Let's go through the division step by step as you've outlined:
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Division Setup:
- We need to divide 127 by 3.
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Expanded Form:
- We write 127 in expanded form: \[ 127 = 100 + 20 + 7 \]
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Regrouping:
- We can regroup the hundreds piece (100) into 10 tens, which gives us: \[ 127 = 10 \times 10 + 20 + 7 = 10 \times 10 + 2 \times 10 + 7 \]
- After regrouping the 100 into tens, we have: \[ 127 = 120 + 7 \]
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Performing the Division:
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We will divide 127 by 3:
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Divide 12 (from 120) by 3: \[ 12 \div 3 = 4 \]
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Now, multiply back to find out how many groups of 3 fit into 12: \[ 4 \times 3 = 12 \]
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Subtract to find the remainder: \[ 12 - 12 = 0 \]
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Bring down the next digit (which is 7), making it 07.
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Now divide 7 by 3: \[ 7 \div 3 = 2 \]
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Multiply back to find out how many groups of 3 fit into 7: \[ 2 \times 3 = 6 \]
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Subtract to find the remainder: \[ 7 - 6 = 1 \]
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Quotient and Remainder:
- The quotient from our division is: \[ 42 \]
- And the remainder is: \[ 1 \]
- So, we can write: \[ 127 \div 3 = 42 \text{ R } 1 \]
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Check the Answer:
- To confirm that our answer is correct, we multiply the quotient by the divisor and add the remainder: \[ 42 \times 3 + 1 \]
- First, multiply: \[ 42 \times 3 = 126 \]
- Then, add the remainder: \[ 126 + 1 = 127 \]
Thus, our answer is confirmed. The final result of dividing 127 by 3 is: \[ 42 \text{ R } 1 \]