To divide fractions, you can follow these steps:
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Write the problem: You're asked to divide \(\frac{1}{3}\) by \(\frac{4}{3}\), which can be written mathematically as: \[ \frac{1}{3} \div \frac{4}{3} \]
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Multiply by the reciprocal: Instead of dividing by a fraction, you can multiply by its reciprocal. The reciprocal of \(\frac{4}{3}\) is \(\frac{3}{4}\). Therefore, we rewrite the division as: \[ \frac{1}{3} \times \frac{3}{4} \]
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Multiply the fractions: To multiply the two fractions, multiply the numerators and the denominators: \[ \frac{1 \times 3}{3 \times 4} = \frac{3}{12} \]
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Simplify the fraction: The fraction \(\frac{3}{12}\) can be simplified. Both the numerator and the denominator can be divided by their greatest common divisor, which is 3: \[ \frac{3 \div 3}{12 \div 3} = \frac{1}{4} \]
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Conclusion: The quotient of \(\frac{1}{3} \div \frac{4}{3}\) is \(\frac{1}{4}\).
Thus, the final answer is: \[ \frac{1}{4} \]
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