Subjects algebra

Ratio Table Aea048

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1. **State the problem:** We have a ratio table with two columns. The first column is 12, 24, 48, 72, 84 and the second column is 11, ?, 44, 66, ?. We need to find the missing values in the second column to complete the ratio table. 2. **Understand the ratio:** The ratio between the two columns should be constant. That means \( \frac{\text{second column}}{\text{first column}} \) is the same for all rows. 3. **Find the constant ratio:** Using the first row, the ratio is \( \frac{11}{12} \). 4. **Use the ratio to find missing values:** - For the second row: $$\text{second column} = 24 \times \frac{11}{12}$$ - Simplify: $$24 \times \frac{11}{12} = \cancel{24}^2 \times \frac{11}{\cancel{12}^6} = 2 \times 11 = 22$$ - For the fifth row: $$\text{second column} = 84 \times \frac{11}{12}$$ - Simplify: $$84 \times \frac{11}{12} = \cancel{84}^7 \times \frac{11}{\cancel{12}^1} = 7 \times 11 = 77$$ 5. **Final answer:** The missing values are 22 and 77. Thus, the completed ratio table second column is: 11, 22, 44, 66, 77.