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:

11 3/7 - 8 6/8 = 75/28 = 2 19/28 ≅ 2.6785714

The result spelled out in words is seventy-five twenty-eighths (or two and nineteen twenty-eighths).

How do we solve fractions step by step?

Conversion a mixed number 11 3/7 to a improper fraction: 11 3/7 = 11 3/7 = 11 · 7 + 3/7 = 77 + 3/7 = 80/7

To find a new numerator:
a) Multiply the whole number 11 by the denominator 7. Whole number 11 equally 11 * 7/7 = 77/7
b) Add the answer from the previous step 77 to the numerator 3. New numerator is 77 + 3 = 80
c) Write a previous answer (new numerator 80) over the denominator 7.

Eleven and three sevenths is eighty sevenths.
Conversion a mixed number 8 6/8 to a improper fraction: 8 6/8 = 8 6/8 = 8 · 8 + 6/8 = 64 + 6/8 = 70/8

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 6. New numerator is 64 + 6 = 70
c) Write a previous answer (new numerator 70) over the denominator 8.

Eight and six eighths is seventy eighths.
Subtract: 80/7 - 70/8 = 80 · 8/7 · 8 - 70 · 7/8 · 7 = 640/56 - 490/56 = 640 - 490/56 = 150/56 = 2 · 75/2 · 28 = 75/28
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(7, 8) = 56. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 8 = 56. In the following intermediate step, cancel by a common factor of 2 gives 75/28.
In other words, eighty sevenths minus seventy eighths equals seventy-five twenty-eighths.

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.