Problem 23 - Prealgebra

Question

Change to percent. $$\frac{75}{250}$$

Step-by-Step Solution

Answer

The fraction \( \frac{75}{250} \) is 30%.

Step 1: Understand the Fraction

The given fraction is \( \frac{75}{250} \). It represents the part 75 out of the whole 250.

Step 2: Convert the Fraction to Decimal

Divide the numerator by the denominator: \( \frac{75}{250} = 0.3 \).

Step 3: Convert the Decimal to Percent

To convert a decimal to a percent, multiply the decimal by 100. So, \( 0.3 \times 100 = 30 \).

Step 4: Interpret the Result

Therefore, \( \frac{75}{250} \) is equal to 30%.

Key Concepts

Fractions to Decimals

Converting a fraction to a decimal is a fundamental math skill. A fraction is composed of a numerator and a denominator. The numerator is the top number, and it signifies how many parts you have. The denominator is the bottom number, and it tells you into how many equal parts the whole is divided. To transform a fraction into a decimal, you simply divide the numerator by the denominator. For example, with the fraction \( \frac{75}{250} \):

• Numerator: 75
• Denominator: 250

When you divide 75 by 250, you get the decimal 0.3. This operation essentially shows how much each part (represented by the numerator) is of the whole if the whole is considered as one (represented by the denominator). Converting fractions to decimals allows you to see the same value in a different form, making it easier to perform further mathematical operations.

Decimal to Percent

Once you have transformed a fraction into a decimal, the next step is to convert that decimal into a percentage. Percentages are simply another way to express proportions, and they are incredibly useful for comparing quantities or showing probabilistic outcomes.To convert a decimal to a percent, you multiply the decimal by 100. This shifts the decimal point two places to the right. For example, given the decimal 0.3:

• Multiply by 100: \( 0.3 \times 100 = 30 \)

This means that our fraction \( \frac{75}{250} \), which was converted to the decimal 0.3, is equivalent to 30% when represented as a percentage. Using percentages makes it easier to understand portions of a whole, as people tend to relate better to the concept of "out of 100."

Numerator and Denominator

Understanding the numerator and denominator in a fraction is crucial for effectively working with fractions, decimals, or percentages. The numerator is the top number in a fraction and represents how many parts of the whole you have. For instance, in the fraction \( \frac{75}{250} \), the numerator is 75, representing the parts you are focusing on.
The denominator, conversely, is the bottom number. It tells you how many parts make up the whole. In this fraction, the denominator is 250, representing how many equal parts the whole is divided into.Comprehending these two components will help you perform conversions and grasp mathematical concepts better, from dividing a pizza into slices (fractions) to discussing class attendance (percentages). It's all about parts of a whole!