Add, subtract, multiply and divide fractions.
Enter two fractions and an operation to see the result reduced to lowest terms, as a decimal, and as a mixed number, all worked out step by step.
Your fractions
What this means
The two fractions and the result
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How fractions work
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.
Common questions
What is an improper fraction?
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.
Why can't you divide by a fraction with a zero denominator?
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.
How do I find the least common 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.
Can I use negative numbers in fractions?
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.
For learning and quick reference. Always double-check critical calculations by hand.