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Percentage word problems often ask you to find what fraction of one number another number is, expressed as a percentage. To tackle these problems, you need to set up the correct equation. Use the formula: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]
Let's break this down with an example problem: 'What percent of 260 is 78?'
In this scenario:
- The 'Part' is the smaller number you want to compare, which is 78.
- The 'Whole' is the larger number you are comparing the part to, which is 260.
After identifying the part and the whole, you substitute them into the formula to find the percentage. By practicing these steps, you can master percentage word problems with ease!

Converting fractions to percentages is a crucial skill in algebra and everyday math. The process essentially involves two steps:
- First, divide the numerator (top number) of the fraction by the denominator (bottom number) to get a decimal value.
- Then, multiply the decimal by 100 to convert it into a percentage.
For instance, using the fraction in the exercise \( \frac{78}{260} \), you first simplify the fraction if possible. Simplification helps in easier calculation and clarity. \[ \frac{78}{260} = \frac{39}{130} \] Then, divide the simplified numerator by the denominator: \[ \frac{39}{130} ≈ 0.3 \] Finally, multiply by 100 to convert it to a percentage: \[ 0.3 \times 100 = 30\text{\textpercent} \]
This method gives you a clear, efficient way to handle fraction-to-percentage conversions.

Understanding how to set up and solve algebraic equations is essential in solving percentage problems. The basic algebraic form for percentage calculation is \[ \frac{\text{Part}}{\text{Whole}} \times 100 \] An equation is a statement that shows the equality of two expressions. In our percentage problem example, we form the equation by comparing 78 to 260. The steps to solve this equation include:
1. **Identify the Variables**: In the context of our problem, the 'Part' (78) and the 'Whole' (260) are our variables to be substituted into our formula.
2. **Simplify the Equation**: To simplify fraction calculations, it's often helpful to reduce the fraction to its simplest form. For example, \[ \frac{78}{260} = \frac{39}{130} \]
3. **Perform the Arithmetic Operations**: Division and multiplication operations come next: dividing the numerator by the denominator and then multiplying the result by 100. This step transforms the fraction to a decimal and then to a percentage.
By systematically breaking down the problem into these steps, solving percentage word problems becomes straightforward.