🔢 Enter Your Fractions
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Mixed Numbers (include whole numbers)
Fraction 1
+
Fraction 2
=
Result
5
6
📊 Your Result
✅ Simplified Result
5
6
Also expressed as
0.8333
✅ Already Simplified!
5/6 is in simplest form — GCF of 5 and 6 is 1!
📋 Step-by-Step Working
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Fraction Calculator — Complete Guide to Fractions
Fractions are one of the most fundamental concepts in mathematics — used in cooking recipes, construction measurements, financial calculations and everyday problem solving. Whether you are adding fractions for a recipe, dividing fractions in algebra or working with mixed numbers in construction our fraction calculator handles every operation instantly and shows you the exact step-by-step working so you can learn as you calculate.
How to Add and Subtract Fractions — Step by Step
Adding and subtracting fractions requires a common denominator. Unlike multiplication and division where you operate directly on numerators and denominators separately, addition and subtraction require both fractions to have the same denominator before combining numerators.
Adding Fractions with Different Denominators:
Step 1: Find the Least Common Denominator (LCD)
Step 2: Convert each fraction to have the LCD
Step 3: Add or subtract the numerators only
Step 4: Keep the denominator, then simplify
Example: 1/3 + 1/4
LCD of 3 and 4 = 12
1/3 = 4/12 (multiply top and bottom by 4)
1/4 = 3/12 (multiply top and bottom by 3)
4/12 + 3/12 = 7/12
Example: 3/4 + 2/3
LCD = 12
3/4 = 9/12 2/3 = 8/12
9/12 + 8/12 = 17/12 = 1 and 5/12 (as mixed number)
How to Multiply and Divide Fractions
Multiplication and division are simpler than addition — no common denominator needed. For multiplication simply multiply numerators together and denominators together. For division use the KCF rule: Keep, Change, Flip.
Multiplying Fractions:
a/b x c/d = (a x c) / (b x d)
Example: 2/3 x 3/4 = 6/12 = 1/2
Cross-cancel before multiplying to simplify:
2/3 x 3/4 (cancel the 3s) = 2/1 x 1/4 = 2/4 = 1/2
Dividing Fractions (KCF Method):
Keep: keep the first fraction unchanged
Change: change division sign to multiplication
Flip: take the reciprocal of the second fraction
Example: 2/3 divided by 4/5
= 2/3 x 5/4 (flipped 4/5 to 5/4)
= 10/12 = 5/6
How to Work with Mixed Numbers
A mixed number combines a whole number and a fraction — like 2 and 3/4. Convert to improper fractions before performing arithmetic. An improper fraction has a numerator larger than its denominator.
Converting Mixed Number to Improper Fraction:
Formula: (whole x denominator + numerator) / denominator
Example: 2 and 3/4 = (2 x 4 + 3) / 4 = 11/4
Example: 3 and 1/2 = (3 x 2 + 1) / 2 = 7/2
Converting Improper Fraction back to Mixed Number:
Divide numerator by denominator
Quotient is the whole number
Remainder over original denominator is the fraction
Example: 17/5 = 3 remainder 2 = 3 and 2/5
How to Simplify (Reduce) Fractions
A fraction is in simplest form when numerator and denominator share no common factors except 1. Divide both by their Greatest Common Factor (GCF).
| Original Fraction | GCF | Simplified | Decimal |
|---|---|---|---|
| 2/4 | 2 | 1/2 | 0.5 |
| 6/9 | 3 | 2/3 | 0.667 |
| 12/18 | 6 | 2/3 | 0.667 |
| 15/25 | 5 | 3/5 | 0.6 |
| 24/36 | 12 | 2/3 | 0.667 |
| 100/150 | 50 | 2/3 | 0.667 |
Common Fraction to Decimal Conversion Reference Chart
Knowing these common fraction-decimal equivalents saves time in exams, cooking, construction and financial calculations. These are the most frequently encountered fractions in everyday mathematics.
| Fraction | Decimal | Percentage | Common Use |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half of anything |
| 1/3 | 0.333... | 33.3% | Splitting three ways |
| 1/4 | 0.25 | 25% | Quarter — cooking, money |
| 3/4 | 0.75 | 75% | Three quarters |
| 1/5 | 0.2 | 20% | Tax rates, discounts |
| 1/8 | 0.125 | 12.5% | Cooking measurements |
| 2/3 | 0.667... | 66.7% | Recipes, two thirds |
| 3/8 | 0.375 | 37.5% | Construction, imperial |
Real-World Uses of Fraction Calculations
- Cooking and baking: Scaling recipes requires fraction arithmetic. Tripling a recipe needing 2/3 cup requires 2/3 x 3 = 2 cups. Halving 3/4 teaspoon requires 3/4 divided by 2 = 3/8 teaspoon.
