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:

18 3/4 - 5 7/8 = 103/8 = 12 7/8 = 12.875

The result spelled out in words is one hundred three eighths (or twelve and seven eighths).

How do we solve fractions step by step?

Conversion a mixed number 18 3/4 to a improper fraction: 18 3/4 = 18 3/4 = 18 · 4 + 3/4 = 72 + 3/4 = 75/4

To find a new numerator:
a) Multiply the whole number 18 by the denominator 4. Whole number 18 equally 18 * 4/4 = 72/4
b) Add the answer from the previous step 72 to the numerator 3. New numerator is 72 + 3 = 75
c) Write a previous answer (new numerator 75) over the denominator 4.

Eighteen and three quarters is seventy-five quarters.
Conversion a mixed number 5 7/8 to a improper fraction: 5 7/8 = 5 7/8 = 5 · 8 + 7/8 = 40 + 7/8 = 47/8

To find a new numerator:
a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47
c) Write a previous answer (new numerator 47) over the denominator 8.

Five and seven eighths is forty-seven eighths.
Subtract: 75/4 - 47/8 = 75 · 2/4 · 2 - 47/8 = 150/8 - 47/8 = 150 - 47/8 = 103/8
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(4, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, seventy-five quarters minus forty-seven eighths equals one hundred three 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

Op	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.