Convert Fraction to Ratio

Calculator and formula to convert a fraction into a ratio

Fraction to Ratio Calculator

What is calculated?

This function converts a fraction into a ratio. The entered fraction is simplified when possible and then displayed as a ratio in the format a:b.

Enter fraction




Result
Ratio: :
The ratio is displayed in simplified form

Fraction - Ratio Info

What is a ratio?

A ratio is another notation for a fraction:

  • Format: a : b
  • Meaning: a to b
  • Equivalent to fraction a/b
  • Shows proportions

Tip: Ratios are commonly used in practice, e.g. for mixing colors, recipes or scales.

Simple examples
1/2 = 1:2
One part to two parts
3/4 = 3:4
Three parts to four parts
5/10 = 1:2
After simplifying: one part to two parts
6/9 = 2:3
After simplifying: two parts to three parts
Mixed fractions

For negative mixed fractions: the negative sign before the whole number applies to the entire fraction.
Example: -2⅔ = -(2⅔)

Formulas and conversion rules

Basic formula
\[\frac{a}{b} = a:b\] Fraction to ratio
Mixed fraction
\[c\frac{a}{b} = \frac{c \cdot b + a}{b} = (c \cdot b + a):b\] Convert mixed fraction
Simplify
\[\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}\] Simplify using gcd
Expand ratio
\[a:b = (a \cdot k):(b \cdot k)\] Expand by factor k
Inverse
\[a:b = \frac{a}{b}\] Ratio to fraction
Percent
\[a:b = \frac{a}{b} \cdot 100\%\] As percentage

Detailed computation example

Example: convert fraction 50/125 to a ratio

Step 1: Simplify fraction

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

gcd(50, 125) = 25

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

Step 2: Write as ratio

\[\frac{2}{5} = \color{blue}{2:5}\]

Meaning: 2 parts to 5 parts

Result: The fraction 50/125 corresponds to the ratio 2:5

Mixed fraction example

Example: convert mixed fraction 2⅔ to a ratio

Step 1: Convert to improper fraction

\[2\frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3}\]

Step 2: Represent as ratio

\[\frac{8}{3} = \color{blue}{8:3}\]

Interpretation: 8 parts to 3 parts, approximately 2.67:1

Practical applications

Mixing ratios

Example: mixing colors

Ratio 3:1 means: 3 parts color A to 1 part color B

\[\frac{3}{4} \text{ color A}, \quad \frac{1}{4} \text{ color B}\]
Scale

Example: map scale

Scale 1:50,000 means: 1 cm on the map equals 50,000 cm in reality

\[1 \text{ cm} = 500 \text{ m}\]
Recipes

Ratio 2:3 for flour to water means: For 2 parts flour use 3 parts water

Geometry

Side ratios in similar triangles remain constant and can be expressed as ratios

Definition and mathematical foundations

Mathematical definition

A ratio is a representation of the relationship between two quantities. It describes how many times one quantity is contained in another or in which proportional relation the two quantities stand.

Properties of ratios

Ratios can be simplified and expanded just like fractions. They remain equivalent in value. This makes them useful for practical applications.

Key properties
  • Order matters: a:b ≠ b:a
  • Simplification: (a·k):(b·k) = a:b
  • Expansion: a:b = (a·k):(b·k)
  • Decimal form: a:b = a/b = 0,...

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  •