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:

8 4/6 - 5 8/12 = 3/1 = 3

The result spelled out in words is three.

How do we solve fractions step by step?

Conversion a mixed number 8 4/6 to a improper fraction: 8 4/6 = 8 4/6 = 8 · 6 + 4/6 = 48 + 4/6 = 52/6

To find a new numerator:
a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6
b) Add the answer from the previous step 48 to the numerator 4. New numerator is 48 + 4 = 52
c) Write a previous answer (new numerator 52) over the denominator 6.

Eight and four sixths is fifty-two sixths.
Conversion a mixed number 5 8/12 to a improper fraction: 5 8/12 = 5 8/12 = 5 · 12 + 8/12 = 60 + 8/12 = 68/12

To find a new numerator:
a) Multiply the whole number 5 by the denominator 12. Whole number 5 equally 5 * 12/12 = 60/12
b) Add the answer from the previous step 60 to the numerator 8. New numerator is 60 + 8 = 68
c) Write a previous answer (new numerator 68) over the denominator 12.

Five and eight twelfths is sixty-eight twelfths.
Subtract: 52/6 - 68/12 = 52 · 2/6 · 2 - 68/12 = 104/12 - 68/12 = 104 - 68/12 = 36/12 = 12 · 3/12 · 1 = 3
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(6, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 12 = 72. In the following intermediate step, cancel by a common factor of 12 gives 3/1.
In other words, fifty-two sixths minus sixty-eight twelfths equals three.

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.