# 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:

### 75/12 - 21/2 = 59/12 = 4 11/12 ≅ 4.9166667

Spelled result in words is fifty-nine twelfths (or four and eleven twelfths).

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

1. Conversion a mixed number 7 5/12 to a improper fraction: 7 5/12 = 7 5/12 = 7 · 12 + 5/12 = 84 + 5/12 = 89/12

To find a new numerator:
a) Multiply the whole number 7 by the denominator 12. Whole number 7 equally 7 * 12/12 = 84/12
b) Add the answer from the previous step 84 to the numerator 5. New numerator is 84 + 5 = 89
c) Write a previous answer (new numerator 89) over the denominator 12.

Seven and five twelfths is eighty-nine twelfths.
2. Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

To find a new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
b) Add the answer from the previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs.
3. Subtract: 89/12 - 5/2 = 89/12 - 5 · 6/2 · 6 = 89/12 - 30/12 = 89 - 30/12 = 59/12
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, 2) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 2 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eighty-nine twelfths minus five halfs is fifty-nine twelfths.

#### 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 evaluate from left to right.