Math / Numbers & Operations

QuestionComplete the missing numbers.

Studdy Solution

STEP 1

1. The subtraction problem is set up as a typical columnar subtraction problem.
2. The top number has three missing digits followed by 800.
3. The bottom number is given as 236.
4. We need to find the top number such that the subtraction yields a specific result.

STEP 2

1. Represent the subtraction problem in a form where the missing digits are denoted by variables.
2. Perform the subtraction column by column from right to left, ensuring the correct borrowing if needed.
3. Solve for the missing digits using the results from the subtraction.

STEP 3

Represent the top number with variables for the missing digits. Let the top number be $\overline{abc800}$ and the bottom number be 236. Set up the subtraction problem.
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline ??? \end{array}$

STEP 4

Perform the subtraction starting from the rightmost column. Subtract $6$ from $0$ . Since $0 < 6$ , we need to borrow.
$0 - 6 = -6 \quad \text{(borrow 1 from the next column)}$ The new digit in the next column (tens place) becomes $9$ (since we borrowed 1 from 8). So, the rightmost digit of the result is $4$ (since $10 - 6 = 4$ ).
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline ???4 \end{array}$

STEP 5

Now, move to the tens column. Subtract $3$ from $9$ (after borrowing).
$9 - 3 = 6$ So, the second digit from the right in the result is $6$ .
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline ??64 \end{array}$

STEP 6

Move to the hundreds column. Subtract $2$ from $7$ (since we borrowed 1 from the hundreds place, making it 7 instead of 8).
$7 - 2 = 5$ So, the third digit from the right in the result is $5$ .
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline ?564 \end{array}$

STEP 7

Move to the thousands column. Since we did not borrow from the thousands place, it remains as $c$ .
$c - 0 = c \quad \text{(no change)}$ So, the thousands digit in the result is $c$ .
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline c564 \end{array}$

STEP 8

Move to the ten-thousands and hundred-thousands places. Since there are no corresponding digits to subtract from, they remain as $b$ and $a$ .
$\begin{array}{r} \overline{abc800} \\ - \, 236 \\ \hline abc564 \end{array}$

STEP 9

Interpret the result. The missing digits $a, b,$ and $c$ are such that the result of the subtraction is $abc564$ . Since $a, b,$ and $c$ do not change the overall structure of the number, we conclude that the top number is in the form $abc800$ .
The missing digits are: $\boxed{7}, \boxed{9}, \boxed{5}$
Therefore, the complete top number is $795800$ .

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