AI Math Assistant
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About This Calculator
Fractions represent parts of a whole and require specific rules for addition, subtraction, multiplication, and division that differ from whole number arithmetic. This calculator performs all four operations, simplifies results to lowest terms, and converts between fractions, mixed numbers, and decimals. Proper fraction handling is crucial in cooking measurements, construction tolerances, and any field where exact rational values matter more than decimal approximations.
Quick Tips
- 1 Find a common denominator before adding or subtracting fractions.
- 2 Dividing by a fraction means multiplying by its reciprocal (flip and multiply).
- 3 Always reduce your final answer to the simplest form using the GCF.
Example Calculation
A recipe: 3/4 cup of milk plus 2/3 cup of cream.
3/4 + 2/3 = 17/12 = 1 5/12 cups | Decimal: 1.4167 cups | Common denominator: 12
How to Add and Subtract Fractions
To add or subtract fractions, find a common denominator. The LCD (least common denominator) is the LCM of the denominators. Convert each fraction to the common denominator, then add or subtract the numerators. Example: 3/4 + 1/2 = 3/4 + 2/4 = 5/4.
How to Multiply and Divide Fractions
To multiply fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = ac/bd. To divide, multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc. Always simplify the result.
Simplifying Fractions
To simplify (reduce) a fraction, divide both numerator and denominator by their greatest common factor (GCF). For example, 12/18: GCF of 12 and 18 is 6, so 12/18 = 2/3. A fraction is fully simplified when the GCF of its numerator and denominator is 1.
Converting Between Fractions and Decimals
To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert a decimal to a fraction, write the decimal over the appropriate power of 10 and simplify: 0.75 = 75/100 = 3/4. Repeating decimals like 0.333... = 1/3.
Frequently Asked Questions
An improper fraction has a numerator larger than the denominator (e.g., 5/4). It can be converted to a mixed number: 5/4 = 1¼. Both representations are mathematically equivalent.
Division by zero is undefined in mathematics. A fraction with a zero denominator has no value. The calculator will show an error if you enter 0 as any denominator.
The LCD is the least common multiple (LCM) of the denominators. For 3/4 and 1/6, the LCM of 4 and 6 is 12. So convert to 9/12 and 2/12 before adding or subtracting.
Yes. A negative sign can be placed on the numerator, denominator, or in front of the fraction — all are equivalent. By convention, the negative sign is usually placed on the numerator or in front: -3/4.