Addition of Fractions Calculator

Published on: February 25, 2024
Final Answer: Free • Full Steps: Free

This Addition of Fractions Calculator helps you add two fractions and shows the working clearly step by step. First find a common denominator, then rewrite the fractions so they have the same bottom number. Add the numerators, keep the denominator the same, and simplify the final fraction if possible. It is a simple way to check answers, understand fraction addition, and practise basic arithmetic step by step.

Step-by-step method

  1. Set up the problem.
  2. Make the bottom numbers match. (Same bottom = same-size pieces.)
  3. Add the top numbers. Keep the bottom the same.
  4. Simplify if you can (divide top and bottom by the same number).

Example 1: \(\frac{1}{2} + \frac{3}{4}\)

Step 1 - Set up the problem.

In this problem: We are adding \(\frac{1}{2}\) and \(\frac{3}{4}\).

\(\frac{1}{2} + \frac{3}{4}\)

Step 2 - Make the bottom numbers match. (Same bottom = same-size pieces.)

In this problem: The bottom numbers are \(2\) and \(4\). A good shared bottom number is \(4\). So we change both fractions into equal fractions with the same bottom number.

\(\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}\)
\(\frac{3}{4} \times 1 = \frac{3}{4}\)

Step 3 - Add the top numbers. Keep the bottom the same.

In this problem: Now both fractions have bottom \(4\), so we add the top numbers: \(2 + 3 = 5\).

\(\frac{2}{4} + \frac{3}{4} = \frac{5}{4}\)

Step 4 - Simplify if you can (divide top and bottom by the same number).

In this problem: The numbers \(5\) and \(4\) do not share a bigger common factor, so it is already simplified.

\(\frac{5}{4}\)

Final answer: \(\frac{1}{2} + \frac{3}{4} = \frac{5}{4}\)

Example 2: \(\frac{5}{6} + \frac{1}{3}\)

Step 1 - Set up the problem.

In this problem: We are adding \(\frac{5}{6}\) and \(\frac{1}{3}\).

\(\frac{5}{6} + \frac{1}{3}\)

Step 2 - Make the bottom numbers match. (Same bottom = same-size pieces.)

In this problem: The bottom numbers are \(6\) and \(3\). A good shared bottom number is \(6\). So we change both fractions into equal fractions with the same bottom number.

\(\frac{5}{6} \times 1 = \frac{5}{6}\)
\(\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}\)

Step 3 - Add the top numbers. Keep the bottom the same.

In this problem: Now both fractions have bottom \(6\), so we add the top numbers: \(5 + 2 = 7\).

\(\frac{5}{6} + \frac{2}{6} = \frac{7}{6}\)

Step 4 - Simplify if you can (divide top and bottom by the same number).

In this problem: The numbers \(7\) and \(6\) do not share a bigger common factor, so it is already simplified.

\(\frac{7}{6}\)

Final answer: \(\frac{5}{6} + \frac{1}{3} = \frac{7}{6}\)