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 + 0.413 + 0.173 = 3293/500 = 6 293/500 = 6.586

The result spelled out in words is three thousand two hundred ninety-three five-hundredths (or six and two hundred ninety-three five-hundredths).

How do we solve fractions step by step?

Conversion a decimal number to a fraction: 0.413 = 413/1000 = 413/1000

a) Write down the decimal 0.413 divided by 1: 0.413 = 0.413/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.413/1 = 4.13/10 = 41.3/100 = 413/1000
Note: 413/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
413/1000 = 413 * 1/1000 * 1 = 413 * 1/1000 * 1
Add: 6 + 0.413 = 6/1 + 413/1000 = 6 · 1000/1 · 1000 + 413/1000 = 6000/1000 + 413/1000 = 6000 + 413/1000 = 6413/1000
The first operand is an integer. It is equivalent to a fraction 6/1. 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(1, 1000) = 1000. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 1000 = 1000. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, six plus four hundred thirteen thousandths equals six thousand four hundred thirteen thousandths.
Conversion a decimal number to a fraction: 0.173 = 173/1000 = 173/1000

a) Write down the decimal 0.173 divided by 1: 0.173 = 0.173/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.173/1 = 1.73/10 = 17.3/100 = 173/1000
Note: 173/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
173/1000 = 173 * 1/1000 * 1 = 173 * 1/1000 * 1
Add: the result of step No. 2 + 0.173 = 6413/1000 + 0.173 = 6413/1000 + 173/1000 = 6413 + 173/1000 = 6586/1000 = 2 · 3293/2 · 500 = 3293/500
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, cancel by a common factor of 2 gives 3293/500.
In other words, six thousand four hundred thirteen thousandths plus one hundred seventy-three thousandths equals three thousand two hundred ninety-three five-hundredths.

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.