Add Fractions Calculator
Add, subtract, multiply, and divide fractions
How to Use
- Select the operation (add, subtract, multiply, or divide)
- Enter the numerator and denominator for the first fraction
- Enter the numerator and denominator for the second fraction
- Click calculate to see the result, simplified fraction, and steps
What are Fractions?
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). The numerator tells you how many parts you have, while the denominator tells you how many equal parts make up the whole.
Example
In the fraction 3/4, the numerator is 3 (you have 3 parts) and the denominator is 4 (the whole is divided into 4 equal parts).
Fraction Operations
Adding and Subtracting Fractions
Step 1: Find a common denominator (usually the Least Common Multiple)
Step 2: Convert each fraction to have the common denominator
Step 3: Add or subtract the numerators, keeping the denominator the same
Step 4: Simplify the result if possible
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Multiplying Fractions
Step 1: Multiply the numerators together
Step 2: Multiply the denominators together
Step 3: Simplify the result if possible
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing Fractions
Step 1: Flip the second fraction (find its reciprocal)
Step 2: Multiply the first fraction by the reciprocal
Step 3: Simplify the result if possible
Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9
Simplifying Fractions
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD).
Example
To simplify 6/8:
1. Find the GCD of 6 and 8, which is 2
2. Divide both by 2: 6÷2 = 3, 8÷2 = 4
3. Result: 6/8 = 3/4
Real-World Applications
Fractions are used in many everyday situations:
Common Uses
- Cooking: Recipe measurements (1/2 cup, 3/4 teaspoon)
- Construction: Measurements and dimensions
- Time: Portions of an hour (1/4 hour = 15 minutes)
- Finance: Portions of currency or shares
- Sports: Statistics and performance metrics
Frequently Asked Questions
- Why do I need a common denominator to add fractions?
- You need a common denominator because you can only add or subtract parts that are the same size. Just like you can't add 2 apples and 3 oranges to get 5 apples, you can't add halves and thirds directly. Converting to a common denominator makes the parts the same size.
- How do I find the least common denominator (LCD)?
- The LCD is the Least Common Multiple (LCM) of the denominators. You can find it by listing multiples of each denominator until you find the smallest one they share, or by multiplying the denominators and dividing by their GCD.
- Why do we flip and multiply when dividing fractions?
- Dividing by a fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as asking 'how many halves are in this number?' which is the same as multiplying by 2.
- What if my result is an improper fraction?
- An improper fraction (where the numerator is larger than the denominator) is still a valid answer. You can convert it to a mixed number if needed. For example, 7/4 = 1 3/4.