Calculator Input
Use the ratio field or enter both terms separately. The page stays single column, while the calculator uses a responsive three, two, and one column form grid.
Example Data Table
| Ratio | Simplified Ratio | Fraction | Decimal | Percent | First Share |
|---|---|---|---|---|---|
| 2:3 | 2:3 | 2/3 | 0.6667 | 66.67% | 2/5 |
| 15:20 | 3:4 | 3/4 | 0.75 | 75% | 3/7 |
| 1.5:2.25 | 2:3 | 2/3 | 0.6667 | 66.67% | 2/5 |
| 9:12 | 3:4 | 3/4 | 0.75 | 75% | 3/7 |
| 25:100 | 1:4 | 1/4 | 0.25 | 25% | 1/5 |
Formula Used
Core conversion: For a ratio a:b, the basic fraction is a/b.
Simplification rule: Let g = gcd(a, b). Then the simplified fraction becomes (a ÷ g)/(b ÷ g).
Decimal ratios: If a ratio contains decimals, multiply both terms by the same power of ten first. That creates whole numbers before simplification.
Share of total: First-term share is a/(a+b). Second-term share is b/(a+b).
Percentage conversion: Multiply any decimal result by 100 to express it as a percent.
How to Use This Calculator
- Enter the ratio in one field, such as 3:4, 3/4, or 3 to 4.
- Or leave that field blank and enter the first and second terms separately.
- Select the primary result view you want highlighted above the form.
- Choose decimal precision and how many equivalent fractions to display.
- Press Convert Ratio to see the result, table, steps, chart, and exports.
- Use the CSV or PDF buttons to download the displayed calculation summary.
FAQs
1. What does ratio to fraction conversion mean?
A ratio a:b can be written as the fraction a/b. The calculator also simplifies that fraction, shows the decimal form, and gives the percentage form automatically.
2. Can I enter decimal ratios?
Yes. Decimal ratios are accepted. The calculator first scales both terms by the same power of ten, then simplifies the whole-number ratio into the final fraction.
3. Why is 15:20 equal to 3/4?
Both ratio terms share a common factor of 5. Dividing 15 and 20 by 5 gives 3 and 4, so the simplified fraction becomes 3/4.
4. What is the first-term share result?
It shows how much of the total belongs to the first term. For 3:4, the first-term share is 3/(3+4), which equals 3/7.
5. Does the calculator work with negative values?
Yes, it can process negative numbers mathematically. Still, most classroom ratio problems use positive values because ratios usually compare magnitudes or counts.
6. What happens if the second term is zero?
The direct fraction a/b becomes undefined because division by zero is not allowed. The calculator still shows other related information when possible.
7. Why are equivalent fractions useful?
Equivalent fractions help you see that many fractions represent the same value. For example, 1/2, 2/4, and 3/6 all describe the same proportion.
8. Can I use this for homework checking?
Yes. It is useful for homework checking, revision practice, and quick classroom verification because it shows the simplified answer and the working steps.