Questions: Solve the proportion equation. 6 2/5 / 11 1/2 = 9 1/4 / n

Solution Steps

To solve the proportion equation, we need to first convert the mixed numbers into improper fractions. Then, we can set up the equation in terms of \( n \) and solve for \( n \) by cross-multiplying and simplifying the resulting equation.

We start by converting the mixed numbers into improper fractions: \[ 6 \frac{2}{5} = \frac{32}{5}, \quad 11 \frac{1}{2} = \frac{23}{2}, \quad 9 \frac{1}{4} = \frac{37}{4} \]

The proportion can be expressed as: \[ \frac{6 \frac{2}{5}}{11 \frac{1}{2}} = \frac{9 \frac{1}{4}}{n} \] Substituting the improper fractions, we have: \[ \frac{\frac{32}{5}}{\frac{23}{2}} = \frac{\frac{37}{4}}{n} \]

Cross-multiplying gives us: \[ 32 \cdot 2 \cdot n = 37 \cdot 5 \cdot 23 \] This simplifies to: \[ 64n = 4255 \] Thus, solving for \( n \): \[ n = \frac{4255}{64} \]

Final Answer