To solve \( 4 \frac{1}{2} \div 1 \frac{1}{4} \), we first convert the mixed numbers into improper fractions.
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Convert \( 4 \frac{1}{2} \): \[ 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \]
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Convert \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]
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Perform the division: \[ \frac{9}{2} \div \frac{5}{4} = \frac{9}{2} \times \frac{4}{5} = \frac{9 \times 4}{2 \times 5} = \frac{36}{10} \]
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Simplify the fraction: \[ \frac{36}{10} = \frac{18}{5} \]
Now, we have \( \frac{18}{5} \). To represent this in the format \( \text{StartFraction} b \text{Over} c \text{EndFraction} \), we see that \( a = 3 \), \( b = 18 \), and \( c = 5 \).
However, none of the provided options match \( a = 3, b = 18, c = 5 \). Let's analyze them:
- Option 1: \( a = 3, b = 6, c = 10 \) corresponds to \( \frac{6}{10} = \frac{3}{5} \).
- Option 2: \( a = 3, b = 3, c = 5 \) corresponds to \( \frac{3}{5} \).
- Option 3: \( a = 5, b = 3, c = 3 \) corresponds to \( \frac{3}{3} = 1 \).
None of these options match \( \frac{18}{5} \). Therefore, none of the values of \( a \), \( b \), and \( c \) provided represent the answer in the correct simplest form based on the given problem.
The correct answer in simplest form is \( a = 3, b = 18, c = 5 \).
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