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Whole Numbers, Exercise 2.1, Question 1., Write the next three natural numbers after 10999., Solution:, The next three natural numbers after 10999 are 11000, 11001 and 11002., , Question 2., Write three whole numbers occurring just before 10001., Solution:, 10001 – 1 = 10000, 10000 – 1 = 9999, 9999 – 1 = 9998, Hence, three whole numbers just before 10001 are 10000, 9999 and 9998., , Question 3., Which is the smallest whole number?, Solution:, 0 is the smallest whole number., , Question 4., How many whole numbers are there between 32 and 53?, Solution:, The whole numbers between 32 and 53 are 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48,, 49, 50, 51, 52.

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Question 5., Write the successor of:, (a) 2440701, Solution:, Successor of 244070 is 244070 + 1 = 244071, Hence, successor of 244070 is 244071., (b) 100199, Solution:, Successor of 100199 is 100199 + 1 = 100200, Hence, successor of 100199 is 100200., , (c) 1099999, Solution:, Successor of 1099999 is 1099999 + 1 = 1100000, Hence, successor of 1099999 is 1100000., , (d) 2345670, Solution:, Successor of 2345670 is 2345670 + 1 = 2345671, Hence, successor of 2345670 is 2345671, , Question 6., Write the predecessor of:, (a) 94, Solutiion:, Predecessor of 94 is 94 – 1 = 93, Hence, predecessor of 94 is 93., (b) 10000

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Solutiion:, Predecessor of 1000 is 10000 – 1 = 9999, Hence, predecessor of 10000 is 9999, (c) 208090, Solutiion:, Predecessor of 208090 is 208090 -1 = 208089, Hence, predecessor of 208090 is 208089., (d) 7654321, Solutiion:, Predecessor of 7654321 is 7654321 – 1 = 7654320, Hence, predecessor of 7654321 is 7654320., , Question 7., In each of the following pairs of numbers, state which whole number is on the left of the other, number on the number line. Also write them with the appropriate sign (>, <) between them,, (a) 530, 503, Solution:, Clearly 503 is smaller than 530., Hence, 503 will be on left side of 530 on number line., Expression: 503 < 530 or 530 > 503, , (b) 370, 307, Solution:, Clearly 307 is smaller than 370., Hence, 307 will be on the left side of 370 on number line., Expression: 307 < 370 or 370 > 307., , (c) 98765, 56789, Solution:, Clearly 56789 is smaller than 98765., Hence, 56789 will be on left side of 98765 on number line.

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Expression: 56789 < 98765 or 98765 > 56789., , (d) 9830415,10023001, Solution:, Clearly, 9830415 is smaller than 10023001, Hence, 9830415 will be on the left side of 10023001 on the number line., Expression: 9830415 < 10023001 or 10023001 > 9830415., , Question 8., Which of the following statements are true (T) and which are false (F)?, (a) Zero is the smallest natural number., This statement is false (F), (b) 400 is the predecessor of 399., This statement is false (F), (c) Zero is the smallest whole number., This statement is true (T), (d) 600 is the successor of 599., This statement is true (T), (e) All natural numbers are whole numbers., This statement is true (T), (f) All whole numbers are natural numbers., This statement is false (F), (g) The predecessor of a two-digit number is never a single-digit number., This statement is false (F), (h) 1 is the smallest whole number., This statement is false (F), (i) The natural number 1 has no predecessor., This statement is true (T), (j) The whole number 1 has no predecessor., This statement is false (F)

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(k) The whole number 13 lies between 11 and 12., This statement is false (F), (l) The whole number 0 has no predecessor., This statement is true (T), (m) The successor of a two-digit number is always a two-digit number., This statement is false (F)., , Exercise 2.2, Question 1., Find the sum by suitable arrangement:, (a) 837 + 208 + 363, Solution:, 837 + 208 + 363, = (837 + 363) + 208, = 1200 + 208, = 1408, , [Using associative property], , (b) 1962 + 453 + 1538 + 647, Solution:, 1962 + 453 + 1538 + 647, = (1962 + 1538) + (453 + 647), = 3500 + 1100, = 4600, , Question 2., Find the product by suitable arrangement:, (а) 2 x 1768 x 50, Solution:, 2 x 1768 x 50, = (2 x 50) x 1768, = 176800

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(b) 4 x 166 x 25, Solution:, 4 x 166 x 25, = 166 x (25 x 4), = 166 x 100, = 16600, (c) 8 x 291 x 125, Solution:, 8 x 291 x 125, = (8 x 125) x 291, = 1000 x 291, = 291000, (d) 625 x 279 x 16, Solution:, 625 x 279 x 16, = (625 x 16) x 279, = 10000 x 279, = 2790000, (e) 285 x 5 x 60, Solution:, 285 x 5 x 60, = 285 x (5 x 60), = 285 x 300, = (300 – 15)x 300, = 300 x 300 – 15 x 300, = 90000 – 4500, = 85500, (f) 125 x 40 x 8 x 25, Solution:, 125 x 40 x 8 x 25, = (125 x 8) x (40 x 25), = 1000 X 1000, = 1000000

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Question 3., Find the value of the following:, (а) 297 x 17 + 297 x 3, Solution:, 297 x 17 x 297 x 3, = 297 x (17 + 3), = 297 x 20, = 297 x 2 x 10, = 594 x 10, = 5940, , (б) 54279 x 92 + 8 x 54279, Solution:, 54279 x 92 + 8 x 54279, = 54279 x (92 + 8), = 54279 x 100, = 5427900, (c) 81265 x 169 – 81265 x 69, Solution:, 81265 x 169 – 81265 x 69, = 81265 x (169 – 69), = 81265 x 100, = 8126500, (d) 3845 x 5 x 782 + 769 x 25 x 218, Solution:, 3845 x 5 x 782 + 769 x 25 x 218, = 3845 x 5 x 782 + 769 x 5 x 5 x 218, = 3845 x 5 x 782 + (769 x 5) x 5 x 218, = 3845 x 5 x 782 + 3845 x 5 x 218, = 3845 x 5 x (782 + 218), = 3845 x 5 x 1000, = 19225 x 1000, = 19225000, , Question 4.

