Simplifying a ratio of multivar Simplify. \( \frac{32 a b c}{40 b c} \)

To simplify the ratio \(\frac{32 a b c}{40 b c}\), follow these steps: 1. **Factor the Coefficients:** - Simplify the numerical part \(\frac{32}{40}\). - Both 32 and 40 are divisible by 8: \[ \frac{32 \div 8}{40 \div 8} = \frac{4}{5} \] 2. **Cancel Common Variables:** - The variables \(b\) and \(c\) appear in both the numerator and the denominator. They can be canceled out: \[ \frac{a \cancel{b} \cancel{c}}{\cancel{b} \cancel{c}} = a \] 3. **Combine the Simplified Parts:** - Multiply the simplified numerical coefficient by the remaining variable: \[ \frac{4}{5} \times a = \frac{4a}{5} \] **Final Simplified Form:** \[ \frac{4a}{5} \]