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Page 1 Exercise 4.1 PAGE: 4.4 1. Fill in the blanks to make each of the following a true statement: (i) 359 + 476 = 476 + ….. (ii) …. + 1952 = 1952 + 2008 (iii) 90758 + 0 = …. (iv) 54321 + (489 + 699) = 489 + (54321 + …..) Solution: (i) 359 + 476 = 476 + 359 using commutativity (ii) 2008 + 1952 = 1952 + 2008 using commutativity (iii) 90758 + 0 = 90758 using the additive identity (iv) 54321 + (489 + 699) = 489 + (54321 + 699) using associativity 2. Add each of the following and check by reversing the order of addends: (i) 5628 + 39784 (ii) 923584 + 178 (iii) 15409 + 112 (iv) 2359 + 641 Solution: (i) We get 5628 + 39784 = 45412 By reversing the order of addends 39784 + 5628 = 45412 (ii) We get 923584 + 178 = 923762 By reversing the order of addends 178 + 923584 = 923762 (iii) We get 15409 + 112 = 15521 By reversing the order of addends 112 + 15409 = 15521 (iv) We get 2359 + 641 = 3000 By reversing the order of addends 641 + 2359 = 3000 3. Determine the sum by suitable rearrangements: (i) 953 + 407 + 647 (ii) 15409 + 178 + 591 + 322 (iii) 2359 + 10001 + 2641 + 9999 (iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999 (v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 Page 2 Exercise 4.1 PAGE: 4.4 1. Fill in the blanks to make each of the following a true statement: (i) 359 + 476 = 476 + ….. (ii) …. + 1952 = 1952 + 2008 (iii) 90758 + 0 = …. (iv) 54321 + (489 + 699) = 489 + (54321 + …..) Solution: (i) 359 + 476 = 476 + 359 using commutativity (ii) 2008 + 1952 = 1952 + 2008 using commutativity (iii) 90758 + 0 = 90758 using the additive identity (iv) 54321 + (489 + 699) = 489 + (54321 + 699) using associativity 2. Add each of the following and check by reversing the order of addends: (i) 5628 + 39784 (ii) 923584 + 178 (iii) 15409 + 112 (iv) 2359 + 641 Solution: (i) We get 5628 + 39784 = 45412 By reversing the order of addends 39784 + 5628 = 45412 (ii) We get 923584 + 178 = 923762 By reversing the order of addends 178 + 923584 = 923762 (iii) We get 15409 + 112 = 15521 By reversing the order of addends 112 + 15409 = 15521 (iv) We get 2359 + 641 = 3000 By reversing the order of addends 641 + 2359 = 3000 3. Determine the sum by suitable rearrangements: (i) 953 + 407 + 647 (ii) 15409 + 178 + 591 + 322 (iii) 2359 + 10001 + 2641 + 9999 (iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999 (v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 Solution: (i) 953 + 407 + 647 We know that 53 + 47 = 100 It can be written as (953 + 647) + 407 = 1600 + 407 On further calculation (953 + 647) + 407 = 2007 (ii) 15409 + 178 + 591 + 322 We know that 409 + 91 = 500 and 78 + 22 = 100 It can be written as (15409 + 591) + (178 + 322) = 16000 + 500 On further calculation (15409 + 591) + (178 + 322) = 16500 (iii) 2359 + 10001 + 2641 + 9999 We know that 59 + 41 = 100 and 99 + 01 = 100 It can be written as (2359 + 2641) + (10001 + 9999) = 5000 + 20000 On further calculation (2359 + 2641) + (10001 + 9999) = 25000 (iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999 We know that 99 + 1 = 100, 98 + 2 = 100, 97 + 3 = 100 and 96 + 4 = 100 It can be written as (1 + 1999) + (2 + 1998) + (3 + 1997) + (4 + 1996) = 2000 + 2000 + 2000 + 2000 On further calculation (1 + 1999) + (2 + 1998) + (3 + 1997) + (4 + 1996) = 8000 (v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 We know that 10 + 20 = 30, 1 + 9 = 10, 2 + 8 = 10, 3 + 7 = 10 and 4 + 6 = 10 It can be written as (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) = 30 + 30 + 30 + 30 + 30 + 15 On further calculation (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) = 150 + 15 = 165 4. Which of the following statements are true and which are false: (i) The sum of two odd numbers is an odd number. (ii) The sum of two odd numbers is an even number. (iii) The sum of two even numbers is an even number. (iv) The sum of two even numbers is an odd number. (v) The sum of an even number and an odd number is an odd number. (vi) The sum of an odd number and an even number is an even number. (vii) Every whole number is a natural number. Page 