) 
By using distributivity of multiplication over subtraction of whole numbers 
= (736 × 100) - (736 × 7) 
On further calculation 
= 73600 – 5152 
We get 
= 68448 
 
(ii) 816 × 745 
It can be written as 
= 816 × (750 – 5) 
By using distributivity of multiplication over subtraction of whole numbers 
= (816 × 750) - (816 × 5) 
On further calculation 
= 612000 – 4080 
We get 
= 607920 
 
(iii) 2032 × 613 
It can be written as 
= 2032 × (600 + 13) 
By using distributivity of multiplication over addition of whole numbers 
= (2032 × 600) + (2032 × 13) 
On further calculation 
= 1219200 + 26416 
We get 
= 1245616 
 
5. Find the values of each of the following using properties: 
(i) 493 × 8 + 493 × 2 
(ii) 24579 × 93 + 7 × 24579 
(iii) 1568 × 184 – 1568 × 84 
(iv) 15625 × 15625 – 15625 × 5625 
Solution: 
 
(i) 493 × 8 + 493 × 2 
It can be written as 
= 493 × (8 + 2) 
By using distributivity of multiplication over addition of whole numbers 
 
 
= 493 × 10 
On further calculation 
= 4930 
(ii) 24579 × 93 + 7 × 24579
It can be written as
= 24579 × (93 + 7)
By using distributivity of multiplication over addition of whole numbers = 
24579 × 100
On further calculation
= 2457900
(iii) 1568 × 184 – 1568 × 84
It can be written as
= 1568 × (184 - 84)
By using distributivity of multiplication over subtraction of whole numbers 
= 1568 × 100
On further calculation
= 156800
(iv)15625 × 15625 – 15625 × 5625
It can be written as
= 15625 × (15625 - 5625)
By using distributivity of multiplication over subtraction of whole numbers 
= 15625 × 10000
On further calculation
= 156250000
6. Determine the product of:
(i) the greatest number of four digits and the smallest number of three digits.
(ii) the greatest number of five digits and the greatest number of three digits.
Solution:
(i) We know that
Largest four digit number = 9999
Smallest three digit number = 100
Product of both = 9999 × 100 = 999900
Hence, the product of the greatest number of four digits and the smallest number of three digits is 999900. 
(ii) We know that
Largest five digit number = 99999
Largest three digit number = 999
Product of both = 99999 × 999
It can be written as
= 99999 × (1000 – 1)
By using distributivity of multiplication over subtraction of whole numbers 
= (99999 × 1000) – (99999 × 1)
On further calculation
= 99999000 – 99999
Page 5


 
 
 
 
 
 
Exercise 4.3                                                                      page: 4.14 
1. Fill in the blanks to make each of the following a true statement: 
(i) 785 × 0 = ….. 
(ii) 4567 × 1 = ….. 
(iii) 475 × 129 = 129 × ….. 
(iv) ….. × 8975 = 8975 × 1243 
(v) 10 × 100 × …. = 10000 
(vi) 27 × 18 = 27 × 9 + 27 × ….. + 27 × 5 
(vii) 12 × 45 = 12 × 50 – 12 × ….. 
(viii) 78 × 89 = 78 × 100 – 78 × ….. + 78 × 5 
(ix) 66 × 85 = 66 × 90 – 66 × ….. – 66 
(x) 49 × 66 + 49 × 34 = 49 × (….. + …..) 
Solution: 
 
(i) 785 × 0 = 0 
 
(ii) 4567 × 1 = 4567 based on multiplicative identity 
 
(iii) 475 × 129 = 129 × 475 based on commutativity 
 
(iv) 1243 × 8975 = 8975 × 1243 based on commutativity 
 
(v) 10 × 100 × 10 = 10000 
 
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5 
 
(vii) 12 × 45 = 12 × 50 – 12 × 5 
 
(viii) 78 × 89 = 78 × 100 – 78 × 16 + 78 × 5 
 
(ix) 66 × 85 = 66 × 90 – 66 × 4 – 66 
 
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34) 
 
2. Determine each of the following products by suitable rearrangements: 
(i) 2 × 1497 × 50 
(ii) 4 × 358 × 25 
(iii) 495 × 625 × 16 
(iv) 625 × 20 × 8 × 50 
Solution: 
 
(i) 2 × 1497 × 50 
It can be written as 
2 × 1497 × 50 = (2 × 50) × 1497 
                        = 100 × 1497  
                        = 149700 
  
(ii) 4 × 358 × 25 
It can be written as 
 
 
 
 
 
 
4 × 358 × 25 = (4 × 25) × 358 
                       = 100 × 358 
                       = 35800 
 
(iii) 495 × 625 × 16 
It can be written as 
495 × 625 × 16 = (625 × 16) × 495 
                          = 10000 × 495 
                          = 4950000 
 
(iv) 625 × 20 × 8 × 50 
It can be written as 
625 × 20 × 8 × 50 = (625 × 8) × (20 × 50) 
                              = 5000 × 1000 
                              = 5000000 
 
