Example Question - base 7 subtraction
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Base 7 Number Subtraction
The image shows a math problem asking to determine the difference between two numbers in base 7. The problem is: \( 6412_{seven} - 5603_{seven} \) To find the difference, we'll subtract the numbers just like we do in base 10, but we need to remember that we're working in base 7, which means that instead of "carrying over" when we reach 10 as in base 10, we do so when we reach 7. Here's a step-by-step subtraction: Starting from the right (the units place): 2 (in base 7) - 3 (in base 7) cannot be done without borrowing since 2 is less than 3. In base 7, borrowing means that we take 1 from the next higher place value, which is normally equivalent to the base we're using, so we take 7 (in base 7) and add it to the 2. Before we do that, we reduce 1 in the next column to the left. So the number becomes: \( (6402_{seven} + 7_{seven}) - 5603_{seven} \), which is, \( 640(2+7)_{seven} - 5603_{seven} \), or, \( 6409_{seven} - 5603_{seven} \). Now, let's try subtracting again: Units place: 9 (in base 7) - 3 (in base 7) = 6 (in base 7) Tens place: 0 (in base 7) - 0 (in base 7) = 0 (in base 7) Hundreds place: 4 (in base 7) - 6 (in base 7) cannot be done without borrowing. Borrowing 1 from the next column, the thousands place, we have: \( 5(40_{seven} + 7_{seven}) - 5603_{seven} \), which is, \( 5(47_{seven}) - 5603_{seven} \). Now, the subtraction looks like this: Hundreds place: \( 47_{seven} - 6_{seven} \) = \( 41_{seven} \) (we converted the hundreds place, 4, to 47 by borrowing 1 from the thousands column and reduced the thousands place by 1). Thousands place: 5 - 5 (in base 7) = 0 (in base 7) So, adding the results from each place, we get: \( 6412_{seven} - 5603_{seven} = 406_{seven} \). The answer is \( 406_{seven} \).
Base 7 Subtraction Calculation
The question asks to determine the difference between 6442 in base 7 and 5603 in base 7. To perform the subtraction, we need to subtract each digit, starting from the rightmost and moving to the left. If a digit in the subtrahend is larger than the digit in the minuend, we need to borrow from the next left digit in the minuend. Starting from the ones place: 2 (base 7) - 3 (base 7) cannot be done directly because 2 is less than 3, so we borrow from the next digit. 12 (base 7) - 3 (base 7) = 6 Moving to the tens place, since we have borrowed 1 from it: 3 (base 7) becomes 2 (base 7) now. 4 (base 7) - 0 (base 7) remains as is, since there's nothing to subtract. 2 (base 7) - 2 (base 7) = 0 Next, the hundreds place: 4 (base 7) - 6 (base 7) cannot be done directly, so we borrow from the next digit. 14 (base 7) - 6 (base 7) = 8 (since when we borrow in base 7, we're borrowing a group of 7, 7 + 4 = 11, but we're in base 7, so it reads as 14). For the thousands place: 6 (base 7) becomes 5 (base 7) because we just borrowed 1. 5 (base 7) - 5 (base 7) = 0 Write down the digits we've calculated from right to left to find the answer: (0)8076 (base 7) Therefore, the difference is 8076 in base 7.
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