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:

1/2 - 1/5 - 5 = -47/10 = -4 7/10 = -4.7

The result spelled out in words is minus forty-seven tenths (or minus four and seven tenths).

How do we solve fractions step by step?

Subtract: 1/2 - 1/5 = 1 · 5/2 · 5 - 1 · 2/5 · 2 = 5/10 - 2/10 = 5 - 2/10 = 3/10
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 5) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, one half minus one fifth equals three tenths.
Subtract: the result of step No. 1 - 5 = 3/10 - 5 = 3/10 - 5/1 = 3/10 - 5 · 10/1 · 10 = 3/10 - 50/10 = 3 - 50/10 = -47/10
The second operand is an integer. It is equivalent to the fraction 5/1. It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 1) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 1 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, three tenths minus five equals minus forty-seven tenths.

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.