Explain the steps used in the ratio and proportion formula.

The ratio and proportion formula is a method used to compare two ratios and determine if they are equal. The formula is based on the principle that if two ratios are equal, then the product of the means (the terms that are not the extremes) is equal to the product of the extremes. Here are the steps used in the ratio and proportion formula: 1. **Identify the Ratios**: Let's say you have two ratios, a:b and c:d. In these ratios, a and c are the extremes (the terms that are not the means), and b and d are the means (the terms that are not the extremes). 2. **Set Up the Proportion**: Write the two ratios as a proportion by placing them over each other with a colon (:) or an equal sign (=). The proportion will look like this: a:b = c:d. 3. **Cross-Multiply**: Multiply the extremes of one ratio by the means of the other ratio. This means you will multiply a by d and b by c. The cross-multiplication looks like this: a * d = b * c. 4. **Solve for the Unknown**: If you are given one of the ratios and need to find the other, you can solve for the unknown by dividing one side of the cross-multiplication equation by the known value. For example, if you know a:b = 3:4 and you want to find the value of b when a = 9, you would set up the equation 9 * 4 = b * 3 and solve for b. 5. **Check for Proportionality**: After solving for the unknown, you can check if the two ratios are indeed proportional by substituting the values back into the original proportion and seeing if it holds true. Here's an example to illustrate the steps: **Example**: If 3:4 = x:12, find the value of x. 1. Identify the ratios: 3:4 and x:12. 2. Set up the proportion: 3:4 = x:12. 3. Cross-multiply: 3 * 12 = 4 * x. 4. Solve for x: 36 = 4x, so x = 36 / 4, which gives x = 9. 5. Check for proportionality: 3:4 = 9:12, which is true because both ratios simplify to 3:4. By following these steps, you can use the ratio and proportion formula to solve a variety of problems involving proportional relationships.