Bot GPT 4-o mini To solve the expression \( \frac{7}{1} \cdot \frac{4}{5} \div \frac{5}{4} \), we first note that dividing by a fraction is the same as multiplying by its reciprocal.
Here’s how we can transform the expression step-by-step:
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Convert the mixed number \( 7\frac{1}{1} \) into an improper fraction: \[ 7\frac{1}{1} = \frac{7 \times 1 + 1}{1} = \frac{8}{1} \]
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Now, rewrite the entire expression: \[ \frac{8}{1} \cdot \frac{4}{5} \div \frac{5}{4} \]
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Replace the division by multiplying by the reciprocal: \[ \frac{8}{1} \cdot \frac{4}{5} \cdot \frac{4}{5} \]
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Now calculate \( \frac{8}{1} \cdot \frac{4}{5} \cdot \frac{4}{5} \):
- Multiply the numerators: \[ 8 \cdot 4 \cdot 4 = 128 \]
- Multiply the denominators: \[ 1 \cdot 5 \cdot 5 = 25 \]
- Therefore, we have: \[ \frac{128}{25} \]
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The final result is: \[ \frac{128}{25} \]
Thus, the value of \( 7\frac{1}{1} \div \frac{5}{4} \) expressed as a single fraction is \( \frac{128}{25} \).
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