Fraction calculator

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

The result:

5 5/6 - 6 1/6 = -1/3 ≅ -0.3333333

The result spelled out in words is minus one third.

How do we solve fractions step by step?

Conversion a mixed number 5 5/6 to a improper fraction: 5 5/6 = 5 5/6 = 5 · 6 + 5/6 = 30 + 5/6 = 35/6

To find a new numerator:
a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6
b) Add the answer from the previous step 30 to the numerator 5. New numerator is 30 + 5 = 35
c) Write a previous answer (new numerator 35) over the denominator 6.

Five and five sixths is thirty-five sixths.
Conversion a mixed number 6 1/6 to a improper fraction: 6 1/6 = 6 1/6 = 6 · 6 + 1/6 = 36 + 1/6 = 37/6

To find a new numerator:
a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6
b) Add the answer from the previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
c) Write a previous answer (new numerator 37) over the denominator 6.

Six and one sixth is thirty-seven sixths.
Subtract: 35/6 - 37/6 = 35 - 37/6 = -2/6 = 2 · -1/2 · 3 = -1/3
Both fractions have the same denominator, which is then the common denominator in the subtracting them. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-five sixths minus thirty-seven sixths equals minus one third.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . and they are automatically converted to fractions - i.e. 1.45.

Math Symbols

Symbol	Symbol name	Symbol Meaning	Example
+	plus sign	addition	1/2 + 1/3
-	minus sign	subtraction	1 1/2 - 2/3
*	asterisk	multiplication	*2/3 3/4**
×	times sign	multiplication	2/3 × 5/6
:	division sign	division	1/2 : 3
/	division slash	division	1/3 / 5
:	colon	complex fraction	1/2 : 1/3
^	caret	exponentiation / power	1/4^3
()	parentheses	calculate 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 are:

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
GEMDAS: Grouping symbols (brackets: `(){}`), Exponents, Multiplication, Division, Addition, Subtraction.
MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.

Important Notes:
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., `+` and `-`, or `*` and `/`) must be evaluated from left to right.