Problem 75 - Algebra 1: Concepts and Skills

Question

Write the fraction as a percent. $$ \frac{5}{8} $$

Step-by-Step Solution

Answer

The fraction \( \frac{5}{8} \) as a percent is 62.5%.

Step 1: Division

Divide 5 by 8 (the numerator by the denominator). This will transform the fraction into decimal form.

Step 2: Multiply by 100

Multiply the decimal result by 100. This converts the decimal into percentage form.

Step 3: Add the Percentage (%) Symbol

Add the percentage (%) symbol to your final answer to indicate that it represents a percentage.

Key Concepts

Understanding Division

Division is a basic mathematical operation that involves determining how many times one number (the divisor) can be subtracted from another (the dividend). In the case of converting fractions to percentages, we use division to transform the fraction into a decimal. This is achieved by dividing the numerator (the top number of the fraction) by the denominator (the bottom number).
For instance, with the fraction \( \frac{5}{8} \), the division operation would be 5 divided by 8, resulting in a decimal of approximately 0.625.

• Start with the numerator (5) as the dividend.
• The denominator (8) serves as the divisor.
• Perform the division: \( 5 \div 8 = 0.625 \).

This decimal form is critical because it is the stepping stone to converting the fraction into a percentage.

The Role of Multiplication in Conversion

Once you've obtained the decimal from division, the next step is to use multiplication. Multiplication, another fundamental arithmetic operation, involves adding a number to itself a specified number of times. For converting a decimal to a percentage, you multiply the decimal by 100.
This step is straightforward, as percentages are essentially fractions out of 100. Therefore, multiplying the decimal by 100 scales it to what it would be if over 100.

• Take your decimal result from the division (e.g., 0.625).
• Multiply by 100 to convert to a percentage: \( 0.625 \times 100 = 62.5 \).

This tells us that \( \frac{5}{8} \) is equivalent to 62.5%.

Understanding Fractions and Percentages

Fractions and percentages are two ways to represent parts of a whole. A fraction consists of a numerator and a denominator, expressing how many parts of a certain size there are. On the other hand, a percentage expresses a number as a part of 100, providing a more intuitive sense of proportion and size.
Converting a fraction like \( \frac{5}{8} \) to a percentage offers a clearer and more relatable understanding of its value. Here's a breakdown of the process:

• Fractions (e.g., \( \frac{5}{8} \)) tell us that we are considering 5 parts out of 8 total parts.
• Percentages (e.g., 62.5%) let us quickly understand the size of the fraction in relation to 100, simplifying comparison and comprehension.
• To move from fraction to percentage, we first divide to form a decimal, then multiply to align with the percentage scale.

This conversion helps in various real-life applications, such as understanding discounts, statistics, and proportions more effectively.