Add, subtract, multiply, and divide fractions and mixed numbers. Shows simplified fraction, decimal equivalent, and step-by-step working.
Fractions are one of the foundational concepts in mathematics, appearing throughout education from primary school through university, and in countless practical real-world situations from cooking and construction to finance and engineering. This free fraction calculator handles all four arithmetic operations on fractions and mixed numbers, automatically simplifies the result to its lowest terms, and shows the decimal and mixed number equivalents.
Whether you are a student working through homework, a teacher preparing examples, a baker scaling a recipe, or a tradesperson calculating measurements, this tool gives you instant, accurate answers along with the step-by-step working so you understand exactly how the result was derived.
A fraction represents a part of a whole. It consists of two parts: the numerator (the number on top) and the denominator (the number on the bottom). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.
For example, 3/4 means the whole is divided into 4 equal parts and you have 3 of them. Fractions where the numerator is less than the denominator are called proper fractions. When the numerator equals or exceeds the denominator (like 7/4), it is an improper fraction. Mixed numbers (like 1¾) combine a whole number with a proper fraction.
To add fractions, both fractions must have the same denominator (called the common denominator). If they already share one, simply add the numerators. If they don't, find the Lowest Common Multiple (LCM) of the two denominators.
Formula: a/b + c/d = (a×d + c×b) / (b×d), then simplify.
Example: 1/3 + 1/4 = (4 + 3) / 12 = 7/12
Step-by-step: The LCM of 3 and 4 is 12. Convert 1/3 to 4/12 and 1/4 to 3/12. Add the numerators: 4 + 3 = 7. Result: 7/12.
Subtracting fractions follows the same process as addition — find a common denominator, then subtract the numerators.
Formula: a/b − c/d = (a×d − c×b) / (b×d), then simplify.
Example: 3/4 − 1/3 = (9 − 4) / 12 = 5/12
Multiplying fractions is more straightforward than adding or subtracting — you simply multiply numerator by numerator and denominator by denominator, then simplify.
Formula: a/b × c/d = (a×c) / (b×d), then simplify.
Example: 2/3 × 3/4 = 6/12 = 1/2
To divide by a fraction, multiply by its reciprocal (flip the second fraction). This is often remembered by the phrase "keep, change, flip."
Formula: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c), then simplify.
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
A fraction is in its simplest (lowest) form when the numerator and denominator share no common factors other than 1. To simplify, divide both by their Greatest Common Factor (GCF).
Example: Simplify 12/18. GCF(12, 18) = 6. 12÷6 = 2, 18÷6 = 3. Simplified: 2/3.
A mixed number like 2¾ can be converted to an improper fraction: multiply the whole number by the denominator and add the numerator: (2×4 + 3) / 4 = 11/4. This calculator handles mixed number inputs in the "Whole Number" fields.
Fractions are especially important in US customary measurements. Cooking recipes use cups measured in fractions: ¼ cup, ⅓ cup, ½ cup, ⅔ cup, ¾ cup. Woodworking and construction use fractions of an inch: ⅛ inch, ¼ inch, ⅜ inch, ½ inch, ¾ inch. Pipe sizes, drill bits, and hardware are all specified in fractional inches across the United States.
In the United Kingdom, imperial measurements are still common in construction and some cooking contexts — particularly older recipes. Timber is sold in metric but often specified in legacy fractional inch equivalents. Understanding fractions is essential for anyone working with imperial measurements in either country.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.666... | 66.7% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
Find the LCM of both denominators, convert each fraction to use that denominator, then add the numerators. Example: 1/3 + 1/4 — LCM is 12, so convert to 4/12 + 3/12 = 7/12.
Multiply the first fraction by the reciprocal of the second (flip the second fraction). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
A mixed number combines a whole number and a proper fraction, like 2¾. To calculate with it, convert to an improper fraction first: 2¾ = (2×4+3)/4 = 11/4.
Find the GCF (Greatest Common Factor) of the numerator and denominator, then divide both by it. Example: 12/18 — GCF is 6, so 12÷6=2, 18÷6=3, simplified to 2/3.
A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator equal to or greater than the denominator (e.g., 5/3). Improper fractions are equivalent to mixed numbers (5/3 = 1⅔).
US and UK recipes commonly use fractions for measurements: ¼ teaspoon, ½ cup, ¾ pound. When scaling recipes up or down, you multiply or divide fractions — exactly what this calculator does.
Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. For recurring decimals like 1/3, the result is 0.333... (rounded to 0.33 for most practical purposes).
A fraction in lowest terms has no common factors between its numerator and denominator other than 1. This calculator automatically simplifies all results. For example, 6/8 simplifies to 3/4 because GCF(6,8) = 2.
Results are for educational purposes. While every effort is made for accuracy, always verify critical calculations independently, especially in professional, academic, or safety-critical contexts.
Adds, subtracts, multiplies, divides, and simplifies fractions. Mixed-number ↔ improper-fraction conversion. To add fractions: find common denominator, add numerators. 1/3 + 1/4 = 4/12 + 3/12 = 7/12. To multiply: multiply numerators together, denominators together: 2/3 × 4/5 = 8/15. To divide: invert the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
To simplify 48/60: find the Greatest Common Divisor (GCD) of 48 and 60, then divide both by it. Euclidean algorithm: 60 = 48 × 1 + 12; 48 = 12 × 4 + 0. GCD = 12. So 48/60 = 4/5. The calculator shows each step. Always simplify your final answer unless the problem specifically asks otherwise.
A mixed number is whole + fraction: 2 ⅓. The same value as an improper fraction: 7/3. Mixed → improper: multiply whole by denominator, add numerator: 2 × 3 + 1 = 7, over the same denominator 3 → 7/3. Improper → mixed: divide numerator by denominator: 7 ÷ 3 = 2 remainder 1 → 2 ⅓.
Any common multiple of the denominators works to add fractions, but the Least Common Denominator (LCD) keeps the numbers smaller. For 1/4 + 1/6: a common denominator is 24 (4 × 6), but the LCD is 12 (LCM of 4 and 6). LCD = LCM of the denominators. Always use LCD where possible — answers simplify faster.
Recipes: doubling a recipe that calls for ¾ cup flour → ¾ × 2 = 6/4 = 1½ cups. Imperial measurements: ⅛-inch increments on a ruler. Probability: rolling a 1 on a fair die = 1/6. Sport statistics: a batting average of 32/100 = 0.32 (32 hits per 100 at-bats). Mastering fractions builds intuition for percentages, decimals, and ratios — all the same underlying maths.
Find the GCD of numerator and denominator, then divide both by it. Use the Euclidean algorithm for large numbers.
Multiply the whole number by the denominator, then add the numerator. Keep the same denominator. 2⅓ = (2×3 + 1)/3 = 7/3.
Find the Least Common Denominator (LCD), rewrite each fraction with that denominator, then add the numerators.
Multiply the numerators together; multiply the denominators together; simplify. 2/3 × 4/5 = 8/15.
Invert the second fraction and multiply. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.