Use the quotient property to generate an equivalent expression to 9 3/5 / 9 1/5. What is the simplified exponent.

Answer 1

To simplify the expression \( 9 \frac{3}{5} \div 9 \frac{1}{5} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 9 \frac{3}{5} \): \[ 9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{45}{5} + \frac{3}{5} = \frac{48}{5} \]

2. Convert \( 9 \frac{1}{5} \): \[ 9 \frac{1}{5} = 9 + \frac{1}{5} = \frac{45}{5} + \frac{1}{5} = \frac{46}{5} \]

Now, we can rewrite the division: \[ 9 \frac{3}{5} \div 9 \frac{1}{5} = \frac{48}{5} \div \frac{46}{5} \]

By the property of dividing fractions, we multiply by the reciprocal: \[ \frac{48}{5} \div \frac{46}{5} = \frac{48}{5} \times \frac{5}{46} \]

The \( 5 \) in the numerator and the \( 5 \) in the denominator cancel: \[ \frac{48}{46} \]

Now we simplify this fraction: \[ \frac{48}{46} = \frac{24}{23} \]

Thus, the equivalent expression to \( 9 \frac{3}{5} \div 9 \frac{1}{5} \) simplifies to \( \frac{24}{23} \).

Finally, noting that there are no exponents involved in this computation, there will be no simplified exponent to provide in this context. Therefore, the final answer for the simplified expression is: \[ \frac{24}{23} \]