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:

-8 3/8 - 10 1/6 = -445/24 = -18 13/24 ≅ -18.5416667

The result spelled out in words is minus four hundred forty-five twenty-fourths (or minus eighteen and thirteen twenty-fourths).

How do we solve fractions step by step?

Conversion a mixed number 8 3/8 to a improper fraction: 8 3/8 = 8 3/8 = 8 · 8 + 3/8 = 64 + 3/8 = 67/8

To find a new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from the previous step 64 to the numerator 3. New numerator is 64 + 3 = 67
c) Write a previous answer (new numerator 67) over the denominator 8.

Eight and three eighths is sixty-seven eighths.
Unary minus: -67/8 = -67/8
Conversion a mixed number 10 1/6 to a improper fraction: 10 1/6 = 10 1/6 = 10 · 6 + 1/6 = 60 + 1/6 = 61/6

To find a new numerator:
a) Multiply the whole number 10 by the denominator 6. Whole number 10 equally 10 * 6/6 = 60/6
b) Add the answer from the previous step 60 to the numerator 1. New numerator is 60 + 1 = 61
c) Write a previous answer (new numerator 61) over the denominator 6.

Ten and one sixth is sixty-one sixths.
Subtract: the result of step No. 2 - 61/6 = -67/8 - 61/6 = -67 · 3/8 · 3 - 61 · 4/6 · 4 = -201/24 - 244/24 = -201 - 244/24 = -445/24
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, minus sixty-seven eighths minus sixty-one sixths equals minus four hundred forty-five twenty-fourths.

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.