Question

enter a digit in each box to complete the division problem.
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$$\begin{array}{r}\\ 3\\ 1\\ \\square\\ \\text{r}7\\\\ 8\\overline{)2\\ \\square\\ 2\\ 7}\\\\ -2\\ 4\\ \\ \\ \\ \\ \\ \\ \\\\ \\hline \\ \\ \\ 1\\ 2\\ \\ \\ \\ \\\\ -\\ \\ \\ \\ 8\\ \\ \\ \\\\ \\hline \\ \\ \\ \\ \\square\\ 7\\\\ -\\ \\ \\ 4\\ 0\\\\ \\hline \\ \\ \\ \\ \\ \\ \\ 7\\end{array}$$

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Explanation:

Step1: Find the final dividend digit

We know that after subtracting 40 from the two-digit number ending in 7, we get 7. Let the tens digit be $x$. So $10x + 7 - 40 = 7$. Rearranged: $10x = 40$, so $x=4$.

Step2: Find the quotient's final digit

The divisor is 8, and we multiplied it by this digit to get 40. Let the digit be $y$. So $8y=40$, so $y=\frac{40}{8}=5$.

Step3: Find the dividend's thousands digit

First, calculate the remainder after first subtraction: $24$ is subtracted from the first two digits of the dividend. The result is 1, so the first two digits of the dividend are $24 + 1 = 25$. So the missing digit is 5.

Answer:

• Quotient missing digit: 5
• Dividend missing digit: 5
• Final subtraction missing digit: 4

Completed division:

    3 1 5 R7
8 |2,5 2 7
  -2 4
  -----
    1 2
  -   8
  -----
      4 7
    - 4 0
    -----
        7