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 at every step. Fractions can only be added when their bottom numbers match, so the first job is giving both of them the same bottom number. Once they match, add the top numbers together and leave the bottom number 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 bottom numbers match.
  3. Add the top numbers. Keep the bottom the same.
  4. Do a simplifying of fractions at the end if you can.

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 bottom number.

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 bottom numbers match.
  3. Add the top numbers. Keep the bottom the same.
  4. Do a simplifying of fractions at the end if you can.

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 bottom numbers match.

In this problem: The bottom numbers 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 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

Step 4 - Do a simplifying of fractions at the end if you can.

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 bottom numbers match.
  3. Add the top numbers. Keep the bottom the same.
  4. Do a simplifying of fractions at the end if you can.

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 bottom numbers match.

In this problem: The bottom numbers 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 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

Step 4 - Do a simplifying of fractions at the end if you can.

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

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