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:

3 4/9 - 1 6/9 = 16/9 = 1 7/9 ≅ 1.7777778

The result spelled out in words is sixteen ninths (or one and seven ninths).

How do we solve fractions step by step?

Conversion a mixed number 3 4/9 to a improper fraction: 3 4/9 = 3 4/9 = 3 · 9 + 4/9 = 27 + 4/9 = 31/9

To find a new numerator:
a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 9/9 = 27/9
b) Add the answer from the previous step 27 to the numerator 4. New numerator is 27 + 4 = 31
c) Write a previous answer (new numerator 31) over the denominator 9.

Three and four ninths is thirty-one ninths.
Conversion a mixed number 1 6/9 to a improper fraction: 1 6/9 = 1 6/9 = 1 · 9 + 6/9 = 9 + 6/9 = 15/9

To find a new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9
b) Add the answer from the previous step 9 to the numerator 6. New numerator is 9 + 6 = 15
c) Write a previous answer (new numerator 15) over the denominator 9.

One and six ninths is fifteen ninths.
Subtract: 31/9 - 15/9 = 31 - 15/9 = 16/9
Both fractions have the same denominator, which is then the common denominator in the subtracting them. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-one ninths minus fifteen ninths equals sixteen ninths.

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.