To divide 585 by 13 using the method of partial quotients, we start with the following setup:
- Write the dividend (585) and the divisor (13).
- We will estimate how many times 13 can fit into 585 by subtracting multiples of 13 from 585 until we reach a remainder of less than 13.
Here's how the process works:
- Start with 585. We can try subtracting multiples of 13:
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First Subtraction: \[ 585 - 130 = 455 \quad (\text{since } 13 \times 10 = 130) \] We take note that we have subtracted 10 from our partial quotient.
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Second Subtraction: \[ 455 - 130 = 325 \quad (\text{another } 13 \times 10 = 130) \] We now add another 10 to our partial quotient (total: 20).
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Third Subtraction: \[ 325 - 130 = 195 \] Again, we subtract another 10 (total: 30).
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Fourth Subtraction: \[ 195 - 130 = 65 \] Subtracting another 10 gives us a total of 40 so far.
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Fifth Subtraction: \[ 65 - 52 = 13 \quad (\text{since } 13 \times 4 = 52) \] Now, we add 4 to our partial quotient (total: 44).
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Final Subtraction: \[ 13 - 13 = 0 \] Subtracting one time gives us another 1 (total: 45).
Putting this all together, we find that the total we have accumulated in the partial quotients is: \[ 10 + 10 + 10 + 10 + 4 + 1 = 45 \]
Thus, the answer to \( 585 \div 13 \) is \( 45 \).
The correct answer is 45.