Ratio Calculator
Simplify, compare, and scale ratios with step-by-step work.
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How to Simplify and Use Ratios
A ratio expresses the relationship between two or more quantities. Ratios appear in cooking (ingredient proportions), maps (scale ratios like 1:50,000), finance (debt-to-equity), and engineering (gear ratios). A ratio A:B means "for every A parts of the first quantity, there are B parts of the second."
Simplifying a Ratio
To simplify a ratio, divide both parts by their Greatest Common Factor (GCF). For example, 12:8 — GCF is 4 — simplifies to 3:2. A simplified ratio is in lowest terms when the GCF is 1.
Equivalent Ratios
Multiply or divide both parts of a ratio by the same number to create an equivalent ratio. 3:2 is equivalent to 6:4, 9:6, 15:10, and so on. This is useful for scaling recipes, blueprints, or any proportional relationship.
Ratios as Fractions and Percentages
A ratio A:B can be expressed as the fraction A/B or as a percentage (A/B × 100%). The ratio 3:2 = 1.5 as a decimal and means A is 150% of B, or A is 60% of the total (A+B).
Three-part ratios (A:B:C) are used in chemistry (reaction ratios), finance (asset allocation), and mixing (concrete mix ratios). Simplify by dividing all three parts by their shared GCF.
Worked Example: Dividing in a Given Ratio
Three partners share profits in the ratio 2:3:5. Their total profit is $80,000. How much does each receive?
Total parts: 2+3+5 = 10. Each part = $80,000/10 = $8,000. Partner A: 2×$8,000 = $16,000. Partner B: 3×$8,000 = $24,000. Partner C: 5×$8,000 = $40,000. Check: 16,000+24,000+40,000 = $80,000 ✓
Real-World Ratio Applications
| Context | Ratio | Meaning |
|---|---|---|
| Concrete mix | 1:2:3 | 1 cement : 2 sand : 3 gravel |
| Map scale | 1:50,000 | 1 cm on map = 500 m real |
| Debt-to-equity | 0.5:1 | $0.50 debt per $1.00 equity |
| Screen aspect | 16:9 | 16 units wide for every 9 tall |
| Fuel mix | 50:1 | 50 parts gasoline : 1 part oil |
Frequently Asked Questions
Divide both parts by their GCF. Example: 18:12 — GCF is 6 — simplifies to 3:2.
Multiply both parts by the same number. To scale 3:2 so A = 15: multiply both by 5 → 15:10.
A fraction compares a part to a whole (3/8 means 3 out of 8 total). A ratio compares two separate quantities (3:5 means 3 parts of A for every 5 parts of B, total = 8 parts).
Divide the first part by the total (A+B) and multiply by 100. Ratio 3:7 → A is 3/(3+7) × 100 = 30% of the total.
Yes. Multiply 2:3 by 2 to get 4:6. They express the same proportional relationship — for every 2 of A there are 3 of B.
Add the parts of the ratio to get the total number of shares. Divide the quantity by total shares to get one share's value, then multiply each part. For example, divide $500 in ratio 3:2: total parts = 5, one share = $100. First person gets 3×100=$300, second gets 2×100=$200.
The golden ratio φ ≈ 1:1.618 (or equivalently, 1.618:1) is defined as the ratio where the whole is to the larger part as the larger part is to the smaller. Mathematically, φ = (1+√5)/2. It appears in Fibonacci numbers (consecutive Fibonacci terms approach this ratio), classical architecture, and is considered aesthetically pleasing in art and design.