To find the quotient of the fractions \( \frac{1}{3} \) and \( \frac{4}{3} \), follow these steps:
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Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
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Write the Expression: Start with the division of fractions: \[ \frac{1}{3} \div \frac{4}{3} \]
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Convert to Multiplication: Change the division to multiplication by using the reciprocal of \( \frac{4}{3} \): \[ \frac{1}{3} \div \frac{4}{3} = \frac{1}{3} \times \frac{3}{4} \]
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Multiply the Numerators and the Denominators: Multiply the numerators together and the denominators together: \[ \frac{1 \times 3}{3 \times 4} = \frac{3}{12} \]
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Simplify the Result: Now, simplify \( \frac{3}{12} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3: \[ \frac{3 \div 3}{12 \div 3} = \frac{1}{4} \]
Thus, the quotient of \( \frac{1}{3} \div \frac{4}{3} \) is \( \frac{1}{4} \).