Operations With Fractions Calculator

[ 19 Votes ]

The Operations With Fractions Calculator will calculate:

  1. The sum, difference, product and quotient of two given fractions and provide the result as a fraction, an equivalent decimal number and a rounded number

Operations With Fractions Calculator Parameters: All numerators and denominators are integers

Operations With Fractions Calculator
Select Fraction Operation for Calculation


Operations With Fractions Calculator Results (detailed calculations and formula below)

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each operations with fractions calculation, the Operations With Fractions Calculator will automatically calculate the results and update the formula elements with each element of the operations with fractions calculation. You can then email or print this operations with fractions calculation as required for later use.

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[ 19 Votes ]
Operations With Fractions. This image shows the properties and operations with fractions formula for the Operations With Fractions

Theoretical description

Fractions represent a specific part of a whole. They are an alternative method to express a division between two numbers, where the dividend is called numerator and divisor is called denominator.

We can add, subtract, multiply or divide fractions with each other. In addition, we can raise a fraction at a given power exactly as we do with integers. The rules for each operation are as follows:

Addition and subtraction of fractions with the same denominator.

When we add or subtract two or more fractions with the same denominator, only numerators are added/subtracted while the denominator does not change. In symbols, we have:

a/c ± b/c = a ± b/c

For example,

5/14 + 3/14 = 8/14

and

5/14 - 3/14 = 2/14

Addition and subtraction of fractions with different denominators.

When adding or subtracting two or more fractions with different denominators, we first write the fractions involved in the operation at the same denominator and then we add/subtract them using the method above. In symbols, we have

a/b ± c/d = a × d ± b × c/b × d

It is better if we use the LCM of denominators as a common denominator as this avoids the necessity of further simplifications.

For example,

2/3 + 4/7 = 2 × 7 + 4 × 3/3 × 7 = 14 + 12/21 = 26/21

and

2/3 - 4/7 = 2 × 7 - 4 × 3/3 × 7 = 14 - 12/21 = 2/21

Multiplication of fractions

When two or more fractions are multiplied, all numerators are multiplied separately and all denominators are also multiplied separately. The two numbers obtained represent the numerator and denominator of the product. In symbols, we have

a/b × c/d = a × c/b × c

For example,

3/4 × 2/11 = 3 × 2/4 × 11 = 6/44

Division of fractions

In division of two fractions, the second fraction is inverted down and eventually the multiplication rules are applied. In symbols, we have

a/b ÷ c/d = a/b × d/c = a × d/b × c

This rule derives from the fact that division is a multiplication by the inverse.

For example,

5/6 ÷ 2/3 = 5/6 × 3/2 = 5 × 3/6 × 2 = 15/12

Power of a fraction

When a fraction is raised in a certain power, both numerator and denominator of the given fraction are raised in that power. The general rule applied in this case is

(a/b)n = a/b × a/b × (n times) = a × a × (n times)/b × b × (n times) = an/bn

For example,

(3/5)4 = 3/5 × 3/5 × 3/5 × 3/5 = 3 × 3 × 3 × 3/5 × 5 × 5 × 5 = 34/54 = 81/625

In addition, we can use the PEMDAS Rule (see the Arithmetic Expressions Calculator for more info about this rule) in operations with fractions as well, when more than one operation with fractions is involved in a certain expression. For example, in the expression

5/3 - 1/2 ÷ 2/7

we first find the value of division and then we do the subtraction. Hence,

5/3 - 1/2 ÷ 2/7 = 5/3 - 1/2 × 7/2
= 5/3 - 7/4
= 5 × 4/3 × 4 - 7 × 3/4 × 3
= 20/12 - 21/12
= -1/12

Fractions Math Tutorials associated with the Operations With Fractions Calculator

The following Math tutorials are provided within the Fractions section of our Free Math Tutorials. Each Fractions tutorial includes detailed Fractions formula and example of how to calculate and resolve specific Fractions questions and problems. At the end of each Fractions tutorial you will find Fractions revision questions with a hidden answer that reveal when clicked. This allows you to learn about Fractions and test your knowledge of Math by answering the revision questions on Fractions.