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Find the missing digits in the subtraction problems.

Mathematics

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Answers

2 parts
b

8, 8, 4\text{8, 8, 4}

c

7, 7, 3\text{7, 7, 3}

Step-by-step solution

10 steps

Let's find the missing digits for the subtraction problems.

Part b· 5 steps

We need to find the missing digits in the subtrahend (the number being subtracted).

TThThHTO96347−42__12063\begin{array}{ccccc} \text{TTh} & \text{Th} & \text{H} & \text{T} & \text{O} \\ 9 & 6 & 3 & 4 & 7 \\ - & 4 & 2 & \_ & \_ \\ \hline 1 & 2 & 0 & 6 & 3 \\ \end{array}
  1. Find the missing digit in the Ones (O) column.

    We have 7 - \text{_} = 3.
    So, the missing digit is 7−3=47 - 3 = 4.

  2. Find the missing digit in the Tens (T) column.

    We have 4 - \text{_} = 6. Since 4<64 < 6, we need to borrow from the Hundreds column. The 4 becomes 14.
    So, 14 - \text{_} = 6.
    The missing digit is 14−6=814 - 6 = 8.

  3. Check the Hundreds (H) column.

    The 3 in the Hundreds column became 2 after borrowing for the Tens column.
    We have 2−2=02 - 2 = 0. This matches the result.

  4. Check the Thousands (Th) column.

    We have 6−4=26 - 4 = 2. This matches the result.

  5. Find the missing digit in the Ten Thousands (TTh) column.

    We have 9 - \text{_} = 1.
    So, the missing digit is 9−1=89 - 1 = 8.

    The completed subtraction for (b) is:

    TThThHTO96347−8428412063\begin{array}{ccccc} \text{TTh} & \text{Th} & \text{H} & \text{T} & \text{O} \\ 9 & 6 & 3 & 4 & 7 \\ - 8 & 4 & 2 & 8 & 4 \\ \hline 1 & 2 & 0 & 6 & 3 \\ \end{array}

    The missing digits are 8, 8, 4\boxed{\text{8, 8, 4}}.

Part c

7, 7, 3\text{7, 7, 3}

We need to find the missing digits in the minuend (the top number).

\begin{array}{ccccc} \text{TTh} & \text{Th} & \text{H} & \text{T} & \text{O} \\ \text{_} & 5 & \_ & 4 & \_ \\ - 2 & 9 & 3 & 8 & 1 \\ \hline 4 & 6 & 3 & 6 & 2 \\ \end{array}
  1. Find the missing digit in the Ones (O) column.

    We have \text{_} - 1 = 2.
    So, the missing digit is 2+1=32 + 1 = 3.

  2. Check the Tens (T) column.

    We have 4−8=64 - 8 = 6. This means we borrowed from the Hundreds column. The 4 became 14.
    So, 14−8=614 - 8 = 6. This matches the result.

  3. Find the missing digit in the Hundreds (H) column.

    Let the missing digit be AA. Since we borrowed 1 from it for the Tens column, it became A−1A-1.
    We have (A−1)−3=3(A-1) - 3 = 3.
    So, A−1=3+3=6A-1 = 3 + 3 = 6.
    Therefore, A=6+1=7A = 6 + 1 = 7.

  4. Check the Thousands (Th) column.

    We have 5−9=65 - 9 = 6. This means we borrowed from the Ten Thousands column. The 5 became 15.
    So, 15−9=615 - 9 = 6. This matches the result.

  5. Find the missing digit in the Ten Thousands (TTh) column.

    Let the missing digit be XX. Since we borrowed 1 from it for the Thousands column, it became X−1X-1.
    We have (X−1)−2=4(X-1) - 2 = 4.
    So, X−1=4+2=6X-1 = 4 + 2 = 6.
    Therefore, X=6+1=7X = 6 + 1 = 7.

    The completed subtraction for (c) is:

    TThThHTO75743−2938146362\begin{array}{ccccc} \text{TTh} & \text{Th} & \text{H} & \text{T} & \text{O} \\ 7 & 5 & 7 & 4 & 3 \\ - 2 & 9 & 3 & 8 & 1 \\ \hline 4 & 6 & 3 & 6 & 2 \\ \end{array}

    The missing digits are 7, 7, 3\boxed{\text{7, 7, 3}}.

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