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:

6 2/5 + 3 1/8 + 2/3 = 1223/120 = 10 23/120 ≅ 10.1916667

The result spelled out in words is one thousand two hundred twenty-three one-hundred twentieths (or ten and twenty-three one-hundred twentieths).

How do we solve fractions step by step?

Conversion a mixed number 6 2/5 to a improper fraction: 6 2/5 = 6 2/5 = 6 · 5 + 2/5 = 30 + 2/5 = 32/5

To find a new numerator:
a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5
b) Add the answer from the previous step 30 to the numerator 2. New numerator is 30 + 2 = 32
c) Write a previous answer (new numerator 32) over the denominator 5.

Six and two fifths is thirty-two fifths.
Conversion a mixed number 3 1/8 to a improper fraction: 3 1/8 = 3 1/8 = 3 · 8 + 1/8 = 24 + 1/8 = 25/8

To find a new numerator:
a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 8.

Three and one eighth is twenty-five eighths.
Add: 32/5 + 25/8 = 32 · 8/5 · 8 + 25 · 5/8 · 5 = 256/40 + 125/40 = 256 + 125/40 = 381/40
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(5, 8) = 40. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-two fifths plus twenty-five eighths equals three hundred eighty-one fortieths.
Add: the result of step No. 3 + 2/3 = 381/40 + 2/3 = 381 · 3/40 · 3 + 2 · 40/3 · 40 = 1143/120 + 80/120 = 1143 + 80/120 = 1223/120
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(40, 3) = 120. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 40 × 3 = 120. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, three hundred eighty-one fortieths plus two thirds equals one thousand two hundred twenty-three one-hundred twentieths.

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.