3. Using distributivity of multiplication over addition of whole numbers, find each of the following 
products: 
(i) 736 × 103 
(ii) 258 × 1008  
(iii) 258 × 1008 
Solution: 
 
(i) 736 × 103 
It can be written as 
= 736 × (100 + 3) 
By using distributivity of multiplication over addition of whole numbers 
= (736 × 100) + (736 × 3) 
On further calculation 
= 73600 + 2208  
We get 
= 75808 
 
(ii) 258 × 1008  
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
We get 
= 260064 
 
(iii) 258 × 1008 
It can be written as 
= 258 × (1000 + 8) 
By using distributivity of multiplication over addition of whole numbers 
= (258 × 1000) + (258 × 8) 
On further calculation 
= 258000 + 2064  
 
 
 
 
 
 
We get 
= 260064 
 
4. Find each of the following products: 
(i) 736 × 93 
(ii) 816 × 745 
(iii) 2032 × 613 
Solution: 
 
(i) 736 × 93 
It can be written as 
= 736 × (100 – 7) 
By using distributivity of multiplication over subtraction of whole numbers 
= (736 × 100) - (736 × 7) 
On further calculation 
= 73600 – 5152 
We get 
= 68448 
 
(ii) 816 × 745 
It can be written as 
= 816 × (750 – 5) 
By using distributivity of multiplication over subtraction of whole numbers 
= (816 × 750) - (816 × 5) 
On further calculation 
= 612000 – 4080 
We get 
= 607920 
 
(iii) 2032 × 613 
It can be written as 
= 2032 × (600 + 13) 
By using distributivity of multiplication over addition of whole numbers 
= (2032 × 600) + (2032 × 13) 
On further calculation 
= 1219200 + 26416 
We get 
= 1245616 
 
5. Find the values of each of the following using properties: 
(i) 493 × 8 + 493 × 2 
(ii) 24579 × 93 + 7 × 24579 
(iii) 1568 × 184 – 1568 × 84 
(iv) 15625 × 15625 – 15625 × 5625 
Solution: 
 
(i) 493 × 8 + 493 × 2 
It can be written as 
= 493 × (8 + 2) 
By using distributivity of multiplication over addition of whole numbers 
 
 
= 493 × 10 
On further calculation 
= 4930 
(ii) 24579 × 93 + 7 × 24579
It can be written as
= 24579 × (93 + 7)
By using distributivity of multiplication over addition of whole numbers = 
24579 × 100
On further calculation
= 2457900
(iii) 1568 × 184 – 1568 × 84
It can be written as
= 1568 × (184 - 84)
By using distributivity of multiplication over subtraction of whole numbers 
= 1568 × 100
On further calculation
= 156800
(iv)15625 × 15625 – 15625 × 5625
It can be written as
= 15625 × (15625 - 5625)
By using distributivity of multiplication over subtraction of whole numbers 
= 15625 × 10000
On further calculation
= 156250000
6. Determine the product of:
(i) the greatest number of four digits and the smallest number of three digits.
(ii) the greatest number of five digits and the greatest number of three digits.
Solution:
(i) We know that
Largest four digit number = 9999
Smallest three digit number = 100
Product of both = 9999 × 100 = 999900
Hence, the product of the greatest number of four digits and the smallest number of three digits is 999900. 
(ii) We know that
Largest five digit number = 99999
Largest three digit number = 999
Product of both = 99999 × 999
It can be written as
= 99999 × (1000 – 1)
By using distributivity of multiplication over subtraction of whole numbers 
= (99999 × 1000) – (99999 × 1)
On further calculation
= 99999000 – 99999
 
 
 
 
 
 
We get 
= 99899001 
 
7. In each of the following, fill in the blanks, so that the statement is true: 
(i) (500 + 7) (300 – 1) = 299 × ….. 
(ii) 888 + 777 + 555 = 111 × ….. 
(iii) 75 × 425 = (70 + 5) (….. + 85) 
(iv) 89 × (100 – 2) = 98 × (100 - …..) 
(v) (15 + 5) (15 – 5) = 225 - ….. 
(vi) 9 × (10000 + …..) = 98766 
Solution: 
 
(i) By considering LHS 
(500 + 7) (300 – 1) 
We get 
= 507 × 299 
By using commutativity 
= 299 × 507 
 
(ii) By considering LHS 
888 + 777 + 555 
We get 
= 111 (8 + 7 + 5) 
By using distributivity 
= 111 × 20 
 
(iii) By considering LHS 
75 × 425 
We get 
= (70 + 5) × 425 
It can be written as 
= (70 + 5) (340 + 85) 
 
(iv) By considering LHS 
89 × (100 – 2) 
We get 
= 89 × 98 
It can be written as 
= 98 × 89 
By using commutativity 
= 98 × (100 – 11) 
 
(v) By considering LHS 
(15 + 5) (15 – 5) 
We get 
= 20 × 10 
On further calculation 
= 200 
It can be written as 
= 225 – 25