ganak.appFraction Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step solutions. Simplify fractions to lowest terms, convert between decimals and fractions, and see results as fractions, mixed numbers, decimals, and percentages. Includes visual fraction representations and detailed formula breakdowns.
11 of 12 equal parts
Step-by-Step Solution
See how the answer is calculated
What Is a Fraction?
Understanding numerators, denominators, and fraction types
A fraction represents a part of a whole. It consists of two numbers separated by a line: the numerator (top number) tells how many parts you have, and the denominator (bottom number) tells how many equal parts the whole is divided into. For example, 3/4 means 3 out of 4 equal parts.
Fraction Structure
Numerator / Denominator = Part / Whole
Proper fraction: Numerator is less than denominator (e.g., 3/4, 1/2). Value is less than 1.
Improper fraction: Numerator is greater than or equal to denominator (e.g., 7/4, 5/3). Value is 1 or greater.
Mixed number: A whole number combined with a proper fraction (e.g., 1 3/4, 2 1/3). An improper fraction expressed differently.
How to Add and Subtract Fractions
Find a common denominator, then combine numerators
Same Denominator
When fractions share the same denominator, simply add or subtract the numerators and keep the denominator the same.
2/7 + 3/7 = (2 + 3)/7 = 5/7
Different Denominators
Find the Least Common Denominator (LCD), convert each fraction, then add or subtract.
1/4 + 1/6
LCD of 4 and 6 = 12
3/12 + 2/12 = 5/12
General Formula
a/b + c/d = (a×d + c×b) / (b×d)
How to Multiply Fractions
Multiply straight across — numerator by numerator, denominator by denominator
Multiplying fractions is the simplest operation: multiply the numerators together and the denominators together. No common denominator needed. Then simplify the result.
a/b × c/d = (a×c) / (b×d)
Example:
2/3 × 4/5 = (2×4) / (3×5) = 8/15
Tip: You can simplify (cross-cancel) before multiplying to keep numbers smaller. For example, in 4/9 × 3/8, the 4 and 8 share a factor of 4, and the 3 and 9 share a factor of 3, giving 1/3 × 1/2 = 1/6.
How to Divide Fractions
Flip the second fraction and multiply
To divide fractions, multiply the first fraction by the reciprocal (flip) of the second. This is often remembered as “keep, change, flip”: keep the first fraction, change division to multiplication, flip the second fraction.
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example:
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
How to Simplify Fractions
Reduce to lowest terms using the GCD
A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To simplify, find the Greatest Common Divisor (GCD) of both numbers, then divide both by it.
Example: Simplify 18/24
GCD of 18 and 24 = 6
18 ÷ 6 = 3, 24 ÷ 6 = 4
18/24 = 3/4
Converting Between Decimals and Fractions
Switch between decimal and fraction notation
Decimal → Fraction
- 1. Count decimal places
- 2. Write over a power of 10
- 3. Simplify using GCD
- 0.75 = 75/100 = 3/4
Fraction → Decimal
- Divide numerator by denominator
- 3/8 = 3 ÷ 8 = 0.375
- 1/3 = 1 ÷ 3 = 0.333...
Real-World Examples
How fractions appear in everyday life
Cooking & Recipes
A recipe calls for 2/3 cup of flour but you want to make 1.5 batches. How much flour?
2/3 × 3/2 = 6/6 = 1 cup
Construction & Measurement
A board is 5/8 inch thick. You need to stack 3 boards. Total thickness:
5/8 × 3 = 15/8 = 1 7/8 inches
Time & Scheduling
You studied 3/4 hour in the morning and 1/2 hour at night. Total:
3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4 hours
Finance
You own 1/4 of a business. Your partner sells you 1/6 of the company. You now own:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
Common Mistakes When Working with Fractions
Pitfalls to avoid for accurate results
Adding numerators and denominators separately
1/2 + 1/3 is NOT 2/5. You must find a common denominator first: 3/6 + 2/6 = 5/6.
Forgetting to simplify the final answer
Always check if the result can be reduced by finding the GCD of numerator and denominator.
Not converting mixed numbers to improper fractions
For operations, first convert: 2 1/3 = 7/3.
Canceling across addition or subtraction
Cross-cancellation only works with multiplication. You cannot cancel the 3s in 3/7 + 1/3.
Dividing instead of multiplying by the reciprocal
To divide by a fraction, flip the second fraction and multiply. Never divide numerator by numerator.
Frequently Asked Questions
Common questions about fractions, operations, and conversions