CalcPro

Fraction Calculator

Add, subtract, multiply or divide two fractions and reduce the result.

How it works

This calculator performs arithmetic operations on two fractions and automatically reduces the result to its simplest form. You enter two fractions (each as a numerator and denominator), select an operation, and the tool handles the computation and simplification in one step.

Fraction arithmetic follows specific rules depending on the operation. Addition and subtraction require a common denominator, while multiplication and division use their own straightforward processes. Once the result is calculated, the greatest common divisor (GCD) is found and used to reduce the fraction.

The formula

(a/b) ○ (c/d) = result, reduced by dividing both numerator and denominator by their GCD

Where ○ represents your chosen operation:

  • Addition: (a/b) + (c/d) = (ad + bc) / bd
  • Subtraction: (a/b) − (c/d) = (ad − bc) / bd
  • Multiplication: (a/b) × (c/d) = (ac) / (bd)
  • Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc)

Worked example

Adding 3/4 and 2/5:

  1. Set up with a common denominator: 3/4 = 15/20 and 2/5 = 8/20
  2. Add the numerators: 15 + 8 = 23
  3. Result: 23/20
  4. Check if reducible: GCD(23, 20) = 1, so it's already in lowest terms
  5. Final answer: 23/20 (or 1 3/20 as a mixed number)

Multiplying 2/3 by 5/8:

  1. Multiply numerators: 2 × 5 = 10
  2. Multiply denominators: 3 × 8 = 24
  3. Result: 10/24
  4. Find GCD(10, 24) = 2
  5. Divide both by 2: 10 ÷ 2 = 5, and 24 ÷ 2 = 12
  6. Final answer: 5/12

Dividing 7/6 by 2/3:

  1. Flip the second fraction: 2/3 becomes 3/2
  2. Multiply: (7/6) × (3/2) = 21/12
  3. Find GCD(21, 12) = 3
  4. Reduce: 21 ÷ 3 = 7, and 12 ÷ 3 = 4
  5. Final answer: 7/4 (or 1 3/4)

Common mistakes

Wrong: Adding denominators when adding fractions (3/4 + 2/5 ≠ 5/9)

Right: Find a common denominator first. The LCD of 4 and 5 is 20, so convert both fractions, then add numerators only.

Wrong: Forgetting to reduce the final answer. 10/24 looks correct but isn't fully simplified.

Right: Always check the GCD of the final numerator and denominator, and divide both by it. Many fraction problems expect the reduced form.

Wrong: Forgetting to flip the second fraction when dividing. (7/6) ÷ (2/3) is NOT (7×2)/(6×3).

Right: Division of fractions means "multiply by the reciprocal." Flip the second fraction, then multiply normally.

Frequently asked questions

What does it mean to reduce a fraction?

Reducing (or simplifying) a fraction means dividing both the numerator and denominator by their greatest common divisor so the fraction is in its simplest form. For example, 10/24 reduces to 5/12 because both can be divided by 2.

Do I need to find a common denominator before multiplying fractions?

No. Multiplication is straightforward: multiply the numerators together and the denominators together. Only addition and subtraction require a common denominator.

How do I divide fractions?

Division of fractions uses the "multiply by the reciprocal" rule. Flip the second fraction upside down, then multiply. For example, (3/4) ÷ (2/5) becomes (3/4) × (5/2) = 15/8.

Can the result be a whole number?

Yes. If the numerator and denominator are equal after reduction, or if the numerator is a multiple of the denominator, the result simplifies to a whole number. For example, 8/4 = 2.

What if one fraction is negative?

The calculator handles negative numerators. The sign follows normal arithmetic rules: negative ÷ positive = negative, negative × negative = positive, and so on.

Why is my result different from another calculator?

Most likely your result isn't fully reduced. Always check that the GCD of the final numerator and denominator is 1. This calculator automatically reduces for you.

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