Addition of Fractions Notes

Published on: September 29, 2026

This Addition of Fractions Calculator helps you add two fractions and shows the working clearly at every step. Fractions can only be added when their denominators match, so the first job is giving both of them the same denominator. Once they match, add the numerators together and leave the denominator alone. Then check whether the answer can be written with smaller numbers. Following the same pattern every time is what makes adding fractions easy to picture, check, and repeat on your own with any two fractions.

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Add the numerators. Keep the denominator the same.
  4. Simplify the answer at the end if you can. This step is Simplifying of Fractions.

Tip: \(\frac{1}{1}\), \(\frac{2}{2}\) and \(\frac{3}{3}\) are all just \(1\). Multiplying by \(1\) never changes how big a fraction is, so it is safe to do. It only cuts the fraction into more pieces that are smaller, which is what lets both fractions share the same denominator.

See Example 1 Hide Example 1

Problem

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

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Add the numerators. Keep the denominator the same.
  4. Simplify the answer at the end if you can. This step is Simplifying of Fractions.

Step 1

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

Step 2 - Make the denominators match.

In this problem: The denominators are \(2\) and \(4\). The smallest number they both divide into is \(4\), because \(2 \times 2 = 4\) and \(4 \times 1 = 4\). So we multiply the first fraction by \(\frac{2}{2}\) and the second by \(\frac{1}{1}\).

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

Step 3

Step 3 - Add the numerators. Keep the denominator the same.

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

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

Step 4

Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.

In this problem: The only number that divides both \(5\) and \(4\) is \(1\), and \(5 \div 1 = 5\), so nothing changes.

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

Final Answer

\(\frac{1}{2} + \frac{3}{4} = \frac{5}{4}\)
See Example 2 Hide Example 2

Problem

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

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Add the numerators. Keep the denominator the same.
  4. Simplify the answer at the end if you can. This step is Simplifying of Fractions.

Step 1

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

Step 2 - Make the denominators match.

In this problem: The denominators are \(6\) and \(3\). The smallest number they both divide into is \(6\), because \(6 \times 1 = 6\) and \(3 \times 2 = 6\). So we multiply the first fraction by \(\frac{1}{1}\) and the second by \(\frac{2}{2}\).

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

Step 3

Step 3 - Add the numerators. Keep the denominator the same.

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

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

Step 4

Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.

In this problem: The only number that divides both \(7\) and \(6\) is \(1\), and \(7 \div 1 = 7\), so nothing changes.

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

Final Answer

\(\frac{5}{6} + \frac{1}{3} = \frac{7}{6}\)
See Example 3 Hide Example 3

Problem

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

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Add the numerators. Keep the denominator the same.
  4. Simplify the answer at the end if you can. This step is Simplifying of Fractions.

Step 1

Step 1 - Set up the problem.

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

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

Step 2

Step 2 - Make the denominators match.

In this problem: The denominators are \(3\) and \(4\). The smallest number they both divide into is \(12\), because \(3 \times 4 = 12\) and \(4 \times 3 = 12\). So we multiply the first fraction by \(\frac{4}{4}\) and the second by \(\frac{3}{3}\).

\(\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}\)
\(\frac{1}{4} \times \frac{3}{3} = \frac{3}{12}\)

Step 3

Step 3 - Add the numerators. Keep the denominator the same.

In this problem: Now both fractions have denominator \(12\), so we add the numerators: \(8 + 3 = 11\).

\(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\)

Step 4

Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.

In this problem: The only number that divides both \(11\) and \(12\) is \(1\), and \(11 \div 1 = 11\), so nothing changes.

\(\frac{11}{12}\)

Final Answer

\(\frac{2}{3} + \frac{1}{4} = \frac{11}{12}\)
See Example 4 Hide Example 4

Problem

\(\frac{3}{10} + \frac{2}{5}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Add the numerators. Keep the denominator the same.
  4. Simplify the answer at the end if you can. This step is Simplifying of Fractions.

Step 1

Step 1 - Set up the problem.

In this problem: We are adding \(\frac{3}{10}\) and \(\frac{2}{5}\).

\(\frac{3}{10} + \frac{2}{5}\)

Step 2

Step 2 - Make the denominators match.

In this problem: The denominators are \(10\) and \(5\). The smallest number they both divide into is \(10\), because \(10 \times 1 = 10\) and \(5 \times 2 = 10\). So we multiply the first fraction by \(\frac{1}{1}\) and the second by \(\frac{2}{2}\).

\(\frac{3}{10} \times \frac{1}{1} = \frac{3}{10}\)
\(\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}\)

Step 3

Step 3 - Add the numerators. Keep the denominator the same.

In this problem: Now both fractions have denominator \(10\), so we add the numerators: \(3 + 4 = 7\).

\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)

Step 4

Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.

In this problem: The only number that divides both \(7\) and \(10\) is \(1\), and \(7 \div 1 = 7\), so nothing changes.

\(\frac{7}{10}\)

Final Answer

\(\frac{3}{10} + \frac{2}{5} = \frac{7}{10}\)