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:

11.775 * 5 = 471/8 = 58 7/8 = 58.875

The result spelled out in words is four hundred seventy-one eighths (or fifty-eight and seven eighths).

How do we solve fractions step by step?

Conversion a decimal number to a fraction: 11.775 = 11775/1000 = 471/40

a) Write down the decimal 11.775 divided by 1: 11.775 = 11.775/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
11.775/1 = 117.75/10 = 1177.5/100 = 11775/1000
Note: 11775/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
11775/1000 = 471 * 25/40 * 25 = 471 * 25/40 * 25 = 471/40
Multiple: 11.775 * 5 = 471 · 5/40 · 1 = 2355/40 = 471 · 5/8 · 5 = 471/8
The second operand is an integer. It is equivalent to the fraction 5/1. Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2355, 40) = 5. In the following intermediate step, cancel by a common factor of 5 gives 471/8.
In other words, four hundred seventy-one fortieths multiplied by five equals four hundred seventy-one eighths.

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.