Master ratio calculations with our comprehensive GCSE Maths tool. Convert between ratios, fractions, and percentages with detailed working.
Simplify a ratio to its lowest terms
Ratios are simplified by dividing both parts by their greatest common divisor (GCD). This reduces the ratio to its simplest form while maintaining the same proportions.
Reduce ratios to their simplest form using the greatest common divisor
Divide both parts by their GCDExample: 8:12 ÷ 4 = 2:3
Convert ratio parts to fractions of the whole
Part ÷ Total = FractionExample: 3:7 → 3/10 and 7/10
Convert ratio parts to percentages
(Part ÷ Total) × 100 = PercentageExample: 3:7 → 30% and 70%
Multiply or divide ratios to reach a target sum
Ratio × (Target Sum ÷ Current Sum)Example: 2:3 scaled to sum 50 = 20:30
Divide each part by the total to get fractions.
Convert fractions to percentages by multiplying by 100.
Multiply both parts by the same number to scale.
Example: A ratio of 2:3 needs a total of 50 parts.
Current sum = 2 + 3 = 5
Multiplier = 50 ÷ 5 = 10
Scaled ratio = 2 × 10 : 3 × 10 = 20:30
Answer: 20:30
Example: Ratio 2:3, first part is 20.
Multiplier = 20 ÷ 2 = 10
Second part = 3 × 10 = 30
Answer: 20:30
Convert decimals to fractions first, then simplify. For example, 2.5:3.5 becomes 5:7 when multiplied by 2. Alternatively, multiply by 10 or 100 to eliminate decimals, then simplify.
If one part is zero, the ratio is already simplified. For example, 0:5 simplifies to 0:1 (or just 0:1). However, 0:0 is undefined and cannot be simplified.
Find the current sum of the ratio parts, then divide the target sum by this to get a multiplier. Multiply each part by this multiplier. For example, to scale 2:3 to sum 50: multiplier = 50÷5 = 10, so 20:30.
A ratio compares two or more quantities (e.g., 3:4), while a fraction represents one part of a whole (e.g., 3/7). Ratios can be converted to fractions by dividing each part by the total.
Percentage calculations may differ slightly due to rounding. For example, 1/3 as a percentage could be 33.33% or 33.34% depending on rounding precision. Always check the step-by-step working.
Get step-by-step explanations and practice questions with our Maths Genie.