Fractions Calculator – Add, Subtract, Multiply, Divide & Simplify Fractions
This free fractions calculator solves any fraction problem in real time. Use it as a fraction cal to add, subtract, multiply, or divide two fractions, or as a fraction solver that shows every step of the working process. The calculator automatically simplifies the result, displays the decimal and percentage equivalent, and converts improper fractions to mixed numbers. It supports proper fractions, improper fractions, negative fractions, and mixed numbers.
Fractions Calculator
Fraction Calculator
Enter two fractions, select an operation, and get an instant result with full working steps.
The calculator works in real time — adjust any value and the result updates instantly. Enable Mixed Number Mode to enter fractions like 2½ or 3¼ as whole-number and fraction components. The Show Steps button reveals the full working for the selected operation, making this a complete fraction solver for learning and checking work.
Simplify Fractions – Quick Simplifier Tool
Enter any fraction below to reduce it to its simplest form. The tool divides both numerator and denominator by their Greatest Common Factor (GCF) to find the lowest terms.
Simplify a Fraction
Enter a fraction to reduce it to lowest terms instantly.
How Simplification Works
To simplify a fraction, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it.
A fraction is in simplest form (also called lowest terms) when the GCF of the numerator and denominator is exactly 1. No further simplification is possible at that point.
Fractions Chart – Common Fractions, Decimals & Percentages
This fractions chart lists common fractions alongside their decimal and percentage equivalents. Use it as a quick-reference table when working with fractions, decimals, or percentages interchangeably.
| Fraction | Simplified | Decimal | Percentage |
|---|---|---|---|
| Halves | |||
| 1/2 | 1/2 | 0.5 | 50% |
| Thirds | |||
| 1/3 | 1/3 | 0.3333… | 33.33% |
| 2/3 | 2/3 | 0.6667… | 66.67% |
| Quarters (Fourths) | |||
| 1/4 | 1/4 | 0.25 | 25% |
| 2/4 | 1/2 | 0.5 | 50% |
| 3/4 | 3/4 | 0.75 | 75% |
| Fifths | |||
| 1/5 | 1/5 | 0.2 | 20% |
| 2/5 | 2/5 | 0.4 | 40% |
| 3/5 | 3/5 | 0.6 | 60% |
| 4/5 | 4/5 | 0.8 | 80% |
| Sixths | |||
| 1/6 | 1/6 | 0.1667… | 16.67% |
| 2/6 | 1/3 | 0.3333… | 33.33% |
| 3/6 | 1/2 | 0.5 | 50% |
| 4/6 | 2/3 | 0.6667… | 66.67% |
| 5/6 | 5/6 | 0.8333… | 83.33% |
| Eighths | |||
| 1/8 | 1/8 | 0.125 | 12.5% |
| 2/8 | 1/4 | 0.25 | 25% |
| 3/8 | 3/8 | 0.375 | 37.5% |
| 4/8 | 1/2 | 0.5 | 50% |
| 5/8 | 5/8 | 0.625 | 62.5% |
| 6/8 | 3/4 | 0.75 | 75% |
| 7/8 | 7/8 | 0.875 | 87.5% |
| Tenths | |||
| 1/10 | 1/10 | 0.1 | 10% |
| 3/10 | 3/10 | 0.3 | 30% |
| 7/10 | 7/10 | 0.7 | 70% |
| 9/10 | 9/10 | 0.9 | 90% |
| Twelfths | |||
| 1/12 | 1/12 | 0.0833… | 8.33% |
| 3/12 | 1/4 | 0.25 | 25% |
| 4/12 | 1/3 | 0.3333… | 33.33% |
| 6/12 | 1/2 | 0.5 | 50% |
| 8/12 | 2/3 | 0.6667… | 66.67% |
| 9/12 | 3/4 | 0.75 | 75% |
| 11/12 | 11/12 | 0.9167… | 91.67% |
| Sixteenths | |||
| 1/16 | 1/16 | 0.0625 | 6.25% |
| 3/16 | 3/16 | 0.1875 | 18.75% |
| 5/16 | 5/16 | 0.3125 | 31.25% |
| 7/16 | 7/16 | 0.4375 | 43.75% |
| 9/16 | 9/16 | 0.5625 | 56.25% |
| 11/16 | 11/16 | 0.6875 | 68.75% |
| 13/16 | 13/16 | 0.8125 | 81.25% |
| 15/16 | 15/16 | 0.9375 | 93.75% |
How to Calculate Fractions – Step-by-Step Guide
Working with fractions follows a predictable set of rules for each of the four arithmetic operations. The key insight is that addition and subtraction require a common denominator, while multiplication and division do not. Understanding why each rule works — not just memorizing it — makes fraction problems much easier to solve confidently.
