Adding Fractions Calculator

About Adding Fractions Calculator

To add fractions, find a common denominator, convert both fractions, add numerators, and simplify by dividing by the GCD.

How to use this calculator

1. Enter the first fraction as a numerator and denominator.
2. Enter the second fraction as a numerator and denominator.
3. Click calculate to add the fractions.
4. Review the simplified answer and the steps shown by the calculator.

The formula explained

To add \(\frac{a}{b}\) and \(\frac{c}{d}\), first make a common denominator, then combine the numerators: \(\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\). The calculator uses this rule and then simplifies the fraction if possible.

• a = the numerator of the first fraction
• b = the denominator of the first fraction
• c = the numerator of the second fraction
• d = the denominator of the second fraction

Step by step method

1. Multiply the first numerator by the second denominator, and the second numerator by the first denominator.
2. Add those two products to get the new numerator.
3. Multiply the denominators to get the common denominator.
4. Simplify the fraction if the numerator and denominator have a common factor.

Worked example

Problem. Add \(\frac{2}{3}\) and \(\frac{5}{6}\).

1. Use the formula: \(\frac{2}{3} + \frac{5}{6} = \frac{2 \cdot 6 + 5 \cdot 3}{3 \cdot 6}\).
2. Compute the numerator and denominator: \(\frac{12 + 15}{18} = \frac{27}{18}\).
3. Simplify by dividing top and bottom by \(9\): \(\frac{27}{18} = \frac{3}{2}\).

Tips and common mistakes

• Make sure the denominators are multiplied, not added, when you form the common denominator.
• Always simplify the final fraction if possible, because the calculator may show an unreduced answer before simplification.

Frequently asked questions