Subtraction of Fractions Calculator

Published on: March 3, 2024
Final Answer: Free • Full Steps: Free

This Subtraction of Fractions Calculator helps you subtract one fraction from another and shows the working clearly at every step. Fractions can only be subtracted when their denominators match, so the first job is giving both of them the same denominator. Once they match, subtract the numerators 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 subtracting 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. Subtract the numerators. Keep the denominator 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 denominator.

See Example 1 Hide Example 1

Problem

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

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Subtract the numerators. Keep the denominator 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 subtracting \(\frac{1}{2}\) from \(\frac{3}{4}\).

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

Step 2

Step 2 - Make the denominators match.

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

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

Step 3

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

In this problem: Now both fractions have denominator \(4\), so we subtract the numerators: \(3 - 2 = 1\).

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

Step 4

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

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

\(\frac{1}{4}\)

Final Answer

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

Problem

\(\frac{5}{18} - \frac{2}{10}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Make the denominators match.
  3. Subtract the numerators. Keep the denominator 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 subtracting \(\frac{2}{10}\) from \(\frac{5}{18}\).

\(\frac{5}{18} - \frac{2}{10}\)

Step 2

Step 2 - Make the denominators match.

In this problem: The denominators are \(18\) and \(10\). The smallest number they both divide into is \(90\), because \(18 \times 5 = 90\) and \(10 \times 9 = 90\). So we multiply the first fraction by \(\frac{5}{5}\) and the second by \(\frac{9}{9}\).

\(\frac{5}{18} \times \frac{5}{5} = \frac{25}{90}\)
\(\frac{2}{10} \times \frac{9}{9} = \frac{18}{90}\)

Step 3

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

In this problem: Now both fractions have denominator \(90\), so we subtract the numerators: \(25 - 18 = 7\).

\(\frac{25}{90} - \frac{18}{90} = \frac{7}{90}\)

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 \(90\) is \(1\), and \(7 \div 1 = 7\), so nothing changes.

\(\frac{7}{90}\)

Final Answer

\(\frac{5}{18} - \frac{2}{10} = \frac{7}{90}\)

Example Problems

Click one to load it into the box and solve it.