Fraction to Ratio Calculator

What is a fraction to ratio calculator?

A fraction to ratio calculator turns a fraction such as $6/8$ into an equivalent ratio written with a colon, such as $3 : 4$. A fraction and a ratio describe the same relationship between two quantities, so $\tfrac{6}{8}$ and $6 : 8$ are the same comparison. The calculator does one extra step: it reduces the ratio to its simplest whole-number form, so the two terms share no common factor other than 1.

The first term of the ratio (the part that comes from the numerator) is called the antecedent, and the second term (from the denominator) is called the consequent.

How does it work?

The fraction $\tfrac{n}{d}$ has the same value no matter what number you multiply or divide both parts by. To reduce it, divide both the numerator $n$ and the denominator $d$ by their greatest common divisor (GCD):

where $g = \gcd(n, d)$. The GCD is found with the Euclidean algorithm, repeatedly replacing the larger number with the remainder of dividing it by the smaller until the remainder reaches zero. The two reduced parts become the ratio’s first and second terms.

The denominator must be non-zero, since a fraction with a zero denominator is undefined.

How to use it

1. Enter the numerator (the top of the fraction).
2. Enter the denominator (the bottom of the fraction).
3. Read the reduced ratio in the form $n : d$, along with the separate first and second terms.

Worked examples

Convert $6/8$. The GCD of 6 and 8 is 2, so divide both terms by 2:

Convert $10/5$. The GCD of 10 and 5 is 5:

A fraction that is already in lowest terms is unchanged. For $3/4$ the GCD of 3 and 4 is 1, so the ratio is simply $3 : 4$, and $1/2$ becomes $1 : 2$.

FAQ

Is a ratio the same as a fraction? They express the same comparison between two numbers. The fraction $\tfrac{3}{4}$ and the ratio $3 : 4$ both say “3 for every 4”. A fraction is usually read as a single value, while a ratio emphasizes the relationship between the two parts. To go the other way, from a ratio back to a fraction, use a ratio-to-fraction conversion, and a ratio-to-decimal conversion gives the decimal value of the comparison.

Why is the ratio reduced? Reducing gives a unique, canonical form. The ratios $6 : 8$, $3 : 4$, and $30 : 40$ are all equivalent, but $3 : 4$ is the simplest way to write them, which is the same idea behind a fraction simplifier.

What about negative numbers? The calculator divides by the GCD of the absolute values, so the sign of the original fraction carries through to the first term of the ratio.