Calculate with fractions

 Fraction 1: Fraction 2: Operation: Addition (+) Subtraction (−) Multiplication (×) Division (÷)
 Show calculation

The tool performs calculations involving two fractions. The answer is presented as a new fraction in its most simplified form. If "show calculation" is selected the tool will explain in detail how the calculation can be carried out by hand.

To be able to write two fractions that are being added or subtracted on the same line both denominators have to be equal. If the denominators are not equal the fractions will have to be reduced (by dividing both numerator and denominator so that the fraction is written with smaller values) or extended (by multiplying both numerator and denominator so that the fraction is written with larger values) so that the denominators become the same.

It is always possible to extend the fractions to make the denominators equal, but reducing does not always work. If one does not want to calculate the smallest common denominator it is always possible to extend each fraction by multiplying by the denominator of the other fraction. This way always works but often result in numerators and denominators that are unnecessarily large.

a
b
+
c
d
=
a × d
b × d
+
b × c
b × d

When both fractions has the same denominator they can be written on the same line which makes it easy to carry out the addition or subtraction in the numerator.

a
c
+
b
c
=
a + b
c

Multiplication and division of fractions

Division by a fraction is the same as multiplying by the reciprocal (i.e. the inverse). In other words, the division can be substituted with a multiplication if the numerator and denominator are swapped at the same time.

a
b

c
d
=
a
b
×
d
c

Multiplication of two fractions is easy to calculate. The numerators and denominators are multiplied separately to form the resulting fraction.

a
b
×
c
d
=
a × c
b × d

Other tools that use fractions

Write decimal numbers as fractions, either exactly or as approximations with denominators of limited size.
Simplify a fraction as much as possible.
Calculate the lowest common denominator for two or more fractions.