How to Add Fractions
Adding fractions requires a common denominator — both fractions must have the same denominator before you can add the numerators. This is because a denominator names the unit being counted: you can only add "thirds" to "thirds," not "thirds" to "quarters."
- Find the Least Common Denominator (LCD) of the two denominators. The LCD is the smallest number that both denominators divide into evenly. For example, the LCD of 4 and 6 is 12.
- Convert each fraction to an equivalent fraction with the LCD as its denominator by multiplying numerator and denominator by the same value. This does not change the value of the fraction — only its appearance.
- Add the numerators. The denominator stays the same (the LCD).
- Simplify the result by dividing numerator and denominator by their GCF.
How to Subtract Fractions
Subtraction follows the exact same steps as addition, using the LCD and subtracting the numerators instead of adding them. The key rule: find a common denominator first, then subtract only the numerators.
How to Multiply Fractions
Multiplication is the most straightforward operation — no common denominator is needed. You simply multiply "across": numerator times numerator and denominator times denominator. Then simplify the result.
- Multiply the two numerators: a × c
- Multiply the two denominators: b × d
- Write the result as (a × c) / (b × d)
- Simplify by dividing numerator and denominator by their GCF.
How to Divide Fractions
To divide fractions, keep the first fraction, change the division sign to multiplication, and flip the second fraction (find its reciprocal). This is the famous Keep–Change–Flip method. Then follow the multiplication rules.
- Keep the first fraction as it is.
- Change ÷ to ×.
- Flip the second fraction (swap numerator and denominator — this is the reciprocal).
- Multiply numerators and denominators.
- Simplify the result.
How to Find the LCD (Least Common Denominator)
The LCD of two denominators is the same as their Least Common Multiple (LCM). There are two main methods to find it:
- Listing multiples: List multiples of each denominator until you find a common one. Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18… The first match is 12. So LCD(4, 6) = 12.
- Using prime factorization: Find the prime factors of each number and take the highest power of each. 4 = 2² and 6 = 2 × 3. Take 2² and 3¹ → LCD = 4 × 3 = 12.
- Using the GCF formula: LCD(a, b) = (a × b) / GCF(a, b). For 4 and 6: GCF(4, 6) = 2 → LCD = (4 × 6) / 2 = 12.
How to Find the GCF (Greatest Common Factor)
The GCF is needed every time you simplify a fraction. Use the Euclidean algorithm: divide the larger number by the smaller, then replace the larger with the remainder, and repeat until the remainder is zero.
Example — GCF(18, 24): 24 ÷ 18 = 1 remainder 6 → 18 ÷ 6 = 3 remainder 0 → GCF = 6. So 18/24 ÷ 6/6 = 3/4.
Fraction Rules & Formulas – Quick Reference
Equivalent Fractions
Two fractions are equivalent if they represent the same value. You create an equivalent fraction by multiplying (or dividing) both numerator and denominator by the same non-zero number:
Cross-Multiplication (Comparing Fractions)
To compare two fractions without finding a common denominator, use cross-multiplication. Multiply the numerator of the first by the denominator of the second, and vice versa. The larger product belongs to the larger fraction.
Worked Examples
More Complex Examples
Let's work through some more challenging fraction problems that involve multiple steps:
Find LCD(2, 3, 6) = 6. Convert: 3/6 + 2/6 + 1/6 = 6/6 = 1. The result is the whole number 1.
Convert: 7/2 − 7/4. LCD = 4. Adjusted: 14/4 − 7/4 = 7/4 = 1¾.
Convert: 7/3 ÷ 3/2. Flip second: 7/3 × 2/3 = 14/9 = 1⁵⁄₉.
Mixed Numbers & Improper Fractions
A mixed number combines a whole number and a proper fraction (e.g., 2¾). An improper fraction has a numerator greater than or equal to its denominator (e.g., 11/4). Both represent the same value — the calculator works with both forms and converts between them automatically.
