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Page 1 Exercise 4.2 PAGE: 4.8 1. A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares: (i) (ii) Solution: (i) We know that Considering diagonal values 13 + 12 + 11 = 36 So we get No. in the first cell of the first row = 36 – (8 + 13) = 15 No. in the first cell of the second row = 36 – (15 + 11) = 10 No. in the third cell of the second row = 36 – (10 + 12) = 14 No. in the second cell of the third row = 36 – (8 + 12) = 16 No. in the third cell of the third row = 36 – (11 + 16) = 9 (ii) We know that Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 So we get No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 Page 2 Exercise 4.2 PAGE: 4.8 1. A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares: (i) (ii) Solution: (i) We know that Considering diagonal values 13 + 12 + 11 = 36 So we get No. in the first cell of the first row = 36 – (8 + 13) = 15 No. in the first cell of the second row = 36 – (15 + 11) = 10 No. in the third cell of the second row = 36 – (10 + 12) = 14 No. in the second cell of the third row = 36 – (8 + 12) = 16 No. in the third cell of the third row = 36 – (11 + 16) = 9 (ii) We know that Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 So we get No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 2. Perform the following subtractions and check your results by performing corresponding additions: (i) 57839 – 2983 (ii) 92507 – 10879 (iii) 400000 – 98798 (iv) 5050501 – 969696 (v) 200000 – 97531 (vi) 3030301 – 868686 Solution: (i) 57839 – 2983 We know that 57839 – 2983 = 54856 By addition 54856 + 2983 = 57839 (ii) 92507 – 10879 We know that 92507 – 10879 = 81628 By addition 81628 + 10879 = 92507 (iii) 400000 – 98798 We know that 400000 – 98798 = 301202 By addition 301202 + 98798 = 400000 (iv) 5050501 – 969696 We know that 5050501 – 969696 = 4080805 By addition 4080805 + 969696 = 5050501 (v) 200000 – 97531 We know that 200000 – 97531 = 102469 By addition 102469 + 97531 = 200000 (vi) 3030301 – 868686 We know that Page 3 Exercise 4.2 PAGE: 4.8 1. A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares: (i) (ii) Solution: (i) We know that Considering diagonal values 13 + 12 + 11 = 36 So we get No. in the first cell of the first row = 36 – (8 + 13) = 15 No. in the first cell of the second row = 36 – (15 + 11) = 10 No. in the third cell of the second row = 36 – (10 + 12) = 14 No. in the second cell of the third row = 36 – (8 + 12) = 16 No. in the third cell of the third row = 36 – (11 + 16) = 9 (ii) We know that Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 So we get No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 2. Perform the following subtractions and check your results by performing corresponding additions: (i) 57839 – 2983 (ii) 92507 – 10879 (iii) 400000 – 98798 (iv) 5050501 – 969696 (v) 200000 – 97531 (vi) 3030301 – 868686 Solution: (i) 57839 – 2983 We know that 57839 – 2983 = 54856 By addition 54856 + 2983 = 57839 (ii) 92507 – 10879 We know that 92507 – 10879 = 81628 By addition 81628 + 10879 = 92507 (iii) 400000 – 98798 We know that 400000 – 98798 = 301202 By addition 301202 + 98798 = 400000 (iv) 5050501 – 969696 We know that 5050501 – 969696 = 4080805 By addition 4080805 + 969696 = 5050501 (v) 200000 – 97531 We know that 200000 – 97531 = 102469 By addition 102469 + 97531 = 200000 (vi) 3030301 – 868686 We know that 3030301 – 868686 = 2161615 By addition 2161615 + 868686 = 3030301 3. Replace each * by the correct digit in each of the following: (i) (ii) (iii) (iv) (v) (vi) Solution: (i) We know that in the units digit 6  * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place 6 at the units place becomes 16 so 16 – 9 = 7 When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 We know that 8  * = 6 so we get * value as 2 (ii) We know that in the units digit Page 4 Exercise 4.2 PAGE: 4.8 1. A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares: (i) (ii) Solution: (i) We know that Considering diagonal values 13 + 12 + 11 = 36 So we get No. in the first cell of the first row = 36 – (8 + 13) = 15 No. in the first cell of the second row = 36 – (15 + 11) = 10 No. in the third cell of the second row = 36 – (10 + 12) = 14 No. in the second cell of the third row = 36 – (8 + 12) = 16 No. in the third cell of the third row = 36 – (11 + 16) = 9 (ii) We know that Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 So we get No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 2. Perform the following subtractions and check your results by performing corresponding additions: (i) 57839 – 2983 (ii) 92507 – 10879 (iii) 400000 – 98798 (iv) 5050501 – 969696 (v) 200000 – 97531 (vi) 3030301 – 868686 Solution: (i) 57839 – 2983 We know that 57839 – 2983 = 54856 By addition 54856 + 2983 = 57839 (ii) 92507 – 10879 We know that 92507 – 10879 = 81628 By addition 81628 + 10879 = 92507 (iii) 400000 – 98798 We know that 400000 – 98798 = 301202 By addition 301202 + 98798 = 400000 (iv) 5050501 – 969696 We know that 5050501 – 969696 = 4080805 By addition 4080805 + 969696 = 5050501 (v) 200000 – 97531 We know that 200000 – 97531 = 102469 By addition 102469 + 97531 = 200000 (vi) 3030301 – 868686 We know that 3030301 – 868686 = 2161615 By addition 2161615 + 868686 = 3030301 3. Replace each * by the correct digit in each of the following: (i) (ii) (iii) (iv) (v) (vi) Solution: (i) We know that in the units digit 6  * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place 6 at the units place becomes 16 so 16 – 9 = 7 When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 We know that 8  * = 6 so we get * value as 2 (ii) We know that in the units digit 9 – 4 = 5 Tens digit 8 – 3 = 5 So the missing blank can be found by subtracting 3455 from 8989 Difference between them = 3455 So the answer is (iii) We know that in units digit 17 – 8 = 9 Tens digit = 9 – 7 = 2 So we get Hundreds place 10 – 9 = 1 Thousands place 9 – 8 = 1 So the addend difference = 5061129 Subtract 5061129 from 6000107 to get addend So the answer is (iv) We know that in units digit 10 – 1 = 9 Lakhs place 9 – 0 = 9 So the addend difference = 970429 Subtract 970429 from 1000000 to get the addend So the correct answer is (v) We know that in units digit 13 – 7 = 6 Tens digit 9 – 8 = 1 Hundreds place 9 – 9 = 0 Thousands place 10 – 6 = 4 So the addend difference = 4844016 Page 5 Exercise 4.2 PAGE: 4.8 1. A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic squares: (i) (ii) Solution: (i) We know that Considering diagonal values 13 + 12 + 11 = 36 So we get No. in the first cell of the first row = 36 – (8 + 13) = 15 No. in the first cell of the second row = 36 – (15 + 11) = 10 No. in the third cell of the second row = 36 – (10 + 12) = 14 No. in the second cell of the third row = 36 – (8 + 12) = 16 No. in the third cell of the third row = 36 – (11 + 16) = 9 (ii) We know that Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 So we get No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 2. Perform the following subtractions and check your results by performing corresponding additions: (i) 57839 – 2983 (ii) 92507 – 10879 (iii) 400000 – 98798 (iv) 5050501 – 969696 (v) 200000 – 97531 (vi) 3030301 – 868686 Solution: (i) 57839 – 2983 We know that 57839 – 2983 = 54856 By addition 54856 + 2983 = 57839 (ii) 92507 – 10879 We know that 92507 – 10879 = 81628 By addition 81628 + 10879 = 92507 (iii) 400000 – 98798 We know that 400000 – 98798 = 301202 By addition 301202 + 98798 = 400000 (iv) 5050501 – 969696 We know that 5050501 – 969696 = 4080805 By addition 4080805 + 969696 = 5050501 (v) 200000 – 97531 We know that 200000 – 97531 = 102469 By addition 102469 + 97531 = 200000 (vi) 3030301 – 868686 We know that 3030301 – 868686 = 2161615 By addition 2161615 + 868686 = 3030301 3. Replace each * by the correct digit in each of the following: (i) (ii) (iii) (iv) (v) (vi) Solution: (i) We know that in the units digit 6  * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place 6 at the units place becomes 16 so 16 – 9 = 7 When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 We know that 8  * = 6 so we get * value as 2 (ii) We know that in the units digit 9 – 4 = 5 Tens digit 8 – 3 = 5 So the missing blank can be found by subtracting 3455 from 8989 Difference between them = 3455 So the answer is (iii) We know that in units digit 17 – 8 = 9 Tens digit = 9 – 7 = 2 So we get Hundreds place 10 – 9 = 1 Thousands place 9 – 8 = 1 So the addend difference = 5061129 Subtract 5061129 from 6000107 to get addend So the answer is (iv) We know that in units digit 10 – 1 = 9 Lakhs place 9 – 0 = 9 So the addend difference = 970429 Subtract 970429 from 1000000 to get the addend So the correct answer is (v) We know that in units digit 13 – 7 = 6 Tens digit 9 – 8 = 1 Hundreds place 9 – 9 = 0 Thousands place 10 – 6 = 4 So the addend difference = 4844016 Subtract 4844016 from 5001003 to get the addend So the answer is (vi) We know that units digit 11 – 9 = 2 So the addend difference = 54322 Subtract 54322 from 111111 to get the addend So the answer is 4. What is the difference between the largest number of five digits and the smallest number of six digits? Solution: 99999 is the largest number of five digits 100000 is the largest number of six digits Difference = 100000 – 99999 = 1 Therefore, 1 is the difference between the largest number of five digits and smallest number of six digits. 5. Find the difference between the largest number of 4 digits and the smallest number of 7 digits. Solution: 9999 is the largest number of 4 digits 1000000 is the smallest number of 6 digits Difference = 1000000 – 9999 = 990001 Therefore, 990001 is the difference between the largest number of 4 digits and the smallest number of 7 digits. 6. Rohit deposited Rs 125000 in his savings bank account. Later he withdrew Rs 35425 from it. How much money was left in his account? Solution: Money deposited in savings bank account = Rs 125000 Money withdrawn = Rs 35425Read More
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