Find 3 ratios that are equivalent to the given ratio. \( 35: 40 \) Find three ratios that are equivalent to the given ratio. \( \begin{array}{ll}\square \text { A. } 7: 80 & \square \text { B. } 105: 8 \\ \square \text { C. } 7: 120 & \square \text { D. } 70: 8 \\ \square \text { E. } 7: 8 & \square \text { F. } 70: 120 \\ \text { G. } 105: 120 & \square \text { H. } 70: 80\end{array} \)

To determine which of the given ratios are equivalent to \(35:40\), let's first simplify \(35:40\). 1. **Simplify \(35:40\):** - Find the greatest common divisor (GCD) of 35 and 40, which is 5. - Divide both terms by the GCD: \[ \frac{35}{5} : \frac{40}{5} = 7:8 \] - So, the simplified ratio is \(7:8\). 2. **Check Each Given Ratio:** Each equivalent ratio must simplify to \(7:8\). - **A. \(7:80\)** \[ \frac{7}{80} \neq \frac{7}{8} \quad \text{(Not equivalent)} \] - **B. \(105:8\)** \[ \frac{105}{8} \neq \frac{7}{8} \quad \text{(Not equivalent)} \] - **C. \(7:120\)** \[ \frac{7}{120} \neq \frac{7}{8} \quad \text{(Not equivalent)} \] - **D. \(70:8\)** \[ \frac{70}{8} \neq \frac{7}{8} \quad \text{(Not equivalent)} \] - **E. \(7:8\)** \[ \frac{7}{8} = \frac{7}{8} \quad \text{(Equivalent)} \] - **F. \(70:120\)** \[ \frac{70}{120} = \frac{7}{12} \neq \frac{7}{8} \quad \text{(Not equivalent)} \] - **G. \(105:120\)** \[ \frac{105}{120} = \frac{7}{8} \quad \text{(Equivalent)} \] - **H. \(70:80\)** \[ \frac{70}{80} = \frac{7}{8} \quad \text{(Equivalent)} \] 3. **Conclusion:** The ratios that are equivalent to \(35:40\) are: - **E. \(7:8\)** - **G. \(105:120\)** - **H. \(70:80\)** **Answer:** Equivalent ratios are E. 7 : 8, G. 105 : 120, and H. 70 : 80.