Equivalent Ratio Calculator

Find equivalent ratios, simplify to lowest terms using GCD, and scale ratios up or down.

Select Mode & Enter Values

Result

Simplified Ratio
3 : 5
already in lowest terms
Original Ratio3 : 5
As Fraction3/5
As Decimal0.6
GCD1

Step-by-Step Solution

3:5 = 6:10 = 9:15 = 12:20 = 15:25 = 18:30

Understanding Equivalent Ratios

A ratio is a comparison of two quantities, typically written as a:b or a/b. Equivalent ratios are ratios that express the same relationship between two numbers. Just like equivalent fractions, you can create equivalent ratios by multiplying or dividing both terms by the same non-zero number.

For example, 2:3 is equivalent to 4:6, 6:9, and 8:12, because each is obtained by multiplying both terms of 2:3 by 2, 3, or 4 respectively.

Methods for Working with Ratios

Simplify Using GCD

Divide both terms by their Greatest Common Divisor to find the simplest form.

a:b = (a/GCD) : (b/GCD)

Scale Up

Multiply both terms by the same factor to create larger equivalent ratios.

a:b = (a*n) : (b*n)

Compare Ratios

Two ratios a:b and c:d are equivalent if a*d = b*c (cross multiplication).

a:b = c:d if a*d = b*c

Ratio to Fraction

A ratio a:b can be expressed as the fraction a/b for comparison and computation.

a:b = a/b

Practical Applications of Ratios

Ratios are used extensively in everyday life and professional fields. They appear in recipes (ingredient proportions), maps (scale), finance (price-to-earnings ratios), science (mixing solutions), construction (material ratios like concrete mix), and art (golden ratio).

Tips for Working with Ratios

  • Always simplify ratios to their lowest terms for clearest communication.
  • When comparing ratios, simplify both to lowest terms first.
  • Ratios can involve more than two terms (e.g., 1:2:3).
  • The order of terms in a ratio matters: 3:4 is not the same as 4:3.
  • To convert a ratio to a percentage, divide the first term by the sum of all terms.