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:

3.691/5.1 = 3691/5100 ≅ 0.7237255

The result spelled out in words is three thousand six hundred ninety-one over five thousand one hundred.

How do we solve fractions step by step?

Conversion a decimal number to a fraction: 3.691 = 3691/1000 = 3691/1000

a) Write down the decimal 3.691 divided by 1: 3.691 = 3.691/1
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.)
3.691/1 = 36.91/10 = 369.1/100 = 3691/1000
Note: 3691/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
3691/1000 = 369.1 * 10/100 * 10 = 369.1 * 10/100 * 10
Conversion a decimal number to a fraction: 5.1 = 51/10 = 51/10

a) Write down the decimal 5.1 divided by 1: 5.1 = 5.1/1
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.)
5.1/1 = 51/10
Note: 51/10 is called a decimal fraction.

c) Simplify and reduce the fraction
51/10 = 51 * 1/10 * 1 = 51 * 1/10 * 1
Divide: 3.691 / 5.1 = 3691/1000 · 10/51 = 3691 · 10/1000 · 51 = 36910/51000 = 10 · 3691 /10 · 5100 = 3691/5100
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 51/10 is 10/51) 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 10 gives 3691/5100.
In other words, three thousand six hundred ninety-one thousandths divided by fifty-one tenths equals three thousand six hundred ninety-one over five thousand one hundred.

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.