3 Exercise 4.1 PAGE: 4.4 1. Fill in the blanks to make each of the following a true statement: (i) 359 + 476 = 476 + ….. (ii) …. + 1952 = 1952 + 2008 (iii) 90758 + 0 = …. (iv) 54321 + (489 + 699) = 489 + (54321 + …..) Solution: (i) 359 + 476 = 476 + 359 using commutativity (ii) 2008 + 1952 = 1952 + 2008 using commutativity (iii) 90758 + 0 = 90758 using the additive identity (iv) 54321 + (489 + 699) = 489 + (54321 + 699) using associativity 2. Add each of the following and check by reversing the order of addends: (i) 5628 + 39784 (ii) 923584 + 178 (iii) 15409 + 112 (iv) 2359 + 641 Solution: (i) We get 5628 + 39784 = 45412 By reversing the order of addends 39784 + 5628 = 45412 (ii) We get 923584 + 178 = 923762 By reversing the order of addends 178 + 923584 = 923762 (iii) We get 15409 + 112 = 15521 By reversing the order of addends 112 + 15409 = 15521 (iv) We get 2359 + 641 = 3000 By reversing the order of addends 641 + 2359 = 3000 3. Determine the sum by suitable rearrangements: (i) 953 + 407 + 647 (ii) 15409 + 178 + 591 + 322 (iii) 2359 + 10001 + 2641 + 9999 (iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999 (v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 Solution: (i) 953 + 407 + 647 We know that 53 + 47 = 100 It can be written as (953 + 647) + 407 = 1600 + 407 On further calculation (953 + 647) + 407 = 2007 (ii) 15409 + 178 + 591 + 322 We know that 409 + 91 = 500 and 78 + 22 = 100 It can be written as (15409 + 591) + (178 + 322) = 16000 + 500 On further calculation (15409 + 591) + (178 + 322) = 16500 (iii) 2359 + 10001 + 2641 + 9999 We know that 59 + 41 = 100 and 99 + 01 = 100 It can be written as (2359 + 2641) + (10001 + 9999) = 5000 + 20000 On further calculation (2359 + 2641) + (10001 + 9999) = 25000 (iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999 We know that 99 + 1 = 100, 98 + 2 = 100, 97 + 3 = 100 and 96 + 4 = 100 It can be written as (1 + 1999) + (2 + 1998) + (3 + 1997) + (4 + 1996) = 2000 + 2000 + 2000 + 2000 On further calculation (1 + 1999) + (2 + 1998) + (3 + 1997) + (4 + 1996) = 8000 (v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 We know that 10 + 20 = 30, 1 + 9 = 10, 2 + 8 = 10, 3 + 7 = 10 and 4 + 6 = 10 It can be written as (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) = 30 + 30 + 30 + 30 + 30 + 15 On further calculation (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) = 150 + 15 = 165 4. Which of the following statements are true and which are false: (i) The sum of two odd numbers is an odd number. (ii) The sum of two odd numbers is an even number. (iii) The sum of two even numbers is an even number. (iv) The sum of two even numbers is an odd number. (v) The sum of an even number and an odd number is an odd number. (vi) The sum of an odd number and an even number is an even number. (vii) Every whole number is a natural number. (viii) Every natural number is a whole number. (ix) There is a whole number which when added to a whole number, gives that number. (x) There is a natural number which when added to a natural number, gives that number. (xi) Commutativity and associativity are properties of whole numbers. (xii) Commutativity and associativity are properties of addition of whole numbers. Solution: (i) False. We know that, 1 + 3 = 4 where 4 is an even number. (ii) True. We know that, 5 + 7 = 12 where 12 is an even number. (iii) True. We know that, 2 + 4 = 6 where 6 is an even number. (iv) False. We know that, 4 + 6 = 10 where 10 is an even number. (v) True. We know that, 2 + 1 = 3 where 3 is an odd number. (vi) False. We know that, 3 + 2 = 5 where 5 is an odd number. (vii) False. Whole number starts from 0 whereas natural numbers start from 1. (viii) True. All the natural numbers are also whole number. (ix) True. We know that, 1 + 0 = 1 where 1 is a whole number. (x) False. We know that 2 + 1 = 3 which is not that number. (xi) False. Commutativity and associativity are not properties of whole numbers. (xii) True. Commutativity and associativity are properties of addition of whole numbers.Read More
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