Question

Write each fraction as a percent. $$\frac{3}{8}$$

Short answer

Question: Convert the fraction \(\frac{3}{8}\) into a percentage. Answer: 37.5%

Step-by-step solution

Divide the Numerator by the Denominator

Divide the numerator (3) by the denominator (8). The result will be a decimal: $$\frac{3}{8} = 0.375$$

Convert the Decimal to a Percentage

To convert the decimal 0.375 to a percentage, multiply it by 100: $$0.375 \times 100 = 37.5$$ Thus, the fraction \(\frac{3}{8}\) can be written as a percent, 37.5%.

Key concepts

Fraction Conversion

Converting a fraction to another form often helps in understanding and comparing values. A fraction consists of two parts: the numerator (top number) and the denominator (bottom number). To convert a fraction, such as \( \frac{3}{8} \), into a more usable number like a decimal or a percent, you start by dividing the numerator by the denominator. This process simplifies the fraction, making it easier to understand or compare with other numbers.

Decimal Conversion

Decimal conversion is the process of changing a fraction into a decimal by dividing its numerator by its denominator. For instance, with the fraction \( \frac{3}{8} \), you would perform the division \( 3 \div 8 \). Using basic division, this results in the decimal 0.375.

• Decimals are beneficial because they can represent fractions in a format compatible with other mathematical tools.
• They help in comparing values where fractions might seem complicated or confusing.

By converting a fraction to a decimal, you can perform additional calculations more easily.

Percent Calculation

Once you have a decimal, converting it to a percent involves a simple yet crucial step: multiplication by 100. This is because percents are essentially fractions out of 100. Take the decimal \( 0.375 \) obtained from \( \frac{3}{8} \), and multiply by 100 to convert it into a percentage:
\[ 0.375 \times 100 = 37.5 \]
Thus, \( 37.5 \% \) represents the fraction of \( \frac{3}{8} \).

• Percentages provide a clear way to express parts of a whole.
• They are commonly used in everyday scenarios like discounts, interest rates, and statistics.

Knowing how to convert decimals to percentages is key in applying math in real-life situations.

Numerator and Denominator

The numerator and denominator are fundamental components of any fraction. They determine the part-to-whole relationship of the fraction.
The numerator (top number) signifies how many parts you are considering, while the denominator (bottom number) indicates the total number of equal parts. In \( \frac{3}{8} \), the 3 is the numerator, and it tells us we have 3 parts out of a total 8 parts, which is the denominator.

• Understanding these terms is essential for fraction conversion, as they guide the initial step of turning a fraction into a decimal for further calculations.
• The division of numerator by denominator is central to most of fraction-related mathematical operations.

Mathematical Operations

Mathematical operations are tasks that involve the manipulation or comparison of numbers, using functions like addition, subtraction, multiplication, and division. The conversion process touches on a few of these operations; primarily division when converting fractions to decimals, and multiplication when changing decimals into percents.

• Division: Used to convert the fraction \( \frac{3}{8} \) into a decimal.
• Multiplication: Allows transformation of the decimal 0.375 into the percentage 37.5\%.

Understanding these basic operations strengthens your mathematical reasoning and application across various concepts, not just limited to fractions and percentages.