# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### (8/9 - 1/4)-(1/2 + 5/6) = -25/36 ≅ -0.6944444

Spelled result in words is minus twenty-five thirty-sixths.

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

1. Subtract: 8/9 - 1/4 = 8 · 4/9 · 4 - 1 · 9/4 · 9 = 32/36 - 9/36 = 32 - 9/36 = 23/36
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(9, 4) = 36. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 4 = 36. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight ninths minus one quarter is twenty-three thirty-sixths.
2. Add: 1/2 + 5/6 = 1 · 3/2 · 3 + 5/6 = 3/6 + 5/6 = 3 + 5/6 = 8/6 = 2 · 4/2 · 3 = 4/3
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(2, 6) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 6 = 12. In the following intermediate step, cancel by a common factor of 2 gives 4/3.
In other words - one half plus five sixths is four thirds.
3. Subtract: the result of step No. 1 - the result of step No. 2 = 23/36 - 4/3 = 23/36 - 4 · 12/3 · 12 = 23/36 - 48/36 = 23 - 48/36 = -25/36
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(36, 3) = 36. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 36 × 3 = 108. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-three thirty-sixths minus four thirds is minus twenty-five 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.