1. The problem is about comparing quantities, which means understanding ratios, rates, or proportions between different amounts. 2. A common formula used in comparing quantities is the ratio formula: $$\text{Ratio} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$$. This helps us see how many times one quantity contains another. 3. Important rules: - Ratios can be simplified by dividing numerator and denominator by their greatest common divisor. - Ratios can be expressed in different forms: fractions, decimals, or with a colon (e.g., 3:4). 4. Example: If you have 8 apples and 12 oranges, the ratio of apples to oranges is $$\frac{8}{12}$$. 5. Simplify the ratio by dividing numerator and denominator by their greatest common divisor, which is 4: $$\frac{\cancel{8}^2}{\cancel{12}^3} = \frac{2}{3}$$ 6. So, the simplified ratio of apples to oranges is 2:3. 7. This means for every 2 apples, there are 3 oranges. This method can be applied to any quantities you want to compare.