Subjects arithmetic

Missing Digits Subtraction

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Missing Digits Subtraction


1. **State the problem:** We have the subtraction: $$87,031 - 2[\square],669 = [\square]2,36[\square]$$ We need to find the missing digits represented by $\square$. 2. **Analyze the given digits:** The subtraction is: $$87,031 - 2a,669 = b2,36c$$ where $a$, $b$, and $c$ are the missing digits. 3. **Subtract digits from right to left:** Units digit: $1 - 9$ is not possible without borrowing. Borrow $1$ from the tens place (which is $3$), now tens place digit is $2$ and units place becomes $11$. Units: $11 - 9 = 2$ So the units digit of the result $c = 2$. 4. **Tens digit:** After borrowing tens digit is $2$. We calculate: $2 - 6 = ?$ Again $2 < 6$ so we need to borrow 1 from the hundreds place (which is $0$). Hundreds digit is $0$ so we need to borrow 1 from the thousands place. Thousands digit is $7$, after borrowing it becomes $6$. Hundreds place now is $10$ (due to borrow), and we borrow 1 from hundreds to tens. Tens digit now is $12$. Tens: $12 - 6 = 6$ So the tens digit of the result $6$ matches the given $6$ at that place. 5. **Hundreds digit:** Hundreds place after borrowing from thousands is $9$ (10 original + borrowed 10 -1 borrow to tens): $9 - 6 = 3$ The hundreds digit of the answer is $3$, matching provided. 6. **Thousands digit:** Thousands place is $6 - 2a$', where $a$ is unknown. Result thousands digit is $2$, so: $6 - 2a = 2$ Since $2a$ represents a digit in the number $2a,669$, the digit $a$ is the missing digit to find. So: $6 - a = 2$ $\Rightarrow a = 4$ Because $2a$ is two digits: 2 and $a=4$. 7. **Ten-thousands digit:** Ten-thousands digit subtraction: $8 - 2 = b$ So $b = 6$ 8. **Hundred-thousands digit:** There is no digit in hundred-thousands place of subtracted number, so we assume it is $0$. Answer’s hundred-thousands digit is missing, indicated as $b=6$ in step 7. 9. **Fill in all missing digits:** Missing digits are: $\boxed{4}$ for the missing digit in the subtracted number ($2[4],669$) $\boxed{6}$ as the first digit of the answer ($62,362$) $\boxed{2}$ as the last digit of the answer (already found in units place) 10. **Final subtraction:** $$87,031 - 24,669 = 62,362$$ **Answer:** The missing digits are $4$, $6$, and $2$ respectively.