Fraction Calculator
Add, subtract, multiply, and divide fractions with ease
Calculate Fractions
🔢 Quick Answer
1/2 + 1/4 = 3/4 (decimal: 0.7500)
Dr. Snezana Lawrence
Mathematical Historian
15+ years experience
PhD from Yale University. Published mathematical historian ensuring precision in all calculations.
Education
PhD in Mathematical History - Yale University
📑 Table of Contents
➕ How to Add Fractions
To add fractions, you need a common denominator. Here's the step-by-step process:
Formula: a/b + c/d = (ad + bc) / bd
- Find the least common denominator (LCD)
- Convert each fraction to an equivalent fraction with the LCD
- Add the numerators
- Keep the common denominator
- Simplify the result if possible
Example: 1/4 + 2/3
LCD = 12
1/4 = 3/12
2/3 = 8/12
3/12 + 8/12 = 11/12
➖ How to Subtract Fractions
Subtracting fractions follows the same process as addition, but you subtract the numerators:
Formula: a/b - c/d = (ad - bc) / bd
Example: 3/4 - 1/3
LCD = 12
3/4 = 9/12
1/3 = 4/12
9/12 - 4/12 = 5/12
✖️ How to Multiply Fractions
Multiplying fractions is straightforward - no common denominator needed:
Formula: a/b × c/d = (a × c) / (b × d)
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Example: 2/3 × 3/4
Numerators: 2 × 3 = 6
Denominators: 3 × 4 = 12
Result: 6/12 = 1/2
➗ How to Divide Fractions
To divide fractions, multiply by the reciprocal (flip the second fraction):
Formula: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
- Keep the first fraction as is
- Change division to multiplication
- Flip the second fraction (reciprocal)
- Multiply and simplify
Example: 1/2 ÷ 1/4
1/2 ÷ 1/4 = 1/2 × 4/1
= 4/2
= 2
🔽 How to Simplify Fractions
Simplify a fraction by dividing both numerator and denominator by their greatest common divisor (GCD):
- Find the GCD of the numerator and denominator
- Divide both numbers by the GCD
- The result is the simplified fraction
Example: Simplify 12/18
GCD of 12 and 18 = 6
12 ÷ 6 = 2
18 ÷ 6 = 3
Result: 2/3
Common Fractions to Decimals
❓ Frequently Asked Questions
How do you add fractions?
To add fractions: 1) Find a common denominator, 2) Convert each fraction to an equivalent fraction with the common denominator, 3) Add the numerators and keep the denominator, 4) Simplify if possible.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and multiply the denominators together. Then simplify if possible.
How do you divide fractions?
To divide fractions, multiply by the reciprocal. Keep the first fraction, change division to multiplication, and flip the second fraction.
What is a mixed number?
A mixed number combines a whole number and a proper fraction. For example, 2 1/2 (two and one-half) is a mixed number representing 5/2.
What is an improper fraction?
An improper fraction has a numerator larger than or equal to the denominator. For example, 7/4 is improper because 7 > 4. It can be converted to the mixed number 1 3/4.
🔗 Related Calculators
Ratio Calculator
Solve ratio and proportion problems
Percentage Calculator
Calculate percentages easily
Standard Deviation Calculator
Calculate statistics for data sets
Probability Calculator
Calculate probability and odds
Tip Calculator
Calculate tips and split bills
Discount Calculator
Calculate discounts and savings
Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
View LinkedIn Profile