- Construction and carpentry: Imperial measurements require constant fraction work — adding 3 and 5/8 inches to 4 and 7/16 inches, or calculating board lengths in fractional feet.
- Finance and money: Interest rate calculations use fractional percentages. Use our Percentage Calculator to convert fraction results to percentages instantly!
- Academic mathematics: Fractions are the foundation for algebra, calculus and statistics. Strong fraction skills directly improve overall mathematics performance. Track your progress with our Grade Calculator!
- Probability: All probability values are fractions between 0 and 1. Adding probabilities, finding complements and conditional probability all use fraction operations.
Common Fraction Mistakes to Avoid
- Wrong: 1/2 + 1/3 = 2/5 — Never add numerators and denominators separately!
- Correct: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 — Always find common denominator first!
- Wrong: 2/3 divided by 4 = 2/12 — Forgetting to flip the divisor!
- Correct: 2/3 divided by 4 = 2/3 x 1/4 = 2/12 = 1/6 — Flip 4 to 1/4 then multiply!
- Wrong: Leaving 6/12 without simplifying to 1/2!
- Correct: Always divide both numbers by GCF to get simplest form!
📚 Note: This fraction calculator handles all standard operations including mixed numbers and provides step-by-step working for educational purposes. Results are mathematically exact. For complex algebraic fractions with variables use a dedicated computer algebra system.
Frequently Asked Questions
How do you add fractions with different denominators? +
Find the Least Common Denominator (LCD), convert each fraction to have the LCD by multiplying numerator and denominator by the same number, then add the numerators and keep the denominator. Example: 1/3 + 1/4 — LCD = 12 — gives 4/12 + 3/12 = 7/12. Always simplify the result by dividing both numbers by their Greatest Common Factor.
How do you multiply fractions? +
Simply multiply numerator by numerator and denominator by denominator. Example: 2/3 x 3/4 = 6/12 = 1/2. You can simplify before multiplying using cross-cancellation — dividing any numerator and any denominator by their common factor before multiplying — which keeps numbers smaller throughout the calculation.
How do you divide fractions? +
Use KCF — Keep the first fraction unchanged, Change the division sign to multiplication, Flip the second fraction (reciprocal). Example: 2/3 divided by 4/5 = 2/3 x 5/4 = 10/12 = 5/6. This works because dividing by a fraction is mathematically identical to multiplying by its reciprocal.
How do you add mixed numbers? +
Convert mixed numbers to improper fractions first then add normally. Multiply whole number by denominator and add numerator. Example: 2 and 1/3 becomes (2x3+1)/3 = 7/3. Then add improper fractions using the common denominator method and convert the final result back to a mixed number if needed.
How do you simplify a fraction? +
Find the Greatest Common Factor (GCF) of numerator and denominator then divide both by it. Example: 12/18 — GCF of 12 and 18 is 6 — so 12/18 divided by 6/6 = 2/3. A fraction is fully simplified when the GCF equals 1 meaning numerator and denominator share no common factors. Our calculator automatically simplifies all results.
What is an improper fraction? +
An improper fraction has a numerator larger than or equal to its denominator — like 7/4 or 9/3. It represents a value of 1 or greater. Convert to a mixed number by dividing numerator by denominator: the quotient becomes the whole number and the remainder over the original denominator becomes the fraction part. Example: 7 divided by 4 = 1 remainder 3 = 1 and 3/4.
What is the difference between a fraction and a ratio? +
A fraction represents part of a whole — 3/4 means 3 parts out of 4 equal parts of one thing. A ratio compares two separate quantities — 3:4 means for every 3 of one thing there are 4 of another. Fractions convert to decimals by dividing numerator by denominator. While mathematically related they have different contextual meanings in problems.
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