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:

2 5/12 + 3 8/12 = 73/12 = 6 1/12 ≅ 6.0833333

The spelled result in words is seventy-three twelfths (or six and one twelfth).

How do we solve fractions step by step?

Conversion a mixed number 2 5/12 to a improper fraction: 2 5/12 = 2 5/12 = 2 · 12 + 5/12 = 24 + 5/12 = 29/12

To find a new numerator:
a) Multiply the whole number 2 by the denominator 12. Whole number 2 equally 2 * 12/12 = 24/12
b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
c) Write a previous answer (new numerator 29) over the denominator 12.

Two and five twelfths is twenty-nine twelfths.
Conversion a mixed number 3 8/12 to a improper fraction: 3 8/12 = 3 8/12 = 3 · 12 + 8/12 = 36 + 8/12 = 44/12

To find a new numerator:
a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12
b) Add the answer from the previous step 36 to the numerator 8. New numerator is 36 + 8 = 44
c) Write a previous answer (new numerator 44) over the denominator 12.

Three and eight twelfths is forty-four twelfths.
Add: 29/12 + 44/12 = 29 + 44/12 = 73/12
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(12, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 12 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-nine twelfths plus forty-four twelfths is seventy-three twelfths.

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.