Ratio to Fraction Converter

Calculator and formula to convert a ratio into a fraction

Ratio to Fraction Calculator

What is calculated?

This function converts a ratio into a fraction. The input ratio is written as a fraction and simplified when possible.

Enter ratio

:
Examples: 3:4, 2:5, 7:9

Result
The fraction is automatically displayed in simplified form

Ratio-Fraction Info

Conversion logic

The conversion is performed directly:

  • a : b becomes a/b
  • Numerator = first number
  • Denominator = second number
  • Automatic simplification

Reminder: A ratio is another notation for a fraction - both describe the same mathematical concept.

Quick examples
1:2 = 1/2
One to two becomes one half
3:4 = 3/4
Three to four becomes three quarters
6:8 = 3/4
After simplifying: three quarters
5:1 = 5/1 = 5
Five to one becomes five
Special cases

Equal ratio: 5:5 = 1 (whole number)
Improper fraction: 7:3 = 7/3 = 2⅓ (mixed number)


Formulas for Ratio to Fraction

Basic conversion
\[a:b = \frac{a}{b}\] Direct conversion
Reduced form
\[\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}\] Using greatest common divisor
Decimal value
\[a:b = \frac{a}{b} = a \div b\] As decimal
Inverse
\[\frac{a}{b} = a:b\] Fraction to ratio
Mixed number
\[\frac{a}{b} = c\frac{r}{b} \text{ if } a = c \cdot b + r\] For improper fractions
Percent
\[a:b = \frac{a}{b} \times 100\%\] As percentage

Step-by-step example

Example: convert 50:125 to a fraction

1Write ratio as fraction

\[50:125 = \frac{50}{125}\]

50 becomes numerator, 125 becomes denominator

2Find greatest common divisor

\[\gcd(50, 125) = 25\]

50 = 2 × 25, 125 = 5 × 25

3Simplify fraction

\[\frac{50}{125} = \frac{50 \div 25}{125 \div 25} = \color{blue}{\frac{2}{5}}\]

Result: 50:125 = 2/5

Various examples

Simple ratios
3:4 =
3

4
\[3:4 = \frac{3}{4} = 0.75\]
2:3 =
2

3
\[2:3 = \frac{2}{3} \approx 0.667\]
Simplifiable ratios
12:16 =
3

4
(simplified)
\[\frac{12}{16} = \frac{3}{4} = 0.75\]
15:20 =
3

4
(simplified)
\[\frac{15}{20} = \frac{3}{4} = 0.75\]

Special cases

Equal ratio
\[5:5 = \frac{5}{5} = 1\]

Result is a whole number

Improper fraction
\[7:3 = \frac{7}{3} = 2\frac{1}{3}\]

Can be written as a mixed number

Ratio with 1
\[8:1 = \frac{8}{1} = 8\]

Denominator 1 can be omitted

Practical applications

Mixing ratios

Example: mixing colors

Ratio 2:3 (red to blue)

\[2:3 = \frac{2}{3} \approx 0.667\]

Meaning: 2/5 red, 3/5 blue

Profit/Loss distribution

Example: partnership

Ratio 3:2 (partner A to partner B)

\[3:2 = \frac{3}{5} : \frac{2}{5}\]

Partner A: 60%, Partner B: 40%

Recipes and ingredients

Flour to sugar = 4:1 = 4/1 = 4
Meaning: 4 times as much flour as sugar

Geometry and scales

Scale 1:100 = 1/100 = 0.01
1 cm on the drawing = 1 m in reality

Mathematical foundations

Ratio and fraction

A ratio and a fraction are mathematically equivalent. The ratio a:b describes the same as the fraction a/b. Both express how many times the second quantity is contained in the first.

Why convert?

Fractions make arithmetic operations like addition, subtraction, multiplication and division easier. They are also convenient for decimal calculations and percentages.

Key properties
  • Equivalence: a:b = a/b (always)
  • Simplifiability: Both forms can be simplified
  • Arithmetic: Easier with fractions
  • Interpretation: Fractions show parts of a whole




More Ratio Functions

Aspect Ratio  •  Compare Ratios  •  Decimal to Ratio  •  Fraction to Ratio  •  Ratio-Calculator  •  Ratio Simplifier  •  Ratio to Decimal  •  Ratio to Fraction  •  Scale Ratio  •