Equivalent Ratio Calculator
Find missing values in equivalent ratios and solve proportion problems with step-by-step solutions
Calculate Equivalent Ratios
Results
Enter values to calculate the missing ratio component
Leave one field empty to solve for that value
Example Problems
Example 1: Recipe Scaling
Problem: If 2 cups of flour make 12 cookies, how much flour is needed for 18 cookies?
Set up ratio: 2 : 12 = x : 18
Cross multiply: 2 × 18 = 12 × x
Solve: x = (2 × 18) ÷ 12 = 3 cups
Answer: 3 cups of flour needed
Example 2: Currency Exchange
Problem: If 5 USD = 4.2 EUR, how many EUR is 12 USD worth?
Set up ratio: 5 : 4.2 = 12 : x
Cross multiply: 5 × x = 4.2 × 12
Solve: x = (4.2 × 12) ÷ 5 = 10.08 EUR
Answer: 12 USD = 10.08 EUR
Example 3: Speed and Distance
Problem: A car travels 180 miles in 3 hours. How far will it travel in 5 hours?
Set up ratio: 180 : 3 = x : 5
Cross multiply: 180 × 5 = 3 × x
Solve: x = (180 × 5) ÷ 3 = 300 miles
Answer: 300 miles in 5 hours
Ratio Fundamentals
Equivalent Ratios
Ratios that express the same relationship
Cross Multiplication
Method to solve proportions: A/B = C/D → A×D = B×C
Proportions
Equations stating two ratios are equal
Key Formulas
Cross Multiplication
A/B = C/D → A×D = B×C
Find Missing Value
A/B = C/x → x = (B×C)/A
Ratio Simplification
A:B = (A÷GCD):(B÷GCD)
Quick Tips
Equivalent ratios express the same proportion
Cross multiplication solves for missing values
Check your answer by converting to decimals
Ratios can be simplified like fractions
Understanding Equivalent Ratios
What are Equivalent Ratios?
Equivalent ratios are two or more ratios that express the same relationship between quantities. They represent the same proportion even though the actual numbers may be different. For example, 2:4 and 3:6 are equivalent ratios because they both simplify to 1:2.
How to Find Equivalent Ratios
- •Multiply both parts of the ratio by the same number
- •Divide both parts of the ratio by their GCD
- •Use cross multiplication to solve proportions
- •Convert to decimal form to verify equivalence
Cross Multiplication Method
For Two-Number Ratios
A : B = C : D
Cross multiply to get: A × D = B × C
Solve for the unknown variable
For Three-Number Ratios
A : B : C = D : E : F
Use any two corresponding pairs to create a proportion
Example: A/D = B/E or A/D = C/F
Remember: Always check that denominators are not zero and verify your answer by substituting back into the original proportion.
Real-World Applications
Finance
Currency exchange rates, loan calculations, and investment ratios
Cooking
Recipe scaling, ingredient proportions, and serving size adjustments
Engineering
Scale models, gear ratios, and proportional design calculations