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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 – 25Read More
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