Fraction Calculator
Add, subtract, multiply, divide fractions. Results simplified automatically with mixed numbers.
Free · Runs in your browser · No signup
Examples to try
Quick rules
Add/sub: common denominator. Multiply: numerators and denominators. Divide: multiply by reciprocal.
Common mistakes
- Adding denominators when adding fractions.
- Forgetting to simplify the final answer.
- Using zero as a denominator.
Scope: School fraction arithmetic. For percent work, use the percentage helper.
How to Use
Enter your values in the fields above and click Calculate to get instant results. All computations run locally in your browser. No data is ever uploaded or stored.
Related Calculators
Fraction Operation Rules
CalcSolver performs all four basic operations on fractions and automatically reduces the result to lowest terms using the greatest common divisor.
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / cb
Common Fractions → Decimal Equivalents
1/2 = 0.5 · 1/3 ≈ 0.333 · 2/3 ≈ 0.667 · 1/4 = 0.25 · 3/4 = 0.75
1/5 = 0.2 · 2/5 = 0.4 · 3/5 = 0.6 · 4/5 = 0.8
1/8 = 0.125 · 3/8 = 0.375 · 5/8 = 0.625 · 7/8 = 0.875
1/10 = 0.1 · 1/16 = 0.0625 · 1/20 = 0.05
Tip: many recipes use halves, thirds, and quarters — memorize the first row for fast kitchen math.
Fraction Calculator Operations
Working with fractions requires careful handling of numerators, denominators, and common factors. CalcSolver's fraction calculator performs addition, subtraction, multiplication, and division of fractions — automatically simplifying results to their lowest terms and displaying both fraction and decimal equivalents.
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator. The easiest approach is to multiply the two denominators together, but for simpler results, find the Least Common Denominator (LCD). For example: 3/4 + 1/6. The LCD of 4 and 6 is 12. Convert each fraction: 3/4 = 9/12 and 1/6 = 2/12. Then add: 9/12 + 2/12 = 11/12. For subtraction: 5/8 - 1/3 = 15/24 - 8/24 = 7/24. When the denominators are already the same, simply add or subtract the numerators: 2/7 + 3/7 = 5/7.
Multiplying and Dividing Fractions
Multiplication is straightforward: multiply numerators together and denominators together. 2/3 x 4/5 = 8/15. Simplify by dividing both by their GCD if possible. Division uses the "flip and multiply" method: flip the second fraction (reciprocal) and multiply. 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6. Always simplify the final result to its lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator.
Finding Common Denominators
The Least Common Denominator (LCD) is the smallest number that both denominators divide into evenly. To find the LCD: list the multiples of each denominator and find the smallest shared one. For 4 and 6: multiples of 4 are 4, 8, 12, 16... multiples of 6 are 6, 12, 18... The LCD is 12. Alternatively, use the formula: LCD(a,b) = (a x b) / GCD(a,b). For 4 and 6: GCD(4,6) = 2, so LCD = 24/2 = 12. For larger denominators, prime factorization is the most efficient method.
Simplifying Fractions
A fraction is in its simplest form when the GCD of numerator and denominator is 1. To simplify, find the GCD and divide both parts by it. For 18/24: the factors of 18 are 1, 2, 3, 6, 9, 18; the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; the GCD is 6. So 18/24 / 6 = 3/4. Quick checks: if both numbers are even, divide by 2; if both end in 0 or 5, divide by 5; if the digits of both sum to a multiple of 3, divide by 3.
Working with Mixed Numbers
Mixed numbers (like 2 1/3) combine a whole number with a fraction. To use them in calculations, convert to improper fractions first. 2 1/3 = (2 x 3 + 1) / 3 = 7/3. After calculation, convert back if needed: 7/3 = 2 1/3 (divide 7 by 3: quotient 2, remainder 1). For addition of mixed numbers: 1 1/2 + 2 1/3 = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6.
Decimal-to-Fraction Conversion
To convert a decimal to a fraction, identify the place value of the last digit. 0.75 = 75/100 = 3/4 (simplified). 0.333... = 1/3 (repeating decimal). 0.125 = 125/1000 = 1/8. For repeating decimals, use algebra: let x = 0.333..., then 10x = 3.333..., so 10x - x = 3, meaning 9x = 3 and x = 1/3. CalcSolver displays results in both fraction and decimal form, making it easy to see the relationship.
Real-World Examples
Cooking: A recipe calls for 3/4 cup of flour, but you want to make 1.5x the recipe. 3/4 x 3/2 = 9/8 = 1 1/8 cups of flour needed.
Construction: A board is 5 1/2 feet long. You need to cut off 2 3/8 feet. 5 1/2 - 2 3/8 = 11/2 - 19/8 = 44/8 - 19/8 = 25/8 = 3 1/8 feet remaining.
Sharing: 3 friends split 2/3 of a pizza equally. Each gets 2/3 / 3 = 2/3 x 1/3 = 2/9 of the whole pizza.
Tips and Best Practices
- Always simplify your final answer — it is the mathematically correct form.
- Convert mixed numbers to improper fractions before performing any operation.
- For multiplication, simplify cross-factors before multiplying to keep numbers small.
- Check your work by converting fractions to decimals for a quick sanity check.
- Use CalcSolver's percentage calculator and equation solver for related math tools.
Sponsored Content
The following content is provided by our advertising partner and does not affect the calculator experience.
Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator by multiplying the denominators together (or finding the LCM), convert each fraction, then add the numerators. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
How do I simplify a fraction?
Divide both numerator and denominator by their greatest common divisor (GCD). Example: 12/18 → GCD is 6 → 12÷6/18÷6 = 2/3.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. Example: 3/8 = 3 ÷ 8 = 0.375. Our calculator shows results in both fraction and decimal form.
How do I multiply and divide fractions?
Multiply: multiply numerators together and denominators together. Divide: flip the second fraction (reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Example: 3 2/5 = (3 x 5 + 2) / 5 = 17/5. This conversion is necessary before performing any fraction arithmetic.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g., 3/4), representing a value less than 1. An improper fraction has a numerator equal to or larger than the denominator (e.g., 7/4), representing a value of 1 or greater. Improper fractions can be converted to mixed numbers.
How do I convert a repeating decimal to a fraction?
Let x equal the repeating decimal. Multiply by a power of 10 to shift the decimal point past one full repeat cycle, then subtract the original equation. For 0.333...: let x = 0.333..., then 10x = 3.333..., so 9x = 3 and x = 1/3.