Problem 4 - Elementary Algebra

Question

For the following problems, convert each fraction to a percent. $$ \frac{5}{16} $$

Step-by-Step Solution

Answer

Answer: The percentage equivalent of the fraction 5/16 is 31.25%.

Step 1: Division

Divide the numerator (5) by the denominator (16) to get the decimal value: $$ \frac{5}{16} \approx 0.3125 $$

Step 2: Convert to Percentage

Multiply the decimal value by 100 to find the percentage: $$ 0.3125 \times 100\% = 31.25\% $$ The fraction \(\frac{5}{16}\) is equal to \(31.25\%\).

Key Concepts

Understanding Division

When converting a fraction to a percent, the first step is to perform division. A fraction essentially represents a division problem. The number above the line, called the numerator, is divided by the number below the line, called the denominator. Let's take the fraction \( \frac{5}{16} \) as an example:
The numerator is 5 and the denominator is 16. Divide 5 by 16 to start finding the decimal equivalent of the fraction. Using a calculator or long division, we find:

\[ \frac{5}{16} = 0.3125 \]
Thus, the fraction \( \frac{5}{16} \) equals approximately 0.3125 when expressed as a decimal. Remember, division simply answers the question of "how many parts of a whole is each part worth." Keep this in mind as you proceed with converting your fraction to a percent.

Decimal Conversion Essentials

Once you know how to express a fraction as a decimal, converting it to a percent becomes straightforward. Converting a fraction like \( \frac{5}{16} \) to a decimal means working with a number in base 10. For the given faction, our earlier division gives us the decimal 0.3125.

Each fraction has its own unique decimal version, which can be:

• Terminating, meaning it has a finite number of digits (like 0.5 or 0.75).
• Non-terminating but repeating, meaning it continues indefinitely with a repeating pattern of digits (like 0.333... or 0.666...).
• Non-terminating and non-repeating, meaning it continues indefinitely without a pattern (more rare in simple fractions).

Knowing how to work with decimals is important, as they offer an easier format for certain types of calculations compared to fractions. This decimal representation will be the stepping stone for our next operation: converting to a percentage.

The Path to Percentage Calculations

To convert a decimal into a percentage, you multiply it by 100. This is because percentages are essentially decimals multiplied by 100. So, for our decimal of 0.3125, you calculate:

\[ 0.3125 \times 100 = 31.25 \]%
This transformation is essentially scaling the decimal up to a whole number by a factor of 100, providing an intuitive understanding of how much of one whole a number actually represents. So, \( \frac{5}{16} \) converts into a percentage by finding 31.25% of the whole. Remember that percent means "per hundred," emphasizing how it relates a part to a hundred total parts, making comparisons easier in everyday contexts.
Feel free to practice with other fractions; this method of division, decimal conversion, and percentage calculation works universally for any fraction you encounter.