Fraction Calculator

How to Use This Fraction Calculator

Adding thirds to sixths on scratch paper is one of those small tasks that eats up homework time fast—especially when you still have to simplify and check a decimal answer at the end. This calculator takes two fractions, runs the operation you pick, and prints every intermediate step so you can match your workbook layout instead of guessing where the LCD came from.

• Enter both fractions. Type an integer numerator and a non-zero integer denominator for the first and second fraction. Improper fractions (top larger than bottom) and negative numerators are fine.
• Choose an operation. Select addition, subtraction, multiplication, or division from the dropdown, then press Calculate.
• Read the answer block. You get a simplified fraction, a mixed number when one applies, and a decimal rounded to two places for a quick sense-check.
• Follow the step-by-step section. Each stage—common denominator, reciprocal rewrite, or GCD reduction—is spelled out line by line below the result.
• Share or cross-check. Use Share Calculation to copy a link with your inputs baked in, or verify decimals with the Fraction To Decimal Calculator.

Fraction Formulas and Practical Applications

Think of a fraction as a slice of a pizza cut into equal pieces—the denominator names how many slices make the whole, and the numerator counts how many you took. Once that picture clicks, the four operations are just different ways of combining slices.

Addition and subtraction

a/b ± c/d = (a × LCD/b ± c × LCD/d) / LCD

Here LCD is the least common multiple of b and d. Example: 1/3 + 1/6 uses LCD 6, giving 2/6 + 1/6 = 3/6, which reduces to 1/2.

Multiplication and division

(a/b) × (c/d) = ac/bd

(a/b) ÷ (c/d) = (a/b) × (d/c)

Division flips the second fraction (its reciprocal) and multiplies. Recipe scaling and unit-rate problems use multiplication constantly; dividing fractions shows up when you are splitting a partial batch across containers.

Simplification with GCD

a/b in lowest terms = (a ÷ GCD) / (b ÷ GCD)

Every result path ends by dividing numerator and denominator by their greatest common divisor. For related work—comparing two fractions without combining them—try the Fraction Comparison Calculator or the Mixed Fraction Calculator when your inputs include whole parts.

Standard Units and Conversion Tables

Fractions here are pure rational numbers—no measurement units attached. The decimal column is a fixed two-place preview; for full precision division use the dedicated converter:

To go the other direction—from decimal back to a fraction—use the Decimal To Fraction Converter. Browse all math calculators for related tools.

Frequently Asked Questions

What operations does this Fraction Calculator support?

Add, subtract, multiply, and divide two fractions. Addition and subtraction show LCD equivalents; division shows the reciprocal rewrite before multiplication; every path ends with GCD simplification.

Can numerators be negative or larger than denominators?

Yes. Enter any integers for numerators and any non-zero integers for denominators. Improper fractions follow the same rules—the mixed-number output splits out whole units when the answer is greater than one.

How does the calculator find a common denominator?

It computes the least common multiple of the two denominators, rewrites each fraction with that bottom number, then adds or subtracts the adjusted numerators. The step-by-step panel lists each equivalent fraction so you can copy the work onto paper.

Can I share a specific problem with a classmate?

Yes. After calculating, click Share Calculation to copy a URL that restores your operands, operation, and results when opened.

What is the difference between simplified fraction and mixed number output?

The simplified fraction is the answer in lowest terms as one ratio (for example 7/4). The mixed number expresses the same value with a whole part plus a proper fraction (1 3/4). Both lines describe identical quantities.

Disclaimer. RapidRatio is informational only—not academic or professional advice. Verify steps and results with your instructor when grades or credentials are on the line.