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:

4/9 + 5/6 + 7/12 + 11/15 = 467/180 = 2 107/180 ≅ 2.5944444

The result spelled out in words is four hundred sixty-seven one-hundred eightieths (or two and one hundred seven one-hundred eightieths).

How do we solve fractions step by step?

Add: 4/9 + 5/6 = 4 · 2/9 · 2 + 5 · 3/6 · 3 = 8/18 + 15/18 = 8 + 15/18 = 23/18
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(9, 6) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 6 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, four ninths plus five sixths equals twenty-three eighteenths.
Add: the result of step No. 1 + 7/12 = 23/18 + 7/12 = 23 · 2/18 · 2 + 7 · 3/12 · 3 = 46/36 + 21/36 = 46 + 21/36 = 67/36
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(18, 12) = 36. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 18 × 12 = 216. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-three eighteenths plus seven twelfths equals sixty-seven thirty-sixths.
Add: the result of step No. 2 + 11/15 = 67/36 + 11/15 = 67 · 5/36 · 5 + 11 · 12/15 · 12 = 335/180 + 132/180 = 335 + 132/180 = 467/180
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(36, 15) = 180. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 36 × 15 = 540. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, sixty-seven thirty-sixths plus eleven fifteenths equals four hundred sixty-seven one-hundred eightieths.

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.