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:

14 2/3÷2 2/9 = 33/5 = 6 3/5 = 6.6

The result spelled out in words is thirty-three fifths (or six and three fifths).

How do we solve fractions step by step?

Conversion a mixed number 14 2/3 to a improper fraction: 14 2/3 = 14 2/3 = 14 · 3 + 2/3 = 42 + 2/3 = 44/3

To find a new numerator:
a) Multiply the whole number 14 by the denominator 3. Whole number 14 equally 14 * 3/3 = 42/3
b) Add the answer from the previous step 42 to the numerator 2. New numerator is 42 + 2 = 44
c) Write a previous answer (new numerator 44) over the denominator 3.

Fourteen and two thirds is forty-four thirds.
Conversion a mixed number 2 2/9 to a improper fraction: 2 2/9 = 2 2/9 = 2 · 9 + 2/9 = 18 + 2/9 = 20/9

To find a new numerator:
a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 9/9 = 18/9
b) Add the answer from the previous step 18 to the numerator 2. New numerator is 18 + 2 = 20
c) Write a previous answer (new numerator 20) over the denominator 9.

Two and two ninths is twenty ninths.
Divide: 44/3 : 20/9 = 44/3 · 9/20 = 44 · 9/3 · 20 = 396/60 = 12 · 33 /12 · 5 = 33/5
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 20/9 is 9/20) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 12 gives 33/5.
In other words, forty-four thirds divided by twenty ninths equals thirty-three fifths.

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.