Problem 46 - Fundamentals of Mathematics

Question

Convert \(\frac{5}{16}\) to a percent.

Step-by-Step Solution

Answer

\(\frac{5}{16}\) is 31.25%.

Step 1: Understand the Problem

To convert a fraction to a percent, you need to find an equivalent fraction with a denominator of 100. This is because percentages are out of 100.

Step 2: Find the Equivalent Fraction

Multiply the numerator and the denominator of the fraction \(\frac{5}{16}\) by a number that results in a denominator of 100. Since 100 divided by 16 is 6.25, multiply both the top and bottom by 6.25: \(\frac{5 \times 6.25}{16 \times 6.25} = \frac{31.25}{100}\).

Step 3: Convert to Percent

Now that the fraction is \(\frac{31.25}{100}\), it easily converts to a decimal percent form, which is 31.25%. Therefore, \(\frac{5}{16} = 31.25\%\).

Key Concepts

Fraction to Percent

Converting a fraction to a percent is a useful skill that helps in understanding proportions in everyday scenarios. To convert a fraction to a percent, the key is to find an equivalent fraction over 100 because percentages are essentially parts per hundred. Start with the given fraction, such as \(\frac{5}{16}\), and identify what number, when multiplied by 16, would give 100. This number is 6.25 in this case. Then, multiply both the numerator and the denominator of \(\frac{5}{16}\) by 6.25. This turns the fraction into \(\frac{31.25}{100}\).

• The fraction \(\frac{31.25}{100}\) simply represents 31.25 parts out of 100.
• Writing it as 31.25% indicates how much your fraction equals in percentage form.

By following this method, you can efficiently convert any fraction to a percent by setting its denominator to 100.

Equivalent Fraction

Equivalent fractions are simply different expressions of the same value. They appear different but hold the same proportion in value. An equivalent fraction is achieved by multiplying or dividing both the numerator and the denominator by the same non-zero number.
In converting \(\frac{5}{16}\) to a percent, finding an equivalent fraction with 100 as the denominator is our goal. We multiply \(\frac{5}{16}\) by \(\frac{6.25}{6.25}\) to achieve that. This gives us \(\frac{31.25}{100}\), which represents the same value as \(\frac{5}{16}\) but in a form ready to express as a percentage.

• Equivalent fractions are a fundamental concept in mathematics, crucial for understanding proportional relationships.
• They help in simplifying complex fractions or converting them into a more useful form.

Learning to find equivalent fractions builds a strong foundation for handling fractions in various math operations.

Mathematical Conversion

Mathematical conversion is a critical skill that enables us to switch between different forms of numerical representation. When converting fractions to percentages, the goal is to express the same quantity in a different format, often one that's easier to understand or visualize.
For \(\frac{5}{16}\), the conversion process involves:

• Identifying a multiplier that brings the denominator to an easily recognizable form, like 100 for percentages.
• Applying this multiplier equally to both the numerator and the denominator.
• Beyond fractions and percentages, conversions can be between decimals, ratios, and other numerical forms.

This technique not only simplifies calculations but also allows for a better grasp of relationships and comparisons between numbers. Conversion is universal in mathematics, further supporting algebra, geometry, and real-life problem-solving.