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:

2 2/6 + 1 2/8 = 43/12 = 3 7/12 ≅ 3.5833333

The spelled result in words is forty-three twelfths (or three and seven twelfths).

How do we solve fractions step by step?

Conversion a mixed number 2 2/6 to a improper fraction: 2 2/6 = 2 2/6 = 2 · 6 + 2/6 = 12 + 2/6 = 14/6

To find a new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
b) Add the answer from the previous step 12 to the numerator 2. New numerator is 12 + 2 = 14
c) Write a previous answer (new numerator 14) over the denominator 6.

Two and two sixths is fourteen sixths.
Conversion a mixed number 1 2/8 to a improper fraction: 1 2/8 = 1 2/8 = 1 · 8 + 2/8 = 8 + 2/8 = 10/8

To find a new numerator:
a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8
b) Add the answer from the previous step 8 to the numerator 2. New numerator is 8 + 2 = 10
c) Write a previous answer (new numerator 10) over the denominator 8.

One and two eighths is ten eighths.
Add: 14/6 + 10/8 = 14 · 4/6 · 4 + 10 · 3/8 · 3 = 56/24 + 30/24 = 56 + 30/24 = 86/24 = 2 · 43/2 · 12 = 43/12
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, 8) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 8 = 48. In the following intermediate step, cancel by a common factor of 2 gives 43/12.
In other words - fourteen sixths plus ten eighths is forty-three twelfths.

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.