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Ratio to Fraction Calculator

Convert ratios in the form A:B to simplified fractions.

What this tool does

Convert ratios in the form A:B to simplified fractions. You fill in these fields: First part (A) and Second part (B). It shows simplified fraction, numerator, denominator, decimal value, and common factor removed.

Inputs

  • First part (A): A whole number. Must be at least 0. The number before the colon. Whole numbers only.
  • Second part (B): A whole number. Must be at least 0. The number after the colon. Whole numbers only. It becomes the denominator, so it cannot be 0.

How to use

  1. Enter the first part (A).
  2. Enter the second part (B).
  3. Read the result: simplified fraction, numerator, denominator, decimal value, and common factor removed. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • First part (A): 12
  • Second part (B): 16

Results:

  • Simplified fraction: 3/4
  • Numerator: 3
  • Denominator: 4
  • Decimal value: 0.75
  • Common factor removed: 4

How this is worked out: Greatest common divisor of 12 and 16 is 4 (12 = 4 x 3, 16 = 4 x 4, and no larger number divides both). 12 / 4 = 3 and 16 / 4 = 4, so the fraction is 3/4. Decimal 3 / 4 = 0.75.

Example 2. Inputs:

  • First part (A): 5
  • Second part (B): 7

Results:

  • Simplified fraction: 5/7
  • Numerator: 5
  • Denominator: 7
  • Decimal value: 0.714286
  • Common factor removed: 1
  • Note: The two parts share no common factor, so the fraction is already in lowest terms.

How this is worked out: 5 is prime and 7 is prime and they differ, so their greatest common divisor is 1. The fraction stays 5/7. Decimal 5 / 7 = 0.714285714..., rounded here to 0.7142857.

Example 3. Inputs:

  • First part (A): 100
  • Second part (B): 25

Results:

  • Simplified fraction: 4
  • Numerator: 4
  • Denominator: 1
  • Decimal value: 4
  • Common factor removed: 25

How this is worked out: gcd(100, 25) = 25 because 100 = 25 x 4. 100 / 25 = 4 and 25 / 25 = 1, so the fraction is 4/1, shown as the whole number 4. Decimal 4 / 1 = 4.

Example 4. Inputs:

  • First part (A): 0
  • Second part (B): 5

Results:

  • Simplified fraction: 0
  • Numerator: 0
  • Denominator: 1
  • Decimal value: 0
  • Common factor removed: 5

How this is worked out: gcd(0, 5) = 5. 0 / 5 = 0 and 5 / 5 = 1, so the fraction is 0/1, shown as 0. Decimal 0 / 1 = 0.

Where this comes from

A ratio as a fraction. The ratio A:B is read as the fraction A over B and written in lowest terms.

Write a fraction in lowest terms. The numerator and the denominator are both divided by their greatest common divisor. The sign is kept on the numerator. The denominator cannot be 0. Source: Arithmetic: a fraction is in lowest terms when its numerator and denominator have no common divisor above 1, reached by dividing both by their greatest common divisor.

Limitations

  • Accepts whole numbers from 0 up only, so negative and decimal ratio parts are not supported.
  • Handles two parts only. A three-part ratio such as 2:3:4 needs two separate comparisons.

FAQs

Q: Can I enter decimal values for the ratio parts?
A: No. Both parts must be whole numbers. Enter a ratio such as 1.5:2.5 as 3:5 instead.
Q: What happens if the second part is zero?
A: A message asks for a second part that is not zero, because a fraction cannot have a denominator of 0.
Q: Is the fraction always proper?
A: No. If the first part is larger than the second, the result is an improper fraction. For example, 5:3 gives 5/3.

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