To simplify the expression \( 12 - 4 \div 4 / 3 + 1 \), we need to follow the order of operations (PEMDAS/BODMAS):
- Perform division from left to right.
- Then, perform addition and subtraction from left to right.
Let's break it down step by step:
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Start with the expression: \[ 12 - 4 \div 4 / 3 + 1 \]
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Perform \( 4 \div 4 \): \[ 4 \div 4 = 1 \] Now replace \( 4 \div 4 \) in the expression: \[ 12 - 1 / 3 + 1 \]
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Next, perform \( 1 / 3 \): \[ 1 / 3 = \frac{1}{3} \] Now the expression becomes: \[ 12 - \frac{1}{3} + 1 \]
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Now, simplify \( 12 + 1 \): \[ 12 + 1 = 13 \] Replace it in the expression: \[ 13 - \frac{1}{3} \]
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To perform \( 13 - \frac{1}{3} \), convert 13 into a fraction: \[ 13 = \frac{39}{3} \] Now subtract: \[ \frac{39}{3} - \frac{1}{3} = \frac{39 - 1}{3} = \frac{38}{3} \]
Thus, the simplified result is: \[ \frac{38}{3} \]