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Fill in the blanks to make each of the following a true statement:
(i) 359 + 476 = 476 + 359 (Commutativity)
(ii) 2008 + 1952 = 1952 + 2008 (Commutativity)
(iii) 90758 + 0 = 90758 (Additive identity)
(iv) 54321 + (489 + 699) = 489 + (54321 + 699) (Associativity)
Add each of the following and check by reversing the order of addends:
(i) 5628 + 39784 = 45412
And,
39784 + 5628 = 45412
(ii) 923584 + 178 = 923762
178 + 923584 = 923762
(iii) 15409 + 112 = 15521
112 + 15409 = 15521
(iv) 2359 + 641 = 3000
641 + 2359 = 3000
Determine the sum by suitable rearrangements:
(i) 953 + 407 + 647
Therefore, 53 + 47 = 100
Therefore, (953 + 647) + 407 = 1600 + 407 = 2007
(ii) 15409 + 178 + 591 + 322
409 + 91 = 500
78 + 22 = 100
Therefore, (15409 + 591) + (178 + 322) = (16000) + (500)
= 16500
(iii) 2359 + 10001 + 2641 + 9999
Therefore, 59 + 41 = 100
And, 99 + 01 = 100
Therefore, (2359 + 2641) + (10001 + 9999)
= (5000) + (20000)
= 25000
(iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999
Therefore, 99 + 1 = 100
98 + 2 = 100
97 + 3 = 100
And
96 + 4 = 100
Therefore, (1 + 1999) + (2 + 1998) + (3 + 1997) + (4 + 1996)
= 2000 + 2000 + 2000 + 2000
= 8000
(v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20
10 + 20 = 30
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
Therefore, (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16)
= 30 + 30 + 30 + 30 + 30 + 15
= 150 + 15
= 165
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) Commmutativity and associativity are properties of whole numbers.
(xii) Commmutativity and associativity are properties of addition of whole number.
(i) FALSE (3 + 5 = 8; 8 is an even number)
(ii) TRUE (3 + 5 = 8; 8 is an even number)
(iii) TRUE (2 + 4 = 6; 6 is an even number)
(iv) FALSE (2 + 4 = 6; 6 is an even number)
(v) TRUE (2 + 3 = 5; 5 is an odd number)
(vi) FALSE (3 + 2 = 5; 5 is not an even number)
(vii) FALSE [The whole number set is {0, 1, 2, 3, 4 …), whereas the natural number set is {1, 2, 3, 4 …)]
(viii) TRUE [The whole number set is {0, 1, 2, 3, 4 …), whereas the natural number set is {1, 2, 3, 4 …)]
(ix) TRUE [That number is zero.]
(x) FALSE
(xi) FALSE
(xii) TRUE
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Chapter 4: Operations on Whole Numbers –...