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Fraction Calculator

Now you can Add Fractions, Subtract Fractions, Multiply Fractions, or Divide Fractions online. Find your answer in the simplest form with this Online Fraction Calculator.

To reduce a fraction to the simplest form, try our Simplify Fractions Calculator

How do you add fractions?

There are two cases regarding the denominators when we add ordinary fractions that are shown as follow in steps:

Adding fractions that have like denominators:

• Simply add the numerators of the fractions.
• The denominator of the resulting fraction will be the common denominator of the fractions.
• Reduce the resulting fraction.
For example: a/b + d/b = (a + d)/b
or
7/17 + 9/17 = (7 + 9)/17

Adding fractions with different denominators:

• If the denominators don’t match, Multiply the denominators together.
• Adjust your numerators (top numbers) accordingly. E.g. if you doubled the denominator, then double its numerator.
• Add together the numerators, and put this total over the common denominator.
• Simplify the fraction to the smallest possible denominator, with the numerators also reduced proportionately.
Example: a/b + c/d = (ad + cb)/bd
For adding the fractions 1/3 and 1/5,
1/3 + 1/5 = (1*5 + 1*3)/3*5 = 5+3/15 = 8/15
The sum 8/15 is already in its simplest form.

How do you subract fractions?

There are two cases regarding the denominators when we subtract ordinary fractions that are shown as follow with steps:

Subtracting fractions with like denominators:

• Simply subtract the numerators of the fractions.
• The denominator of the resulting fraction will be the common denominator of the fractions.
• Reduce the resulting fraction.
An example
• a/d - c/d = (a-c)/d
• 4/18 - 3/18 = ( 4 - 3)/18 = 1/18

Subtracting fractions with different denominators:

• If the denominators don’t match Multiply the denominators together.
• Adjust your numerators (top numbers) accordingly. E.g. if you doubled the denominator, then double its numerator.
• subtract the numerators, and put this total over the common denominator.
• Simplify the fraction to the smallest possible denominator, with the numerator also reduced proportionately.
a/b - c/d = (ad - cb)/bd
For subtracting the fractions 1/3 and 1/5,
1/3 - 1/5 = (1*5 - 1*3)/3*5 = 5-3/15 = 2/15
Example: For subtracting the fractions 10/15 and 1/5,
10/15 - 1/5 = (10*5 - 1*15)/15*5 = 50-15/75 = 35/75 = 7/15

How do you multiply fractions?

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions, multiplying fractions is shown as follow in steps:

• Simply, the numerators and denominators of each fraction are multiplied.
• The result forms a new numerator and denominator.
• If possible, the solution should be simplified. Refer to the equations below for clarification.
a/b × c/d = a*c / b*d
Example: Multiply the fractions 10/15 and 1/5.
10/15 × 1/5 =10/75
or =2/15
The answer 2/15 is already in its simplest form.

How do you divide fractions?

For dividing the fractions the steps are as follows:
• You first find the reciprocal of the second fraction.
• Then multiply both fractions to get the result.
Example:
For dividing the fraction a/b and c/d the reciprocal of c/d is d/c.
You then multiply the first fraction by the reciprocal of the second fraction.
a/b ÷ c/d =a/b x d/c = a*d / b*c
Example 2: For dividing the fractions 1/5 and 15/4.
1/5 ÷ 15/4 = 1/5 x 4/15 = 4/75
The answer is 4/75. This answer is already in its simplest form. Fraction Calculator

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. This fraction calculator will add, subtract, multiply and divide fractions with like or unlike denominators. You can simplify your complex fractions online here.

How to use the fraction calculator online?

• First, simply input the values of proper or improper fractions e.g. (a, b, c, d) for the fractions in the open box fields.
• Select the mathematical operation you wish to perform (add +, subtract -, multiply x, divide ÷). Then, you hit the calculate button.
• The calculator will instantly and accurately perform the operation and give the answer in the simplest form.
• You can also use the calculator to check your work that you’ve done manually as well as you can read the description where you can easily understand the manual addition, subtraction, multiplication and division of fractions.

Important FAQs

What is meant by the term fraction?

• The term "Fraction" is derived from the Latin word, "Fractus", which means broken. Simple Fractions can also be referred to as "vulgar", or "common" fractions.

How division sign is related to the term fraction?

• The division sign, also sometimes referred to as an "Obelus" is a line with a dot above, and a dot below. If you were to put numbers in the place of the dots, it would look like a fraction.

How to simplify negative fractions online?

• You can use this fraction calculator online for simplifying a negative fraction by inserting a minus sign before the numerator. So if one of your fractions is -9/7, insert -9 in the numerator and 7 in the denominator. You can Add, subtract, multiply and divide negative fractions on this online calculator. What is meant by word ‘Of’ in math problems?
• When you find a math problem that includes the word “of" as in, what is 5/7 of 9/4? Of means you should multiply so you need to solve 5/7 × 9/4.

How to use a whole number in fraction calculator?

• If you want to calculate a fraction with a whole number, simply insert the whole number as a fraction. As an example, if you multiply the fraction 1/2 by 10. First, you enter the fraction in the first two boxes, then enter 10 as a fraction, 10/1.

Random Fraction Facts

• Historical evidence suggests that Egyptians started using fractions about 4,000 years ago.
• There is a legend that one of Pythagoras' realized that the square root of 2 can't be expressed as a fraction. The other followers were outraged by the truth, and drowned him.
• The Vinculum is the line that separates the numerator and the denominator. In medical terms, the vinculum is the band of tissue that connects the flexor tendon to the bone of a finger or toe.
• Some of the first uses for fractions, or how they may have originally been conceived, was through taxation. Dividing up lands and taxing the different sections differently. Ugh, taxes.