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Find the product using suitable properties., (a) 738 x 103, Solution:, 738 x 103, = 738 x (100 + 3), = 738 x 100 + 738 x 3, = 73800 + 2214, = 76014, , [Using distributive property], , (b) 854 x 102, Solution:, 854 x 102, = 854 x (100 + 2), = 854 x 100 + 854 x 2, = 85400 + 1708, = 87108, , [Using distributive property], , (c) 258 x 1008, Solution:, 258 x 1008, = 258 x (1000 + 8), = 258 x 1000 + 258 x 8, = 258000 + 2064, = 260064, , [Using distributive property], , (d) 1005 x 168, Solution:, 1005 x 168, = (1000 + 5) x 168, = 1000 x 168 + 5 x 168, = 168000 + 840, = 168840, , [Using distributive property], , Question 5., A taxidriver filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the, tank with 50 litre of petrol. If the petrol cost ₹44 per litre, how much did he spend in all on petrol?, Solution:

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Petrol filled on Monday, Cost of petrol, , = 40 litres, = Rs 44 per litre, , Petrol filled on Tuesday, Cost of petrol, , = 50 litre, = Rs 44 pet litre, , ∴ Total money spent in all, , = Rs (40 x 44 + 50 x 44), = Rs (40 + 50) x 44, = Rs 90 x 44, = Rs 3960., , Question 6., A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the, milk costs Rs 15 per litre, how much money is due to the vendor per day?, Solution:, Milk supplied in the morning, Cost of milk, Milk supplied in the evening, Cost of milk, , = 32 litres, = Rs 15 per litre, = 68 litres, = Rs 15 per litre, , Total milk supplies in a day, , = 32 + 68 litres, = 100 litres, , Milk costs 1 litre, milk costs 100 litres, , = Rs 15, = Rs 15 x 100, = Rs 1500., , ∴, , Milk costs per day Rs 1500., , Question 7., Match the following:, (i) 425 x 136 = 425 x (6 + 30 + 100), Distributivity of multiplication over addition, (ii) 2 x 49 x 50 = 2 x 50 x 49, Commutativity under multiplication, (iii) 80 + 2005 + 20 = 80 + 20 + 2005, Commutativity under addition, Hence (i) ↔ (c), (ii) ↔ (a) and (iii) ↔ (b)

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Exercise 2.3, Question 1., Which of the following will not represent zero:, (a) 1 + 0, Solution:, 1 + 0 = 1 ≠ 0, does not represent zero, (b) 0 x 0, Solution:, 0 x 0 = 0, represents zero, (c) 02, Solution:, 02 = 0, represents zero., (d) 10−102, Solution:, 10−102 = 02 = 0 represents zero., , Question 2., If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify, through examples., Solution:, Yes, Examples:, 5x0=0, 0x8=0, 0x0=0, Question 3., If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify, through examples., Solution:, This is only true, when each of the number are 1.

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1x1=1, , Question 4., Find using distributive property:, (а) 728 x 101, 728 x 101, = 728 x (100 + 1), = 728 x 100 + 728 x 1, = 72800 + 728, = 73528, (b) 5437 x 1001, 5437 x 1001, = 5437 x (1000 + 1), = 5437 x 1000 + 5437 x 1, = 5437000 + 5437, = 5442437, (c) 824 x 25, 824 x 25, = 824 x (20 + 5), = 824 x 20 + 824 x 5, = 16480 + 4120, = 20600, (d) 4275 x 125, 4275 x 125, = 4275 x (100 + 20 + 5), = 4275 x 100 + 4275 x 20 + 4275 x 5, = 427500 + 85500 + 21375, = 534375, (e) 504 x 35, 504 x 35, = (500 + 4) x 35, = 500 x 35 + 4 x 35, = 17500 + 140, = 17640

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Question 5., Study the pattern:, 1 x 8 + 1= 9, 12 x 8 + 2 = 98, 123 x 8 + 3 = 987, 1234 x 8 + 4 = 9876, 12345 x 8 + 5 = 98765, Write the next two steps. Can you say how the pattern works?, Solution:, Step I: 123456 x 8 + 6 = 987654, Step II: 1234567 x 8 + 7 = 9876543, , Working pattern:, (1) x 8 + 1 = 9, (12) x 8 + 2 = (11 + 1) x 8 + 2 = 98, (123) x 8 + 3 = (111 + 11 + 1) x 8 + 3 = 987, (1234) x 8 + 4 = (1111 + 111 + 11 + 1) x 8 + 4 = 9876, (12345) x 8 + 5 = (11111 + 1111 + 111 + 11 + 1) x 8 + 5 = 98765, , By Kishore Sir