Fraction Calculator
Add, subtract, multiply, divide fractions
4 operations
Auto simplification
Mixed numbers
Decimal conversion
What's 3/4 plus 2/3? Your tape measure shows 5 and 7/16 inches—how do you add that to 3 and 3/4? The recipe needs to be halved: what's half of 2/3 cup?
Fraction math is everywhere—construction, cooking, sewing, woodworking. This calculator handles addition, subtraction, multiplication, division, and simplification of fractions and mixed numbers.
What is Fraction Calculation?
Fractions represent parts of wholes. Unlike decimals, fractions often express exact values (1/3 instead of 0.333...). Operations on fractions require finding common denominators for addition/subtraction and follow specific rules for multiplication/division.
The operations:
Addition/Subtraction: Find common denominator
a/b + c/d = (ad + bc) / bd
Multiplication: Straight across
a/b Ă— c/d = ac / bd
Division: Multiply by reciprocal
a/b Ă· c/d = a/b Ă— d/c = ad / bc
Simplify: Divide by GCD
Do operations first, simplify the result. Simplifying mid-calculation can sometimes help, but always simplify the final answer.
Why People Actually Need This Tool
A tape measure shows 1/16 increments, not 0.0625. Recipes use 1/3 cup, not 0.333 cups. Fractions are the native language of many domains.
-
Woodworking — Add and subtract fractional measurements.
-
Cooking — Scale recipes up or down.
-
Sewing — Calculate fabric with fractional yard measurements.
-
Construction — Work with fractional inch specifications.
-
Education — Check homework and understand concepts.
-
Music — Work with time signatures and note durations.
-
Finance — Calculate with historical stock prices (pre-decimal).
How to Use the Fraction Calculator
-
Enter fractions — Numerator, denominator, and optional whole number.
-
Select operation — Add, subtract, multiply, divide, or simplify.
-
View result — Simplified fraction and decimal equivalent.
| Operation | Method | Example |
|---|---|---|
| Addition | Common denominator, add numerators | 1/2 + 1/3 = 5/6 |
| Subtraction | Common denominator, subtract nums | 3/4 - 1/3 = 5/12 |
| Multiply | Multiply across | 2/3 Ă— 3/4 = 6/12 = 1/2 |
| Division | Multiply by reciprocal | 1/2 Ă· 3/4 = 2/3 |
| Simplify | Divide by GCD | 6/8 = 3/4 |
Convert mixed numbers to improper fractions first: 2 1/3 = 7/3. Then perform operations.
Real-World Use Cases
1. The Measurement Addition
Context: Board length: 5 7/8". Need to add 3 3/4".
Problem: Total length?
Solution: 47/8 + 15/4 = 47/8 + 30/8 = 77/8 = 9 5/8".
Outcome: Accurate measurement for cut list.
2. The Recipe Scaling
Context: Recipe calls for 2/3 cup flour. Making 1.5Ă— the recipe.
Problem: How much flour?
Solution: 2/3 Ă— 3/2 = 6/6 = 1 cup.
Outcome: Correct ingredient amount for scaled recipe.
3. The Fabric Calculation
Context: Pattern needs 2 3/4 yards. Have 5 1/2 yards total.
Problem: How much fabric remains?
Solution: 11/2 - 11/4 = 22/4 - 11/4 = 11/4 = 2 3/4 yards remaining.
Outcome: Know exactly what's left for other projects.
4. The Drill Bit Selection
Context: Hole needs to be 3/8" to 1/2" range. Have 7/16" bit.
Problem: Is 7/16" within range?
Solution: Convert to 16ths: 6/16 < 7/16 < 8/16. Yes, 7/16" is within range.
Outcome: Correct bit selected.
5. The Division Problem
Context: 3/4 of a pizza divided among 3 people.
Problem: How much does each person get?
Solution: 3/4 Ă· 3 = 3/4 Ă— 1/3 = 3/12 = 1/4 each.
Outcome: Fair division calculated.
6. The Music Time
Context: Adding note durations: half note + quarter note + eighth note.
Problem: Total duration in measures (4/4 time)?
Solution: 1/2 + 1/4 + 1/8 = 4/8 + 2/8 + 1/8 = 7/8 of a measure.
Outcome: Note values summed correctly.
7. The Simplification
Context: Calculated result is 24/36.
Problem: Simplify to lowest terms.
Solution: GCD(24, 36) = 12. 24/36 = 2/3.
Outcome: Clean fraction for practical use.
Common Mistakes and How to Avoid Them
1/2 + 1/3 ≠2/5. You need a common denominator: 3/6 + 2/6 = 5/6.
Privacy and Data Handling
This Fraction Calculator operates entirely in your browser.
- No calculations are sent to any server.
- No data is stored.
- No account required.
- Works completely offline.
Your calculations stay private.
Conclusion
Fractions are essential in practical work—measuring, cooking, building, and countless other applications. Understanding fraction operations prevents errors in these important tasks.
This calculator handles all fraction operations, including mixed numbers. Enter any fractions, perform any operation, get simplified results.
Part of the whole, precisely calculated.