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:

1/15 + 9/5 + 3/8 = 269/120 = 2 29/120 ≅ 2.2416667

The result spelled out in words is two hundred sixty-nine one-hundred twentieths (or two and twenty-nine one-hundred twentieths).

How do we solve fractions step by step?

Add: 1/15 + 9/5 = 1/15 + 9 · 3/5 · 3 = 1/15 + 27/15 = 1 + 27/15 = 28/15
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(15, 5) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 5 = 75. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, one fifteenth plus nine fifths equals twenty-eight fifteenths.
Add: the result of step No. 1 + 3/8 = 28/15 + 3/8 = 28 · 8/15 · 8 + 3 · 15/8 · 15 = 224/120 + 45/120 = 224 + 45/120 = 269/120
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(15, 8) = 120. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 8 = 120. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-eight fifteenths plus three eighths equals two hundred sixty-nine one-hundred twentieths.

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.