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:

1 4/11/3 3/5 = 25/66 ≅ 0.3787879

The result spelled out in words is twenty-five sixty-sixths.

How do we solve fractions step by step?

Conversion a mixed number 1 4/11 to a improper fraction: 1 4/11 = 1 4/11 = 1 · 11 + 4/11 = 11 + 4/11 = 15/11

To find a new numerator:
a) Multiply the whole number 1 by the denominator 11. Whole number 1 equally 1 * 11/11 = 11/11
b) Add the answer from the previous step 11 to the numerator 4. New numerator is 11 + 4 = 15
c) Write a previous answer (new numerator 15) over the denominator 11.

One and four elevenths is fifteen elevenths.
Conversion a mixed number 3 3/5 to a improper fraction: 3 3/5 = 3 3/5 = 3 · 5 + 3/5 = 15 + 3/5 = 18/5

To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 3. New numerator is 15 + 3 = 18
c) Write a previous answer (new numerator 18) over the denominator 5.

Three and three fifths is eighteen fifths.
Divide: 15/11 : 18/5 = 15/11 · 5/18 = 15 · 5/11 · 18 = 75/198 = 3 · 25 /3 · 66 = 25/66
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 18/5 is 5/18) 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 3 gives 25/66.
In other words, fifteen elevenths divided by eighteen fifths equals twenty-five sixty-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 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.