1. **State the problem:** We have 7 cups of beans and 1 cup of rice. 2. **Part-to-part ratio of beans to rice:** This ratio compares the amount of beans directly to the amount of rice. $$\text{Beans : Rice} = 7 : 1$$ 3. **Part-to-whole ratio of beans to total cups:** The total cups is beans plus rice. $$\text{Total cups} = 7 + 1 = 8$$ So the part-to-whole ratio of beans to total is: $$\text{Beans : Total} = 7 : 8$$ 4. **Proportion of beans to the whole as a fraction in simplest terms:** This is the fraction of beans out of the total cups. $$\text{Proportion} = \frac{7}{8}$$ Since 7 and 8 have no common factors other than 1, the fraction is already in simplest terms. **Final answers:** - Part-to-part ratio (beans to rice): $7:1$ - Part-to-whole ratio (beans to total): $7:8$ - Proportion of beans to whole (fraction): $\frac{7}{8}$