This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To subtract numbers in base 8, we perform column-by-column subtraction, borrowing from the left when necessary. When we borrow 1 from a column, it adds 8 to the value of the digit in the current column. We need to calculate 73761_8 - 72777_8. Step 1: Subtract the rightmost column (units place). We have 1_8 - 7_8. Since 1 < 7, we borrow from the 6_8 in the next column. The 6_8 becomes 5_8. The 1_8 becomes 1+8 = 9_10. Now, 9_10 - 7_10 = 2_10. So the units digit is 2_8. Step 2: Subtract the next column (eights place). We now have 5_8 - 7_8. Since 5 < 7, we borrow from the 7_8 in the next column. The 7_8 becomes 6_8. The 5_8 becomes 5+8 = 13_10. Now, 13_10 - 7_10 = 6_10. So the eights digit is 6_8. Step 3: Subtract the next column (8^2 place). We now have 6_8 - 7_8. Since 6 < 7, we borrow from the 3_8 in the next column. The 3_8 becomes 2_8. The 6_8 becomes 6+8 = 14_10. Now, 14_10 - 7_10 = 7_10. So the 8^2 digit is 7_8. Step 4: Subtract the next column (8^3 place). We now have 2_8 - 2_8. 2_8 - 2_8 = 0_8. So the 8^3 digit is 0_8. Step 5: Subtract the leftmost column (8^4 place). We have 7_8 - 7_8. 7_8 - 7_8 = 0_8. So the 8^4 digit is 0_8. Combining the results from right to left: cccccc & 7 & 3 & 7 & 6 & 1_8 \\ & 7 & 2 & 7 & 7 & 7_8 \\ & 0 & 0 & 7 & 6 & 2_8 \\ The result is 00762_8, which simplifies to 762_8. The final answer is 762_8. That's 2 down. 3 left today — send the next one.