Fraction calculator

This calculator adds two fractions. First, all fractions are converted to a common denominator when they have different denominators. To do this, find the Least Common Denominator (LCD) or multiply all denominators to determine a common denominator. Once all denominators are the same, add the numerators and place the result over the common denominator. Finally, simplify the result to its lowest terms or convert it to a mixed number.

The result:

11/15 + 12/19 = 389/285 = 1 104/285 ≅ 1.3649123

The result spelled out in words is three hundred eighty-nine two-hundred eighty-fifths (or one and one hundred four two-hundred eighty-fifths).

How do we solve fractions step by step?

Add: 11/15 + 12/19 = 11 · 19/15 · 19 + 12 · 15/19 · 15 = 209/285 + 180/285 = 209 + 180/285 = 389/285
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, 19) = 285. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 19 = 285. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eleven fifteenths plus twelve nineteenths equals three hundred eighty-nine two-hundred eighty-fifths.

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.