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 5/8 + 9 1/2 = 169/8 = 21 1/8 = 21.125

The result spelled out in words is one hundred sixty-nine eighths (or twenty-one and one eighth).

How do we solve fractions step by step?

Conversion a mixed number 11 5/8 to a improper fraction: 11 5/8 = 11 5/8 = 11 · 8 + 5/8 = 88 + 5/8 = 93/8

To find a new numerator:
a) Multiply the whole number 11 by the denominator 8. Whole number 11 equally 11 * 8/8 = 88/8
b) Add the answer from the previous step 88 to the numerator 5. New numerator is 88 + 5 = 93
c) Write a previous answer (new numerator 93) over the denominator 8.

Eleven and five eighths is ninety-three eighths.
Conversion a mixed number 9 1/2 to a improper fraction: 9 1/2 = 9 1/2 = 9 · 2 + 1/2 = 18 + 1/2 = 19/2

To find a new numerator:
a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 2/2 = 18/2
b) Add the answer from the previous step 18 to the numerator 1. New numerator is 18 + 1 = 19
c) Write a previous answer (new numerator 19) over the denominator 2.

Nine and a half is nineteen halves.
Add: 93/8 + 19/2 = 93/8 + 19 · 4/2 · 4 = 93/8 + 76/8 = 93 + 76/8 = 169/8
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 2) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, ninety-three eighths plus nineteen halves equals one hundred sixty-nine 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.