Ratio to Fraction Converter

How it is calculated

The ratio a : b is written as the fraction a / b and reduced to lowest terms. The engine finds the greatest common divisor g of the two numbers with the Euclidean algorithm (repeatedly replacing the pair by the divisor and the remainder until the remainder is 0), then outputs (a ÷ g) / (b ÷ g). It also gives the decimal value a ÷ b to four decimals. Both entries must be whole numbers: a value such as 1.5 returns no result, so multiply both sides by 10 first (1.5 : 3 becomes 15 : 30). The second term cannot be 0 and neither can be negative. A ratio that reduces to a whole number appears with a denominator of 1, for example 3/1.

Common mistakes

• Reading the result as a share of the whole. The ratio 3 : 5 becomes 3/5, a part compared with the other part; the share of the total is 3/8. Add the terms first if you want the part-to-whole fraction.
• Entering decimals such as 2.5 : 4. The tool accepts only whole numbers, so scale both sides to whole numbers first (25 : 40, which reduces to 5/8).
• Reversing the order. 2 : 5 gives 2/5 but 5 : 2 gives 5/2, so check which quantity comes first in your wording.
• Entering a ratio with a zero in the second position. A denominator of 0 is undefined, so there is no result.
• Expecting a mixed number. An improper result like 9/4 is kept as it is; the tool does not write it as 2 1/4.