Convert Fraction to Percentage Calculator

Convert fractions and mixed numbers to percentages with step-by-step solutions.

Enter Fraction

Result

Percentage
75%
3/4
Fraction 3/4
Decimal 0.75
Percentage 75%
Simplified Fraction 3/4

Step-by-Step Solution

Percentage = (3/4) x 100 = 75%

How to Convert a Fraction to a Percentage

Converting a fraction to a percentage is a fundamental math skill. The word "percent" means "per hundred," so converting a fraction to a percentage means finding how many parts out of 100 the fraction represents. The basic formula is straightforward: divide the numerator by the denominator, then multiply by 100.

For example, to convert 3/4 to a percentage: 3 divided by 4 equals 0.75, and 0.75 multiplied by 100 gives 75%. Therefore, 3/4 = 75%.

Conversion Formulas

Simple Fraction

Divide the numerator by the denominator and multiply by 100.

% = (num / den) x 100

Mixed Number

Convert to improper fraction first: (whole x den + num) / den.

% = ((w*d + n) / d) x 100

Decimal to Percentage

Simply multiply the decimal value by 100.

% = decimal x 100

Percentage to Fraction

Divide the percentage by 100 and simplify.

fraction = % / 100

Simplifying Fractions

Divide both numerator and denominator by their GCD.

a/b = (a/GCD) / (b/GCD)

Repeating Decimals

Some fractions produce repeating decimals (e.g., 1/3 = 0.333...).

1/3 = 33.333...%

Common Fraction to Percentage Conversions

Here are some frequently used fraction-to-percentage conversions that are helpful to memorize:

  • 1/2 = 50% — One half
  • 1/3 = 33.33% — One third
  • 1/4 = 25% — One quarter
  • 1/5 = 20% — One fifth
  • 1/6 = 16.67% — One sixth
  • 1/8 = 12.5% — One eighth
  • 2/3 = 66.67% — Two thirds
  • 3/4 = 75% — Three quarters
  • 3/8 = 37.5% — Three eighths
  • 5/8 = 62.5% — Five eighths
  • 7/8 = 87.5% — Seven eighths

Working with Mixed Numbers

A mixed number like 2 1/2 combines a whole number with a fraction. To convert it to a percentage, first convert to an improper fraction: 2 1/2 = (2 x 2 + 1) / 2 = 5/2. Then apply the standard formula: (5/2) x 100 = 250%.

Note that mixed numbers greater than 1 always result in percentages greater than 100%.

Practical Applications

  • Grades: Converting test scores (e.g., 45/50 = 90%).
  • Discounts: Understanding sale prices (e.g., 1/4 off = 25% discount).
  • Cooking: Scaling recipes using fraction-to-percentage conversions.
  • Finance: Interest rates, tax calculations, and investment returns.
  • Statistics: Representing proportions and probabilities as percentages.

Tips for Accurate Conversions

  • Always check that the denominator is not zero before dividing.
  • Simplify the fraction first for easier mental math.
  • Round to the appropriate number of decimal places for your context.
  • Remember that percentages greater than 100% are valid for improper fractions.