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:

7 2/3 + 9 3/4 = 209/12 = 17 5/12 ≅ 17.4166667

The result spelled out in words is two hundred nine twelfths (or seventeen and five twelfths).

How do we solve fractions step by step?

Conversion a mixed number 7 2/3 to a improper fraction: 7 2/3 = 7 2/3 = 7 · 3 + 2/3 = 21 + 2/3 = 23/3

To find a new numerator:
a) Multiply the whole number 7 by the denominator 3. Whole number 7 equally 7 * 3/3 = 21/3
b) Add the answer from the previous step 21 to the numerator 2. New numerator is 21 + 2 = 23
c) Write a previous answer (new numerator 23) over the denominator 3.

Seven and two thirds is twenty-three thirds.
Conversion a mixed number 9 3/4 to a improper fraction: 9 3/4 = 9 3/4 = 9 · 4 + 3/4 = 36 + 3/4 = 39/4

To find a new numerator:
a) Multiply the whole number 9 by the denominator 4. Whole number 9 equally 9 * 4/4 = 36/4
b) Add the answer from the previous step 36 to the numerator 3. New numerator is 36 + 3 = 39
c) Write a previous answer (new numerator 39) over the denominator 4.

Nine and three quarters is thirty-nine quarters.
Add: 23/3 + 39/4 = 23 · 4/3 · 4 + 39 · 3/4 · 3 = 92/12 + 117/12 = 92 + 117/12 = 209/12
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(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-three thirds plus thirty-nine quarters equals two hundred nine twelfths.

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.