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Understanding how to convert a percent into a fraction is a valuable skill. A percent represents a number out of 100. So, when you see 35%, it means 35 per 100 or \( \frac{35}{100} \). Let's break it down. Suppose you have 35% of a pizza. This means that out of every 100 equal parts of that pizza, you have 35 parts. To write this as a fraction, simply place the percent number over 100. This gives you the fraction \( \frac{35}{100} \). It's a straightforward conversion, but it establishes a foundation for moving to more complex calculations.

Simplifying fractions is an essential process to make them easier to understand and work with. Once you have your fraction, like \( \frac{35}{100} \), you need to simplify it to its lowest form.

Simplifying means finding an equivalent fraction where the numerator and denominator (top and bottom numbers) are as small as possible. You do this by dividing both the numerator and denominator by the same number, called the greatest common divisor (GCD). For instance, with \( \frac{35}{100} \), the GCD is 5. So, you divide both 35 and 100 by 5:

\[ \frac{35}{100} \rightarrow \frac{35 \text{ ÷ } 5}{100 \text{ ÷ } 5} = \frac{7}{20} \].

The fraction \( \frac{7}{20} \) can't be simplified further since 7 and 20 have no common divisors other than 1.

Finding the greatest common divisor (GCD) is a crucial step in simplifying fractions. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

Here's how to find the GCD:

• List the factors of each number.
• Identify the largest factor that both numbers share.

For example, with 35 and 100, the factors of 35 are 1, 5, 7, and 35. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The common factors are 1 and 5. The greatest one is 5. Therefore, the GCD of 35 and 100 is 5. This GCD is then used to simplify the fraction \( \frac{35}{100} \) to \( \frac{7}{20} \) by dividing both the numerator and denominator by 5.