Adding Fractions Calculator

Our versatile Add and Subtract Fractions Calculator allows you to easily compute sums and differences of up to nine fractions simultaneously. Whether you are working with proper or improper fractions, or dealing with positive and negative values, this math tool delivers fast and accurate results.

Directions for use

To use this fraction calculator, first select the total number of fractions you wish to add or subtract. Choose a number between 2 and 9 from the drop-down menu. Once selected, the corresponding number of input boxes will appear.

Next, enter the numerators and denominators for each fraction. If a fraction is negative, simply place the minus sign in either the numerator or denominator field. Note that placing a minus sign in both the numerator and denominator fields will result in a positive fraction, because \$\frac{-a}{-b}\$ = \$\frac{a}{b}\$. Also, keep in mind that a denominator cannot equal 0.

Next, select the mathematical sign for each operation using the drop-down menus to Add "+" or Subtract "-". After filling out all input fields and selecting your operators, click "Calculate."

The adding and subtracting fractions calculator will return the final answer alongside a step-by-step, detailed solution. The final result will be displayed as a simplified proper fraction or a mixed number, depending on the calculation.

How to add and subtract fractions

When the denominators are the same

To add or subtract fractions with like denominators, follow these simple steps:

1. Add or subtract the numerators of the given fractions.
2. Use the result from step 1 as the new numerator, and keep the original denominator as the new denominator.
3. Simplify the resulting fraction, if necessary.

For example, let’s solve the following equation:

\$\frac{1}{8}\$ + \$\frac{13}{8}\$ + \$\frac{3}{8}\$ – \$\frac{5}{8}\$ = ?

All of the given fractions share the same denominator. Following the algorithm above, we get:

1. 1 + 13 + 3 - 5 = 12
2. Because 12 is the new numerator and 8 is the shared denominator, our new fraction is: \$\frac{12}{8}\$.

This fraction can be simplified. Let's find the greatest common factor (GCF) of the numerator and denominator.

• The factors of 8: 1, 2, 4, 8.
• The factors of 12: 1, 2, 3, 4, 6, 12.

Therefore, the greatest common factor of 8 and 12 is 4.

By dividing the numerator and denominator by our GCF (4), we get:

\$\frac{12}{8}\$ = \$\frac{12 ÷ 4}{8 ÷ 4}\$ = \$\frac{3}{2}\$

\$\frac{3}{2}\$ is an improper fraction, so it can be rewritten as a mixed number:

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

The final step-by-step solution looks like this:

\$\frac{1}{8}\$ + \$\frac{13}{8}\$ + \$\frac{3}{8}\$ - \$\frac{5}{8}\$ = \$\frac{1 + 13 + 3 - 5}{8}\$ = \$\frac{12}{8}\$ = \$\frac{3}{2}\$ = \$1\frac{1}{2}\$

When the denominators are different

To add or subtract fractions with unlike denominators, follow these steps:

1. Convert all given fractions to a common denominator. You can do this by finding the least common denominator (LCD) and applying it as the new denominator for every fraction.
2. Once the denominators match, follow the steps outlined above for fractions with the same denominator.

For example, let's solve the following problem:

\$\frac{2}{5}\$ + \$\frac{1}{10}\$ + \$\frac{3}{4}\$ = ?

Since these fractions have different denominators, we need to use the unlike denominators method:

1. To find the LCD of \$\frac{2}{5}\$, \$\frac{1}{10}\$, and \$\frac{3}{4}\$, we first need to find the least common multiple (LCM) of the denominators 5, 10, and 4: LCD (\$\frac{2}{5}\$, \$\frac{1}{10}\$, \$\frac{3}{4}\$) = LCM (5, 10, 4).

Let’s find the LCM (5, 10, 4) by listing out their multiples:

• Multiples of 5: 5, 10, 15, 20, 25, 30…

• Multiples of 10: 10, 20, 30, 40…

• Multiples of 4: 4, 8, 12, 16, 20, 24…

• LCM (5, 10, 4) = 20

• LCD (\$\frac{2}{5}\$, \$\frac{1}{10}\$, \$\frac{3}{4}\$) = 20

Converting all the original fractions to have our new LCD of 20, we get:

• \$\frac{2}{5}\$ = \$\frac{2 × 4}{5 × 4}\$ = \$\frac{8}{20}\$
• \$\frac{1}{10}\$ = \$\frac{1 × 2}{10 × 2}\$ = \$\frac{2}{20}\$
• \$\frac{3}{4}\$ = \$\frac{3 × 5}{4 × 5}\$ = \$\frac{15}{20}\$

The original problem can now be rewritten as:

\$\frac{2}{5}\$ + \$\frac{1}{10}\$ + \$\frac{3}{4}\$ = \$\frac{8}{20}\$ + \$\frac{2}{20}\$ + \$\frac{15}{20}\$

2. Now that the denominators match, we simply add the numerators:

• Adding the numerators together, we get: 8 + 2 + 15 = 25
• The new fraction is \$\frac{25}{20}\$
• Simplifying by dividing the numerator and denominator by 5, we get: \$\frac{25}{20}\$ = \$\frac{25 ÷ 5}{20 ÷ 5}\$ = \$\frac{5}{4}\$ = \$1\frac{1}{4}\$

Finally, the complete equation looks like this:

\$\frac{2}{5}\$ + \$\frac{1}{10}\$ + \$\frac{3}{4}\$ = \$\frac{8}{20}\$ + \$\frac{2}{20}\$ + \$\frac{15}{20}\$ = \$\frac{8 + 2 + 15}{20}\$ = \$\frac{25}{20}\$ = \$\frac{5}{4}\$ = \$1\frac{1}{4}\$

Working with negative fractions

When performing mathematical operations with negative fractions, apply the exact same rules you use when adding and subtracting integers or decimals. The rules for combining mathematical signs are summarized in the table below:

Calculation example

Kate is making a pasta sauce that requires 2 cups of passata (tomato puree). However, she only has \$\frac{1}{3}\$ of a cup left in her pantry. How much more passata does she need to complete her recipe?

Solution

We know that Kate needs 2 total cups of passata but only has \$\frac{1}{3}\$ of a cup. To calculate the missing amount, we must subtract the passata she has from the passata she needs: 2 – \$\frac{1}{3}\$. Since 2 is a whole number, we can rewrite it as a fraction: 2 = \$\frac{2}{1}\$. Therefore, our equation becomes:

\$\frac{2}{1}\$ – \$\frac{1}{3}\$ = ?

Because these fractions have different denominators, we first need to find a common denominator.

LCD (\$\frac{2}{1}\$, \$\frac{1}{3}\$) = LCM (1, 3)

LCM (1, 3) = 3

Converting \$\frac{2}{1}\$ into a fraction with 3 as the denominator, we get:

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

We can now rewrite the original equation as follows:

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

Solving this problem using the method for fractions with the same denominator, we subtract the numerators:

\$\frac{2}{1}\$ – \$\frac{1}{3}\$ = \$\frac{6}{3}\$ – \$\frac{1}{3}\$ = \$\frac{6 – 1}{3}\$ = \$\frac{5}{3}\$

Converting our improper fraction into a mixed number, we get:

\$\frac{5}{3}\$ = \$1\frac{2}{3}\$

Answer

Kate needs \$1\frac{2}{3}\$ more cups of passata to finish her sauce.