1. **State the problem:** We have a ratio table with two rows, Fruit and Vegetables, and three columns. The values are: Fruit: 2, 3, 6 Vegetables: 6, 12, ☐ (missing value) We need to find the missing value in the Vegetables row and then write the equivalent ratios. 2. **Understand the ratio relationship:** Ratios in the same column are equivalent. That means the ratio of Fruit to Vegetables in each column should be the same. 3. **Set up the ratios:** Column 1: Fruit : Vegetables = 2 : 6 Column 2: Fruit : Vegetables = 3 : 12 Column 3: Fruit : Vegetables = 6 : ☐ 4. **Check the ratio equivalence for columns 1 and 2:** Simplify 2 : 6 = \frac{2}{6} = \frac{1}{3} Simplify 3 : 12 = \frac{3}{12} = \frac{1}{4} Since \frac{1}{3} \neq \frac{1}{4}, the ratios are not equivalent as given. However, the problem states these are equivalent ratios, so we assume the ratios are proportional by a constant multiplier. 5. **Find the multiplier between Fruit values:** From 2 to 3: multiplier is \frac{3}{2} = 1.5 From 3 to 6: multiplier is \frac{6}{3} = 2 Since the multipliers differ, the ratios are not consistent as is. But the problem likely expects us to find missing values assuming proportionality. 6. **Find the missing Vegetables value in column 3:** We use the ratio from column 1 to find the missing value. Set up the proportion: $$\frac{2}{6} = \frac{6}{x}$$ Cross multiply: $$2 \times x = 6 \times 6$$ $$2x = 36$$ Divide both sides by 2: $$\cancel{2}x = \frac{36}{\cancel{2}}$$ $$x = 18$$ 7. **Find the missing Fruit value in column 2:** Set up the proportion: $$\frac{2}{6} = \frac{y}{12}$$ Cross multiply: $$2 \times 12 = 6 \times y$$ $$24 = 6y$$ Divide both sides by 6: $$\cancel{6} \times 4 = \frac{6y}{\cancel{6}}$$ $$4 = y$$ 8. **Write the equivalent ratios:** From the table, the equivalent ratios are: $$2 : 6, 4 : 12, 6 : 18$$ **Final answer:** The missing values are 4 in the Fruit row (second column) and 18 in the Vegetables row (third column). The equivalent ratios are $2 : 6$, $4 : 12$, and $6 : 18$.