Enter a fraction or a ratio into the calculator to convert to the other.
Assumptions Assumptions
- Inputs represent rational numbers; denominators cannot be zero.
- Fractions and ratios are simplified to lowest terms using the greatest common divisor (GCD).
- Decimals and percentages are converted to fractions (continued-fraction approximation for repeating/long decimals).
- Negative values are allowed; the negative sign is placed on the first term of the ratio (e.g., -3:4).
When to Use This Calculator
- Expressing fractions as clean ratios for recipes, mixes, and scale drawings.
- Turning ratios into fractions for algebra, proportions, and probability problems.
- Normalizing mixed formats (e.g., 1 1/2, 0.75, 75%) into a consistent representation.
Input Definitions
- Fraction — accepts a/b, mixed numbers (e.g., 1 3/4), decimals (0.75), and percents (75%).
- Ratio — accepts a:b or “a to b”; each side may be an integer, decimal, fraction, or percent.
- Conversions — fraction → ratio: a/b ⇒ a:b; ratio → fraction: a:b ⇒ a/b; mixed w n/d ⇒ (w·d + n)/d.
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Fraction to Ratio Formula
The following formulas convert fractions to ratios and back, always simplifying to lowest terms.
\frac{a}{b} \;\equiv\; a:b- a and b are integers with b ≠ 0.
- Mixed number w n/d → (w·d + n)/d before conversion.
- Decimals and percentages are converted to fractions first and then simplified.
- Any negative sign is applied to the first term of the ratio.
Fraction to Ratio Conversion Table
| Fraction | Ratio |
|---|---|
| 1/10 | 1:10 |
| 1/8 | 1:8 |
| 1/6 | 1:6 |
| 1/5 | 1:5 |
| 1/4 | 1:4 |
| 1/3 | 1:3 |
| 3/8 | 3:8 |
| 2/5 | 2:5 |
| 1/2 | 1:2 |
| 3/5 | 3:5 |
| 5/8 | 5:8 |
| 2/3 | 2:3 |
| 3/4 | 3:4 |
| 4/5 | 4:5 |
| 5/6 | 5:6 |
| 7/8 | 7:8 |
| 9/10 | 9:10 |
| 1 | 1:1 |
| 5/4 | 5:4 |
| 3/2 | 3:2 |
| * Simplest form: each pair is reduced by the greatest common divisor (GCD). | |
How do you convert a fraction to a ratio? Simplify the fraction a/b, then write the numerator and denominator as a:b (or “a to b”).
How do you convert a ratio to a fraction? Normalize the ratio to a:b (or “a to b”), then form the fraction a/b and simplify.
Example Problem
Convert 1 3/4 to a ratio in simplest form.
Use the rule: for a fraction a/b, the ratio is a:b; first convert the mixed number 1 3/4 = (1×4+3)/4 = 7/4.
ratio = 7:4