Mixed Number to Improper Fraction
Improper Fraction to Mixed Number
The fractions calculator automatically shows the mixed number form whenever the result is an improper fraction. To enter a mixed number, tick Mixed Number Mode at the top of the calculator and enter the whole number, numerator, and denominator separately.
Operations With Mixed Numbers
The most reliable approach when performing any operation with mixed numbers is to first convert them to improper fractions. Here is why:
- Addition: 1½ + 2⅓ → convert to 3/2 + 7/3 → LCD = 6 → 9/6 + 14/6 = 23/6 = 3⅚
- Subtraction: 5¼ − 2¾ → convert to 21/4 − 11/4 = 10/4 = 5/2 = 2½
- Multiplication: 1½ × 2⅓ → 3/2 × 7/3 = 21/6 = 7/2 = 3½
- Division: 2½ ÷ 1¼ → 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2
Fraction to Decimal and Percentage
Converting a Fraction to a Decimal
Divide the numerator by the denominator. The result is the decimal equivalent.
Converting a Fraction to a Percentage
Convert to a decimal first, then multiply by 100 and add the percent symbol.
The fractions calculator displays both the decimal and percentage equivalents for every result automatically. You can use the fractions chart above as a quick-reference for the most common conversions without needing to calculate.
Terminating vs. Repeating Decimals
Not all fractions produce clean decimal values. When you divide a fraction, the result is either:
- Terminating: The decimal ends. This happens when the denominator (in lowest terms) has only prime factors of 2 and/or 5. Examples: 1/2 = 0.5, 3/4 = 0.75, 7/8 = 0.875, 1/5 = 0.2, 3/20 = 0.15.
- Repeating: A block of digits repeats forever. This happens when the denominator contains prime factors other than 2 or 5. Examples: 1/3 = 0.333…, 2/7 = 0.285714285714…, 5/6 = 0.8333…
When Are Decimal and Percent Forms Useful?
- Comparing fractions: It is easier to compare 0.667 and 0.75 than 2/3 and 3/4, even though the values are the same.
- Test scores and grades: Scores are usually reported as percentages, so knowing that 7/8 = 87.5% is useful for students.
- Money and measurements: Currency and measurements use decimals more naturally than fractions.
- Recipes and quantities: Some conversions between imperial and metric measurements require fraction-to-decimal skills.
Types of Fractions Explained
Not all fractions look the same. Understanding the different types helps you recognize how to handle each one correctly in calculations.
Reciprocals
The reciprocal of a fraction is formed by flipping numerator and denominator. The reciprocal of a/b is b/a. A fraction multiplied by its reciprocal always equals 1:
Common Fraction Mistakes to Avoid
- Adding the denominators instead of finding a common one. The most common error. When adding 1/3 + 1/4, the answer is NOT 2/7. You must find the LCD (12), convert both fractions, and then add: 4/12 + 3/12 = 7/12.
- Forgetting to simplify the final answer. A result like 6/8 is technically correct but is not in simplest form. Reduce every answer by dividing numerator and denominator by their GCF (GCF of 6 and 8 is 2, so 6/8 = 3/4).
- Dividing fractions without flipping the second fraction. For division you must take the reciprocal of the divisor before multiplying. 1/2 ÷ 1/4 is NOT 1/2 × 1/4. The correct method: 1/2 × 4/1 = 4/2 = 2.
- Confusing mixed numbers with improper fractions when multiplying. Convert any mixed number to an improper fraction before performing multiplication or division. Multiplying whole and fractional parts separately gives the wrong answer.
- Sign errors with negative fractions. A negative sign applies to the entire fraction. −3/4 is not the same as (−3)/(−4) = 3/4. The calculator handles negative signs in the numerator field.
- Forgetting that a fraction with denominator 1 is a whole number. 5/1 = 5 and 0/4 = 0. If the denominator divides the numerator exactly, the result is a whole number, not a fraction.
- Rounding repeating decimals incorrectly. 1/3 = 0.3333… is a repeating decimal, not exactly 0.33. Using 0.33 in calculations that feed back into fractions will introduce rounding errors. Work with the fraction form for accuracy.
- Using the wrong LCD. The LCD must be the least common multiple, not just any common multiple. Using a larger common multiple (e.g., 24 instead of 12 for thirds and quarters) gives a correct but unsimplified result that requires extra reduction.
