Fraction Calculator
Solve fraction arithmetic and simplify fractions step-by-step.
Decimal Equivalent: 1.25
What are Fractions and How Are They Calculated?
A fraction represents a part of a whole or a ratio between two integers. It consists of a top number called the numerator (representing how many parts you have) and a bottom number called the denominator (representing how many total equal parts make up a whole). To calculate fractions with different denominators, convert them to share a common denominator before adding or subtracting, or multiply numerators and denominators straight across.
Find smallest common denominator to combine fractions.
Scale numerators by corresponding multipliers.
Keep common denominator and add scaled numerators.
Extract whole part and remainder.
LCD of 2 and 4 is 4. Convert 1/2 to 2/4. Add 2/4 + 3/4 = 5/4 = 1 1/4.
LCD is 4. 3/4 − 2/4 = 1/4.
Multiply numerators (2×3=6) and denominators (3×5=15). Simplify 6/15 by GCD 3 to get 2/5.
Multiply by reciprocal: 2/3 × 5/4 = 10/12. Simplify by GCD 2 to get 5/6.
GCD of 24 and 36 is 12. 24÷12 = 2, 36÷12 = 3.
Common Real-World Use Cases
Accurately halve, double, or scale ingredient measurements like 3/4 cup or 1 1/2 tsp.
Add and subtract fractional inches (e.g. 5/8" + 7/16") when cutting lumber or measuring clearances.
Check homework solutions for fraction addition, subtraction, multiplication, and simplification.
Calculate fabric yardage and seam allowances with mixed fractional measurements.
- 1Select your desired fraction operation: Add (+), Subtract (−), Multiply (×), Divide (÷), Simplify, or Convert.
- 2Enter the numerators and denominators for your fractions (and optional whole numbers for mixed fractions).
- 3Instantly view the simplified fraction result, mixed number representation, and decimal equivalent.
- 4Review the step-by-step mathematical breakdown showing GCD, LCM, and intermediate steps.
- •The denominator represents total equal parts and cannot be zero.
- •Negative signs are automatically normalized to the numerator for standard mathematical formatting.
- •Toggle between improper fraction view and mixed number view depending on your homework or project needs.
Your calculations are performed securely in your browser and are not uploaded.
Frequently Asked Questions
Complete Guide to Fraction Calculations & Math Rules
What is a Fraction?
A fraction represents a part of a whole or a ratio between two integers. It consists of a top number called the numerator (representing how many parts you have) and a bottom number called the denominator (representing how many total equal parts make up a whole).
How to Add Fractions
To add fractions with like denominators, simply add the numerators together while keeping the denominator constant. To add fractions with different denominators, first find the Least Common Denominator (LCD), convert each fraction to an equivalent fraction with the LCD, add the numerators, and simplify.
Example: 1/2 + 3/4 → LCD is 4 → 2/4 + 3/4 = 5/4 (or 1 1/4).
How to Subtract Fractions
Find a common denominator (LCD), convert each fraction so they share the same denominator, subtract the second numerator from the first numerator, and simplify the resulting fraction.
Example: 3/4 − 1/2 → 3/4 − 2/4 = 1/4.
How to Multiply Fractions
Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. You can also cross-cancel common factors before multiplying to make simplification easier.
Example: (2/3) × (3/5) = (2 × 3) / (3 × 5) = 6/15 = 2/5.
How to Divide Fractions
To divide fractions, use the "Keep, Change, Flip" rule: Keep the first fraction, Change the division sign to multiplication, and Flip the second fraction upside down to its reciprocal. Then multiply across and simplify.
Example: (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.
How to Simplify a Fraction
A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the Greatest Common Divisor (GCD) of both numbers and divide both by the GCD.
For 24/36, the GCD is 12. Divide 24 ÷ 12 = 2 and 36 ÷ 12 = 3 to get 2/3.
Common Fraction Calculations Reference
| Calculation | Simplified | Mixed Number | Decimal |
|---|---|---|---|
| 1/2 + 3/4 | 5/4 | 1 1/4 | 1.25 |
| 3/4 − 1/2 | 1/4 | 1/4 | 0.25 |
| 2/3 × 3/5 | 2/5 | 2/5 | 0.4 |
| 2/3 ÷ 4/5 | 5/6 | 5/6 | 0.833333 |
| 24/36 (Simplify) | 2/3 | 2/3 | 0.666667 |
| 7/4 (Convert) | 7/4 | 1 3/4 | 1.75 |
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