How to Calculate a Ratio
A reliable, step-by-step guide to calculating and writing ratios from any two numbers, measurements, or physical quantities.
The 4-Step Ratio Calculation Method
Step 1: Identify and Align the Quantities
Determine the two quantities being compared. Ensure both quantities are expressed in identical units of measurement (e.g. convert grams to grams, or hours to minutes).
Step 2: Write as an Initial Ratio
Place the antecedent (first value) and consequent (second value) side by side separated by a colon: Quantity A : Quantity B.
Step 3: Find the Greatest Common Divisor (GCD)
Identify the largest whole number that divides evenly into both Quantity A and Quantity B.
Step 4: Divide Both Terms by the GCD
Divide both sides by this common factor to reach the simplest integer form.
Worked Example: Mixing Paint
Suppose a painter mixes 450 ml of blue pigment with 750 ml of white base. How do we calculate the ratio of blue to white?
- Units check: Both measurements are already in milliliters (ml).
- Initial ratio: 450 : 750.
- Calculate GCD: GCD(450, 750) = 150.
- Divide both terms: 450 ÷ 150 = 3; and 750 ÷ 150 = 5.
- Final simplified ratio: 3 : 5 (3 parts blue to 5 parts white).
Handling Different Measurement Units
A frequent source of errors in ratio calculations is failing to normalize units. Consider comparing 2 hours to 40 minutes:
- Incorrect: 2 : 40 = 1 : 20 (invalid because hours ≠ minutes).
- Correct: Convert 2 hours to 120 minutes → 120 min : 40 min → 3 : 1.