Fraction calculator



This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

The result:

3/2 - 5/6 - 2/9 = 4/90.4444444

The spelled result in words is four ninths.

How do we solve fractions step by step?

  1. Subtract: 3/2 - 5/6 = 3 · 3/2 · 3 - 5/6 = 9/6 - 5/6 = 9 - 5/6 = 4/6 = 2 · 2/2 · 3 = 2/3
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 6) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 6 = 12. In the following intermediate step, cancel by a common factor of 2 gives 2/3.
    In other words - three halfs minus five sixths is two thirds.
  2. Subtract: the result of step No. 1 - 2/9 = 2/3 - 2/9 = 2 · 3/3 · 3 - 2/9 = 6/9 - 2/9 = 6 - 2/9 = 4/9
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 9) = 9. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - two thirds minus two ninths is four ninths.

Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.


Math Symbols


SymbolSymbol nameSymbol MeaningExample
+plus signaddition 1/2 + 1/3
-minus signsubtraction 1 1/2 - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate expression inside first-3/5 - (-1/4)

The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.


Last Modified: October 9, 2024