Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

The result:

12/13x(3/8 - 1/6) = 5/26 ≅ 0.1923077

The spelled result in words is five twenty-sixths.

How do we solve fractions step by step?

Subtract: 3/8 - 1/6 = 3 · 3/8 · 3 - 1 · 4/6 · 4 = 9/24 - 4/24 = 9 - 4/24 = 5/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three eighths minus one sixth is five twenty-fourths.
Multiple: 12/13 * the result of step No. 1 = 12/13 * 5/24 = 12 · 5/13 · 24 = 60/312 = 5 · 12/26 · 12 = 5/26
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(60, 312) = 12. In the following intermediate step, cancel by a common factor of 12 gives 5/26.
In other words - twelve thirteenths multiplied by five twenty-fourths is five twenty-sixths.

Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by 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 integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . 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 of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.