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Solve the following addition, subtraction and missing digit problems using suitable rearrangement and checking.

Mathematics

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Here are the solutions to the problems:

1. Find the sum of the following numbers by suitable rearrangement.

i) 715+250+335715 + 250 + 335

  1. Group numbers that sum to a multiple of 10 or 100.

    (715+335)+250(715 + 335) + 250
  2. Perform the addition.

    1050+250=13001050 + 250 = \boxed{\text{1300}}

    ii) 829+106+244+121829 + 106 + 244 + 121

  3. Group numbers that sum to a multiple of 10 or 100.

    (829+121)+(106+244)(829 + 121) + (106 + 244)
  4. Perform the additions.

    950+350=1300950 + 350 = \boxed{\text{1300}}

    iii) 488+761+512+239488 + 761 + 512 + 239

  5. Group numbers that sum to a multiple of 10 or 100.

    (488+512)+(761+239)(488 + 512) + (761 + 239)
  6. Perform the additions.

    1000+1000=20001000 + 1000 = \boxed{\text{2000}}

    2. Do the subtraction sums and check your answer by suitable addition.

    i) 70,546−56,92470,546 - 56,924

  7. Perform the subtraction.

    70,546−56,924=13,62270,546 - 56,924 = 13,622
  8. Check the answer by adding the result to the subtrahend.

    13,622+56,924=70,54613,622 + 56,924 = 70,546

    The answer is correct.

    13,622\boxed{\text{13,622}}

    ii) 81,329−76,40881,329 - 76,408

  9. Perform the subtraction.

    81,329−76,408=4,92181,329 - 76,408 = 4,921
  10. Check the answer by adding the result to the subtrahend.

    4,921+76,408=81,3294,921 + 76,408 = 81,329

    The answer is correct.

    4,921\boxed{\text{4,921}}

    3. In the sums given below replace the * with suitable digits.

    i)

  11. Solve for the units column

    5+9=145 + 9 = 14. So, the last ∗* is 4, carry over 1.

  12. Solve for the tens column

    7+6+1(carry over)=147 + 6 + 1 (\text{carry over}) = 14. So, the second to last ∗* is 4, carry over 1.

  13. Solve for the hundreds column

    ∗+5+1(carry over)=9* + 5 + 1 (\text{carry over}) = 9. So, ∗+6=9  ⟹  ∗=3* + 6 = 9 \implies * = 3.

  14. Solve for the thousands column

    2+∗=72 + * = 7. So, ∗=5* = 5.
    The completed sum is:

    2 3 7 5+5 5 6 97 9 4 4\begin{array}{c} 2\,3\,7\,5 \\ + 5\,5\,6\,9 \\ \hline 7\,9\,4\,4 \\ \end{array}

    The missing digits are 3, 5, 4, 4\boxed{\text{3, 5, 4, 4}}.

    ii)

  15. Solve for the units column

    ∗+8=0* + 8 = 0 (meaning 10). So, ∗=2* = 2, carry over 1.

  16. Solve for the tens column

    ∗+6+1(carry over)=2* + 6 + 1 (\text{carry over}) = 2 (meaning 12). So, ∗+7=12  ⟹  ∗=5* + 7 = 12 \implies * = 5, carry over 1.

  17. Solve for the hundreds column

    ∗+4+1(carry over)=0* + 4 + 1 (\text{carry over}) = 0 (meaning 10). So, ∗+5=10  ⟹  ∗=5* + 5 = 10 \implies * = 5, carry over 1.

  18. Solve for the thousands column

    ∗+2+1(carry over)=8* + 2 + 1 (\text{carry over}) = 8. So, ∗+3=8  ⟹  ∗=5* + 3 = 8 \implies * = 5.
    The completed sum is:

    5 5 5 2+2 4 6 88 0 2 0\begin{array}{c} 5\,5\,5\,2 \\ + 2\,4\,6\,8 \\ \hline 8\,0\,2\,0 \\ \end{array}

    The missing digits are 5, 5, 5, 2\boxed{\text{5, 5, 5, 2}}.

    4. Shanu deposited ₹ 1256 in his bank account. Later, he withdrew ₹ 696. How much money was left in his account?

  19. Identify the initial amount and the withdrawn amount.

    Initial amount = ₹ 1256
    Withdrawn amount = ₹ 696

  20. Subtract the withdrawn amount from the initial amount to find the remaining balance.

    1256−696=5601256 - 696 = 560

    The money left in his account is ₹ 560\boxed{\text{₹ 560}}.

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