| Ratio 1 | Ratio 2 | Expected comparison | Why |
|---|---|---|---|
| 3:4 | 9:12 | Equal | Simplify both to 3:4. |
| 5:8 | 2:3 | Less than | 5/8 = 0.625, 2/3 ≈ 0.6667. |
| 7.5:2.5 | 9:3 | Equal | Both unit rates equal 3. |
| 3/4:1/2 | 6:4 | Equal | (3/4)/(1/2)=1.5, 6/4=1.5. |
A ratio A:B can be compared by converting it to a unit rate: A/B. For two ratios A:B and C:D, compare the fractions A/B and C/D.
- Cross multiplication comparison: A/B is greater than C/D if A × D > C × B.
- Equality (proportion): Ratios are equivalent if A × D = C × B.
- Simplifying a ratio: Divide both terms by their greatest common divisor after scaling to integers.
- Select an input format: separate terms or colon ratios.
- Enter Ratio 1 and Ratio 2 values using integers, decimals, or fractions.
- Choose decimal places and optional views like steps or normalized shares.
- Press Compare Ratios to see the result above the form.
- Use Download CSV or Download PDF to export the latest result.
Why ratio comparison matters in problem solving
Ratio comparison turns two-part quantities into one relationship, keeping decisions consistent. In recipes, a 3:4 mix scales to 6:8 without changing taste. In study work, it checks whether two tables follow the same proportional pattern. This calculator standardizes that check by converting each ratio into a unit rate and a simplified form.
Equivalent ratios and proportional reasoning
Two ratios are equivalent when they describe the same proportion, even if the numbers differ. The cross-multiplication test, A×D = C×B, avoids rounding and works with fractions. When equality holds, the ratios scale by one constant factor. Use this to validate conversions, compare map scales, or confirm that a slope matches tabular data.
Unit rates for quick decisions
Unit rate comparison reduces a ratio A:B to A/B, giving one benchmark. Price per kilogram, pages per hour, and points per game are unit rates. The calculator reports both unit rates with chosen decimal precision, then states which is larger. This helps you judge efficiency or value without rewriting the ratios by hand.
Simplification and scaling with exact fractions
Decimals can hide structure, so the calculator converts decimals to exact fractions when possible. It scales both terms to integers using a common denominator and simplifies using the greatest common divisor. The simplified ratio preserves the proportion while using smaller terms for communication. When inputs are huge, the tool still compares safely and signals simplification limits.
Interpreting normalized shares
Normalized shares answer: “What percentage of the total is each term?” For a:b, the shares are a/(a+b) and b/(a+b). This view supports budget splits, workload allocation, and clear reporting. When enabled, the calculator shows percentage shares and plots a stacked comparison so distribution differences are visible.
Export-ready outputs for coursework and audits
Exports keep work repeatable. Include the chosen decimal setting in your notes, because rounding can change perceived differences on close ratios. Re-running the same inputs later reproduces the same comparisons, which supports grading and quality checks. The CSV download captures inputs, unit rates, the comparison outcome, and a timestamp. The PDF button produces a printable summary suitable for assignments, lab notes, or internal reviews. Using exports with the example table helps you verify consistent results across multiple datasets.
FAQs
1) How do I enter fractions or mixed formats?
Type values as integers, decimals, or fractions like 3/4. For colon mode, use A:B. The tool converts decimals to exact fractions when possible, then compares ratios reliably.
2) What does “equal ratios” mean here?
It means the proportions match. The calculator checks whether A×D equals C×B (after exact conversion). If equal, both ratios describe the same scaling relationship.
3) Why is the second term not allowed to be zero?
A ratio A:0 implies division by zero when converting to A/B. Since unit rates and cross-multiplication require valid denominators, the calculator blocks zero second terms to prevent invalid comparisons.
4) What is the normalized share option used for?
It shows each term as a percentage of the pair’s total, a/(a+b) and b/(a+b). This is useful for composition, allocation, and presenting how a ratio is distributed.
5) How is rounding handled?
Rounding is applied only to displayed decimals. Internal comparisons use exact fractions when possible, and safe methods when numbers are large. Adjust decimal places to match your reporting needs.
6) Do downloads include my latest result?
Yes. CSV and PDF exports reflect the most recent comparison displayed above the form. Run a new comparison before downloading again to refresh the export content.