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 information.

The result:

3 4/6 + 9/18 = 25/6 = 4 1/6 ≅ 4.1666667

The spelled result in words is twenty-five sixths (or four and one sixth).

How do we solve fractions step by step?

Conversion a mixed number 3 4/6 to a improper fraction: 3 4/6 = 3 4/6 = 3 · 6 + 4/6 = 18 + 4/6 = 22/6

To find a new numerator:
a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6
b) Add the answer from the previous step 18 to the numerator 4. New numerator is 18 + 4 = 22
c) Write a previous answer (new numerator 22) over the denominator 6.

Three and four sixths is twenty-two sixths.
Add: 22/6 + 9/18 = 22 · 3/6 · 3 + 9/18 = 66/18 + 9/18 = 66 + 9/18 = 75/18 = 3 · 25/3 · 6 = 25/6
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(6, 18) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 18 = 108. In the following intermediate step, cancel by a common factor of 3 gives 25/6.
In other words - twenty-two sixths plus nine eighteenths is twenty-five sixths.

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 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.