Reduce ratios and find equivalent proportional values for mixing, maps, and comparisons.
Overview
A ratio compares two quantities in relative terms, such as 3:5 or 45:60. Unlike a fraction, ratios often describe part-to-part relationships (sugar to flour) rather than part-to-whole. Simplifying a ratio makes the relationship easier to read without changing proportions.
To simplify, divide both terms by their GCF. Scaling multiplies or divides both terms by the same factor to produce equivalent ratios for recipes, models, or dilution tables. Never change only one side, or the relationship breaks.
Ratios appear in map scales, gear teeth, financial leverage summaries, and classroom grading rubrics. When converting to percentages, decide whether each part is compared to the sum (part-to-whole) or to the other part (part-to-part).
Use this ratio calculator to check whether two mixtures are equivalent, to resize batches, and to communicate proportions clearly in tables and charts.
Steps
Input both parts of the ratio a:b.
Divide by GCF to reach lowest terms.
Multiply both terms by the same factor if needed.
Check whether two ratios represent the same proportion.
Translate to fractions or percents when appropriate.
Keep units consistent on each side.
Math
a:b simplified = (a/GCF):(b/GCF); equivalent ratios = (ka):(kb)
Simplification preserves proportion by dividing both terms equally. Scaling applies the same multiplier to both sides.
Worked cases
GCF=15; 45/15 : 60/15
3:4.
Each part = 35/7 = 5; scale factor 5
Equivalent allocation 15:20.
Both simplify to 3:4
The ratios are equivalent.
Why use this
Questions