# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 64/12 - 5/10 = 35/6 = 5 5/6 ≅ 5.8333333

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

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

1. Conversion a mixed number 6 4/12 to a improper fraction: 6 4/12 = 6 4/12 = 6 · 12 + 4/12 = 72 + 4/12 = 76/12

To find a new numerator:
a) Multiply the whole number 6 by the denominator 12. Whole number 6 equally 6 * 12/12 = 72/12
b) Add the answer from the previous step 72 to the numerator 4. New numerator is 72 + 4 = 76
c) Write a previous answer (new numerator 76) over the denominator 12.

Six and four twelfths is seventy-six twelfths.
2. Subtract: 76/12 - 5/10 = 76 · 5/12 · 5 - 5 · 6/10 · 6 = 380/60 - 30/60 = 380 - 30/60 = 350/60 = 10 · 35/10 · 6 = 35/6
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(12, 10) = 60. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 10 = 120. In the following intermediate step, cancel by a common factor of 10 gives 35/6.
In other words - seventy-six twelfths minus five tenths is thirty-five 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.