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 1/5 * 1 1/8 = 18/5 = 3 3/5 = 3.6

The result spelled out in words is eighteen fifths (or three and three fifths).

How do we solve fractions step by step?

Conversion a mixed number 3 1/5 to a improper fraction: 3 1/5 = 3 1/5 = 3 · 5 + 1/5 = 15 + 1/5 = 16/5

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 1. New numerator is 15 + 1 = 16
c) Write a previous answer (new numerator 16) over the denominator 5.

Three and one fifth is sixteen fifths.
Conversion a mixed number 1 1/8 to a improper fraction: 1 1/8 = 1 1/8 = 1 · 8 + 1/8 = 8 + 1/8 = 9/8

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 1. New numerator is 8 + 1 = 9
c) Write a previous answer (new numerator 9) over the denominator 8.

One and one eighth is nine eighths.
Multiple: 16/5 * 9/8 = 16 · 9/5 · 8 = 144/40 = 18 · 8/5 · 8 = 18/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(144, 40) = 8. In the following intermediate step, cancel by a common factor of 8 gives 18/5.
In other words, sixteen fifths multiplied by nine eighths equals eighteen 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.