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:

27 1/3 - 14 7/15 = 193/15 = 12 13/15 ≅ 12.8666667

The result spelled out in words is one hundred ninety-three fifteenths (or twelve and thirteen fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 27 1/3 to a improper fraction: 27 1/3 = 27 1/3 = 27 · 3 + 1/3 = 81 + 1/3 = 82/3

To find a new numerator:
a) Multiply the whole number 27 by the denominator 3. Whole number 27 equally 27 * 3/3 = 81/3
b) Add the answer from the previous step 81 to the numerator 1. New numerator is 81 + 1 = 82
c) Write a previous answer (new numerator 82) over the denominator 3.

Twenty-seven and one third is eighty-two thirds.
Conversion a mixed number 14 7/15 to a improper fraction: 14 7/15 = 14 7/15 = 14 · 15 + 7/15 = 210 + 7/15 = 217/15

To find a new numerator:
a) Multiply the whole number 14 by the denominator 15. Whole number 14 equally 14 * 15/15 = 210/15
b) Add the answer from the previous step 210 to the numerator 7. New numerator is 210 + 7 = 217
c) Write a previous answer (new numerator 217) over the denominator 15.

Fourteen and seven fifteenths is two hundred seventeen fifteenths.
Subtract: 82/3 - 217/15 = 82 · 5/3 · 5 - 217/15 = 410/15 - 217/15 = 410 - 217/15 = 193/15
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 15) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 15 = 45. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eighty-two thirds minus two hundred seventeen fifteenths equals one hundred ninety-three fifteenths.

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.