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:

1/5 + 2/3/1000 = 301/1500 ≅ 0.2006667

The result spelled out in words is three hundred one one-thousand five-hundredths.

How do we solve fractions step by step?

Divide: 2/3 : 1000 = 2/3 · 1/1000 = 2 · 1/3 · 1000 = 2/3000 = 2 · 1 /2 · 1500 = 1/1500
The second operand is an integer. It is equivalent to the fraction 1000/1. Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1000/1 is 1/1000) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 1/1500.
In other words, two thirds divided by one thousand equals one one-thousand five-hundredth.
Add: 1/5 + the result of step No. 1 = 1/5 + 1/1500 = 1 · 300/5 · 300 + 1/1500 = 300/1500 + 1/1500 = 300 + 1/1500 = 301/1500
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, 1500) = 1500. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 1500 = 7500. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, one fifth plus one one-thousand five-hundredth equals three hundred one one-thousand 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.