Math

Verified calculator with a transparent formula

Math

Add Fractions Calculator.

Adds two fractions and returns the result in simplest form.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Find a common denominator by multiplying the two denominators.

  2. 2

    Convert each fraction to an equivalent fraction with that common denominator.

  3. 3

    Add the numerators and keep the common denominator.

  4. 4

    Simplify the resulting fraction if possible.

(numerator1*denominator2 + numerator2*denominator1) / (denominator1*denominator2)

Frequently asked questions

What if the denominators are the same?

Then you can simply add the numerators and keep the denominator, then simplify.

Can I add more than two fractions?

This calculator handles two fractions at a time. For more, add them in pairs.

How do I simplify the result?

Divide the numerator and denominator by their greatest common divisor (GCD).

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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Adds two fractions and returns the result in simplest form.

  1. Find a common denominator by multiplying the two denominators.
  2. Convert each fraction to an equivalent fraction with that common denominator.
  3. Add the numerators and keep the common denominator.
  4. Simplify the resulting fraction if possible.

Formulas

The math behind this calculator, written out so you can verify the result.

Addition of fractions

a/b + c/d = (a*d + c*b) / (b*d)

Multiply the numerator of each fraction by the denominator of the other, sum them, and divide by the product of the denominators.

Example:

Input: 1/2 + 1/3

Calculation: (1*3 + 1*2) / (2*3) = 5/6

Result: ≈ 0.8333

Real-world use cases

Where this calculation shows up in everyday life.

Cooking measurements

Combine fractional ingredient amounts, like 1/2 cup plus 1/3 cup.

Example: 1/2 + 1/3 = 5/6 cup

Time calculations

Add fractional hours or minutes, such as 1/4 hour plus 1/2 hour.

Example: 1/4 + 1/2 = 3/4 hour

Construction and DIY

Sum fractional lengths, like 3/8 inch plus 1/4 inch.

Example: 3/8 + 1/4 = 5/8 inch

Tips and common mistakes

Tips

  • Always check if the denominators are the same first.
  • Simplify the final fraction to its lowest terms.
  • Use negative numerators for negative fractions.
  • Double-check your arithmetic when multiplying large numbers.

Common Mistakes to Avoid

  • Forgetting to multiply the numerator when converting to a common denominator.
  • Adding denominators directly instead of finding a common denominator.
  • Not simplifying the final fraction.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.