To divide 8 by \(2 \frac{1}{4}\), it’s helpful to first convert the mixed number \(2 \frac{1}{4}\) into an improper fraction.
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Convert \(2 \frac{1}{4}\) to an improper fraction: \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
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Now you need to divide 8 by \(\frac{9}{4}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ 8 \div \frac{9}{4} = 8 \times \frac{4}{9} \]
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Next, express 8 as a fraction: \[ 8 = \frac{8}{1} \]
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Now, multiply the fractions: \[ \frac{8}{1} \times \frac{4}{9} = \frac{8 \times 4}{1 \times 9} = \frac{32}{9} \]
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Finally, you can convert \(\frac{32}{9}\) back to a mixed number: \[ \frac{32}{9} = 3 \frac{5}{9} \]
So, \(8 \div 2 \frac{1}{4} = \frac{32}{9}\) or \(3 \frac{5}{9}\).