To divide the fraction \( \frac{2}{3} \) by 4, we can use equivalent fractions to make the division easier. The process involves the following steps:
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Rewrite the Whole Number as a Fraction: First, we convert the whole number 4 into a fraction. Any whole number can be expressed as a fraction by placing it over 1: \[ 4 = \frac{4}{1} \]
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Change the Division to Multiplication: When dividing by a fraction, we multiply by its reciprocal. The reciprocal of \( \frac{4}{1} \) is \( \frac{1}{4} \). Thus, we can rewrite the division as: \[ \frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} \]
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Multiply the Fractions: Now, we can multiply the two fractions: \[ \frac{2 \times 1}{3 \times 4} = \frac{2}{12} \]
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Simplify the Resulting Fraction: Finally, we simplify \( \frac{2}{12} \) by finding the greatest common divisor (GCD) of the numerator and denominator, which is 2: \[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]
So, the quotient of \( \frac{2}{3} \div 4 \) is \( \frac{1}{6} \).
Using equivalent fractions allows us to transform the division into a multiplication problem, making it easier to compute the result.