# Subtracting Fractions Calculator

## How many fractions?

Step-by-step solution:

Use this calculator to subtract two or more fractions. You can perform addition and subtraction operations with up to four fractions. The answer along with the step-by-step solution is displayed on the panel.

## How to use the calculator to subtract fractions?

Step 1: Click on “2”, “3” or “4” depending on the number of fractions you want to use.

Step 2: Write the numerators and denominators of the fractions in the corresponding input boxes.

Step 3: Click on the signs to change to plus or minus if necessary.

Step 4: Click “Subtract”.

Step 5: The answer along with the step-by-step solution will be displayed on the panel.

## How to subtract homogeneous fractions?

Let’s recall that homogeneous fractions are two or more fractions that have the same denominators. We can subtract these types of fractions by combining the denominators and subtracting the numerators.

#### Example 1:

Find the result of $latex \frac{2}{5}-\frac{1}{5}$.

Solution: To subtract two homogeneous fractions, we simply have to combine the denominators and subtract the numerators:

$$\frac{2}{5}-\frac{1}{5}$$

$$=\frac{2-1}{5}$$

$$=\frac{1}{5}$$

#### Example 2:

Determine the result of $latex \frac{5}{6}-\frac{2}{6}+\frac{1}{6}$.

Solution: In this case, we have a subtraction of three homogeneous fractions. To solve this operation, we combine the denominators and subtract the numerators:

$$\frac{5}{6}-\frac{2}{6}-\frac{1}{6}$$

$$=\frac{5-2-1}{6}$$

$$=\frac{2}{6}=\frac{1}{3}$$

## How to subtract heterogeneous fractions?

Let’s recall that heterogeneous fractions are two or more fractions with different denominators. To subtract these types of fractions, we have to start by finding their least common denominator (LCD).

Then, we divide each numerator by the LCD and multiply both the numerator and denominator of each fraction by the result. In this way, we will obtain equivalent fractions, where the denominators are the same.

Once we have fractions with the same denominator, we simply have to combine the denominators and subtract the numerators.

#### Example 1:

Find the result of $latex \frac{2}{3}-\frac{1}{2}$.

Solution: To subtract these heterogeneous fractions, we start by finding the LCD to get like fractions.

In this case, the LCD of 3 and 2 equals 6. Therefore, let’s divide 6 by each denominator and multiply both the numerator and the numerator by the result:

$$\frac{2}{3}-\frac{1}{2}$$

$$=\frac{2\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}$$

$$=\frac{4}{6}-\frac{3}{6}$$

Now, we can easily subtract the homogeneous fractions:

$$\frac{4}{6}-\frac{3}{6}$$

$$=\frac{4-3}{6}$$

$$=\frac{1}{6}$$

#### Example 2:

What is the result of $latex \frac{3}{2}-\frac{2}{3}-\frac{1}{4}$?

Solution: To subtract the three heterogeneous fractions, we have to start by finding the least common denominator to get equivalent homogeneous fractions.

In this case, the LCD of 2, 3, and 4 equals 12. Therefore, let’s divide 12 by each denominator and multiply both the numerator and the numerator by the result:

$$\frac{3}{2}-\frac{2}{3}-\frac{1}{4}$$

$$=\frac{3\times 6}{2\times 6}-\frac{2\times 4}{3\times 4}-\frac{1\times 3}{4\times 3}$$

$$=\frac{18}{12}-\frac{8}{12}-\frac{3}{12}$$

Now, we can add the homogeneous fractions easily:

$$\frac{18}{12}-\frac{8}{12}-\frac{3}{12}$$

$$=\frac{18-8-3}{12}$$

$$=\frac{7}{12}$$

## Related calculators:

You can explore other calculators here.