# Fraction calculator

This 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.

## Result:

### 81/5 - 42/5 = 19/5 = 3 4/5 = 3.8

Spelled result in words is nineteen fifths (or three and four fifths).

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

1. Conversion a mixed number 8 1/5 to a improper fraction: 8 1/5 = 8 1/5 = 8 · 5 + 1/5 = 40 + 1/5 = 41/5

To find a new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 5/5 = 40/5
b) Add the answer from previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
c) Write a previous answer (new numerator 41) over the denominator 5.

Eight and one fifth is forty-one fifths
2. Conversion a mixed number 4 2/5 to a improper fraction: 4 2/5 = 4 2/5 = 4 · 5 + 2/5 = 20 + 2/5 = 22/5

To find a new numerator:
a) Multiply the whole number 4 by the denominator 5. Whole number 4 equally 4 * 5/5 = 20/5
b) Add the answer from previous step 20 to the numerator 2. New numerator is 20 + 2 = 22
c) Write a previous answer (new numerator 22) over the denominator 5.

Four and two fifths is twenty-two fifths
3. Subtract: 41/5 - 22/5 = 41 - 22/5 = 19/5
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-one fifths minus twenty-two fifths is nineteen fifths.

#### 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 signs 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 /) has the same priority and then must evaluate from left to right.