To find the quotient of the fraction \( \frac{2}{3} \div 4 \) using equivalent fractions, we can follow these steps:
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Rewrite the whole number as a fraction: The number 4 can be rewritten as a fraction. Specifically, we can express 4 as \( \frac{4}{1} \).
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Change the division to multiplication by the reciprocal: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{4}{1} \) is \( \frac{1}{4} \). So we can rewrite the expression as: \[ \frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} \]
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Multiply the fractions: Now we multiply the numerators and the denominators: \[ \frac{2 \times 1}{3 \times 4} = \frac{2}{12} \]
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Simplify the fraction: Next, we simplify \( \frac{2}{12} \) by finding the greatest common divisor (GCD) of 2 and 12, which is 2. We divide both the numerator and the denominator by 2: \[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]
Thus, the quotient of \( \frac{2}{3} \div 4 \) is \( \frac{1}{6} \).
In summary, by converting the whole number to a fraction and using multiplication by the reciprocal, we can effectively find the quotient using equivalent fractions.