This online Mixed Fractions Calculator is a free online fraction calculator that allows to add, subtract, multiply and divide fractions. One can use mixed fractions (mixed numbers), improper fractions or whole numbers both positive and negative. The numerator and denominator in a fraction are separated by slash symbol (/). It is important to leave space between the whole number and the fraction part of a mixed number. In case of a negative number the minus sign (-) precedes the fraction or the whole number in a mixed fraction without space between them. Using ‘Mixed’ or ‘Improper’ radio buttons one can choose the form of the resultant fraction representation.
Operations with fractions
In mathematics, a fraction represents a part of a whole or, generally, any number of equal parts of a whole. It is an abstract concept used to indicate amount, length, quantity, etc. not in whole numbers. A common or simple fraction consists of a numerator, displayed above a line (or before a slash), that represents some number of equal parts of a whole, and a non-zero denominator, displayed below that line (or after a slash), that represents the total number of equal parts of a whole. Examples: 1/3 and -15/7. Note that the numerator and denominator are natural numbers.
The fraction is called proper if the numerator is less than the denominator, and improper otherwise. Instead of the improper fractions, mixed fractions (also called mixed numbers) are often used. It is denoted as the sum of a non-zero integer and a proper fraction (examples: 2 1/3 = 7/3 and -1 2/7 = -9/7.
Our online mixed fractions calculator uses the well known math formulas to perform four basic arithmetic operations with mixed numbers. Mixed fractions are first converted to the improper ones, then the following formulas are employed.
Math formula for adding fractions:
$$\frac { A }{ B } +\frac { C }{ D } =\frac { AD+BC }{ BD } $$
Math formula for subtracting fractions:
$$\frac { A }{ B } -\frac { C }{ D } =\frac { AD-BC }{ BD } $$
Math formula for multiplying fractions:
$$\frac { A }{ B } \times \frac { C }{ D } =\frac { AC }{ BD } $$
Math formula for dividing fractions:
$$\frac { A }{ B } \div \frac { C }{ D } =\frac { AD }{ BC } $$
The result can be represented in the form of a mixed number or improper fraction, depending on the option chosen with the help of the ‘Mixed’ and ‘Improper’ radio buttons. One can switch between these options even after the calculation has performed, changing the form of the result representation.
Moreover, you can use our mixed numbers calculator as a mixed numbers converter. Say, you can enter some mixed number in the field ‘Fraction 1’, then put \(0\) in the field ‘Fraction 2’ and choose the ‘+ (Add)’ action. In case the ‘Improper’ radio button is chosen you will get your number in the form of improper fraction in the ‘Result’ field.
If you need to convert a positive decimal number to a fraction please check out our Decimal To Fraction Converter.
Related calculators
Check out our other math calculators such as Comparing Fractions Calculator or Simplify Fraction Calculator.