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:

5/6 + 3/4 + 2/3 = 9/4 = 2 1/4 = 2.25

The result spelled out in words is nine quarters (or two and one quarter).

How do we solve fractions step by step?

Add: 5/6 + 3/4 = 5 · 2/6 · 2 + 3 · 3/4 · 3 = 10/12 + 9/12 = 10 + 9/12 = 19/12
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, five sixths plus three quarters equals nineteen twelfths.
Add: the result of step No. 1 + 2/3 = 19/12 + 2/3 = 19/12 + 2 · 4/3 · 4 = 19/12 + 8/12 = 19 + 8/12 = 27/12 = 3 · 9/3 · 4 = 9/4
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(12, 3) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 3 = 36. In the following intermediate step, cancel by a common factor of 3 gives 9/4.
In other words, nineteen twelfths plus two thirds equals nine quarters.

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.