Adding Fractions Calculator

This calculator allows you to subtract or add fractions. It can be used for proper and improper, positive or negative fractions. The calculator can add and subtract up to 9 fractions.

Directions for use

To use the calculator to add fractions, first select the number of fractions you want to add or subtract. This number must be selected from the drop-down menu and can be anything from 2 to 9. Once you select the number of fractions, you will see the corresponding number of input boxes.

Enter the numerators and the denominators of the given fractions. If any of the given fractions is negative, include the minus sign in one of the fields corresponding to that fraction; the minus sign can be included for either the numerator or the denominator. Note, that if you include the minus sign for both the numerator and the denominator fields of the fraction, the resulting fraction will be positive, since \$\frac{-a}{-b}\$ = \$\frac{a}{b}\$. Note also, that the denominators cannot equal 0.

Then choose the mathematical sign for each operation. You can choose Add “+” or Subtract “-” for each operation. After filling all input fields and choosing all signs, press “Calculate.”

Adding fractions сalculator will return the final answer, as well as the detailed solution to the problem of subtracting and adding fractions. The calculator will display the final answer as a simplified proper fraction or as a mixed number.

How to add and subtract fractions

When the denominators are the same

To add or subtract fractions with the same denominators, follow the steps below:

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

For example, let’s solve the following exercise:

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

All given fractions have the same denominator. Following the algorithm presented above, we get:

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

This fraction can be simplified. Let's simplify it by finding 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 numbers 8 and 12 is 4.

By dividing the numerator and denominator by GCF = 4, we get:

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

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

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

The final solution would look 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 different denominators, follow the steps below:

1. Convert all given fractions to one common denominator, by finding the least common denominator (LCD) and using it as the new denominator for all fractions.
2. Follow the steps of the algorithm for fractions with the same denominator.

For example, lets solve the following exercise:

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

The given fractions have different denominators, therefore, we will use the algorithm for fractions with different denominators:

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

Let’s find LCM (5, 10, 4) by listing 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 given fractions to fractions with LCD = 20 as the denominator, 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 example can be rewritten as:

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

2. Following the steps for performing addition of fractions with the same denominator, we get:

• Adding the numerators, we get: 8 + 2 + 15 = 25
• The new fraction will be \$\frac{25}{20}\$
• Simplifying, we get: \$\frac{25}{20}\$ = \$\frac{25 ÷ 5}{20 ÷ 5}\$ = \$\frac{5}{4}\$ = \$1\frac{1}{4}\$

Finally,

\$\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, follow the same rules as when adding and subtracting integers or decimals. The rules for combining the signs are summarized in the table below:

Operation sign	Fraction sign	Resulting operation
+	+	+
-	-	+
+	-	-
-	+	-

Calculation example

Kate is making a pasta sauce, for which she needs 2 cups of passata (tomato puree). She has \$\frac{1}{3}\$ of a cup of passata left in the pantry. How much more passata does she need to finish the sauce?

Solution

We know that Kate needs 2 cups of passata, and already has \$\frac{1}{3}\$ of a cup. To figure out how much more passata she will need, we need to perform the subtraction: 2 – \$\frac{1}{3}\$. 2 is a whole number, which can be written as a fraction: 2 = \$\frac{2}{1}\$. Therefore, the final equation will be:

\$\frac{2}{1}\$ – \$\frac{1}{3}\$ = ?

These two fractions have different denominators, therefore, we will first need to convert them to one common denominator.

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

LCM (1, 3) = 3

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

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

The original equation can be rewritten as follows:

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

Solving this problem by following the algorithm for fractions with the same denominator, we get:

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

Simplifying, we get:

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

Answer

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