# 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 informations.

## The result:

### 34/9 - 16/9 = 16/9 = 1 7/9 ≅ 1.7777778

The spelled result in words is sixteen ninths (or one and seven ninths).

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

1. Conversion a mixed number 3 4/9 to a improper fraction: 3 4/9 = 3 4/9 = 3 · 9 + 4/9 = 27 + 4/9 = 31/9

To find a new numerator:
a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 9/9 = 27/9
b) Add the answer from the previous step 27 to the numerator 4. New numerator is 27 + 4 = 31
c) Write a previous answer (new numerator 31) over the denominator 9.

Three and four ninths is thirty-one ninths.
2. Conversion a mixed number 1 6/9 to a improper fraction: 1 6/9 = 1 6/9 = 1 · 9 + 6/9 = 9 + 6/9 = 15/9

To find a new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9
b) Add the answer from the previous step 9 to the numerator 6. New numerator is 9 + 6 = 15
c) Write a previous answer (new numerator 15) over the denominator 9.

One and six ninths is fifteen ninths.
3. Subtract: 31/9 - 15/9 = 31 - 15/9 = 16/9
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, 9) = 9. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-one ninths minus fifteen ninths is sixteen ninths.

### 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.