1. **State the problem:** We have a ratio table with two columns. The left column is 5, 25, 50, 75, 80 and the right column has 6, blank, blank, 90, blank. We need to complete the missing values in the right column so that the ratios between the left and right columns remain consistent. 2. **Identify the ratio:** The first pair is 5 and 6, so the ratio is $\frac{5}{6}$. 3. **Use the ratio to find missing values:** For each left value $L$, the corresponding right value $R$ satisfies $\frac{L}{R} = \frac{5}{6}$. 4. **Calculate each missing right value:** - For $L=25$, solve $\frac{25}{R} = \frac{5}{6}$. Multiply both sides by $R$ and then by 6: $$25 \times 6 = 5 \times R$$ $$150 = 5R$$ Divide both sides by 5: $$\cancel{5}R = \frac{150}{\cancel{5}}$$ $$R = 30$$ - For $L=50$, solve $\frac{50}{R} = \frac{5}{6}$. Multiply both sides by $R$ and then by 6: $$50 \times 6 = 5 \times R$$ $$300 = 5R$$ Divide both sides by 5: $$\cancel{5}R = \frac{300}{\cancel{5}}$$ $$R = 60$$ - For $L=75$ and $R=90$, check ratio: $$\frac{75}{90} = \frac{5}{6}$$ Simplify: $$\frac{\cancel{15}5}{\cancel{15}6} = \frac{5}{6}$$ Ratio is consistent. - For $L=80$, solve $\frac{80}{R} = \frac{5}{6}$. Multiply both sides by $R$ and then by 6: $$80 \times 6 = 5 \times R$$ $$480 = 5R$$ Divide both sides by 5: $$\cancel{5}R = \frac{480}{\cancel{5}}$$ $$R = 96$$ 5. **Final completed table:** | Left | Right | |-------|-------| | 5 | 6 | | 25 | 30 | | 50 | 60 | | 75 | 90 | | 80 | 96 |