To solve the problem, we first need to convert the mixed numbers \(3 \frac{1}{4}\) and \(2 \frac{3}{8}\) into improper fractions for easier division.
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Convert \(3 \frac{1}{4}\) to an improper fraction: \[ 3 \frac{1}{4} = 3 \times 4 + 1 = 12 + 1 = \frac{13}{4} \]
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Convert \(2 \frac{3}{8}\) to an improper fraction: \[ 2 \frac{3}{8} = 2 \times 8 + 3 = 16 + 3 = \frac{19}{8} \]
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Now, perform the division: Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{13}{4} \div \frac{19}{8} = \frac{13}{4} \times \frac{8}{19} \]
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Multiply the fractions: \[ \frac{13 \times 8}{4 \times 19} = \frac{104}{76} \]
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Simplify \(\frac{104}{76}\): We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 52. \[ \frac{104 \div 52}{76 \div 52} = \frac{2}{1} \]
Thus, \(3 \frac{1}{4} \div 2 \frac{3}{8} = 2\), which can be represented as a fraction \(\frac{2}{1}\).
Next, we convert this result into the form \(a\) StartFraction \(b\) Over \(c\) EndFraction:
- \(a = 2\), \(b = 2\), \(c = 1\)
From the values given in your question, none of the options match our simplification. However, if we consider the representation:
- The correct answer would indicate that \(a = 2\), \(b = 2\), and \(c = 1\), but this wasn’t provided in the options.
Therefore, based on simplifying \(3 \frac{1}{4}/2 \frac{3}{8}\), no specific option aligns with the result. You may want to double-check the problem setup or provided options. If looking for values that were closest, option consideration might vary, but none directly match the displayed result of \(\frac{2}{1}\).
1 answer