# Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 5/6 + 8/9 - 7/12 = 41/36 = 1 5/36 ≅ 1.1388889

The spelled result in words is forty-one thirty-sixths (or one and five thirty-sixths).

### How do we solve fractions step by step?

1. Add: 5/6 + 8/9 = 5 · 3/6 · 3 + 8 · 2/9 · 2 = 15/18 + 16/18 = 15 + 16/18 = 31/18
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 9) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 9 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - five sixths plus eight ninths is thirty-one eighteenths.
2. Subtract: the result of step No. 1 - 7/12 = 31/18 - 7/12 = 31 · 2/18 · 2 - 7 · 3/12 · 3 = 62/36 - 21/36 = 62 - 21/36 = 41/36
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(18, 12) = 36. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 18 × 12 = 216. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-one eighteenths minus seven twelfths is forty-one thirty-sixths.

### Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by 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 integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

### Math Symbols

SymbolSymbol nameSymbol MeaningExample
-minus signsubtraction 1 1/2 - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate 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 of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.