# 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:

### 203/4 - 182/3 = 25/12 = 2 1/12 ≅ 2.0833333

Spelled result in words is twenty-five twelfths (or two and one twelfth).

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

1. Conversion a mixed number 20 3/4 to a improper fraction: 20 3/4 = 20 3/4 = 20 · 4 + 3/4 = 80 + 3/4 = 83/4

To find a new numerator:
a) Multiply the whole number 20 by the denominator 4. Whole number 20 equally 20 * 4/4 = 80/4
b) Add the answer from the previous step 80 to the numerator 3. New numerator is 80 + 3 = 83
c) Write a previous answer (new numerator 83) over the denominator 4.

Twenty and three quarters is eighty-three quarters.
2. Conversion a mixed number 18 2/3 to a improper fraction: 18 2/3 = 18 2/3 = 18 · 3 + 2/3 = 54 + 2/3 = 56/3

To find a new numerator:
a) Multiply the whole number 18 by the denominator 3. Whole number 18 equally 18 * 3/3 = 54/3
b) Add the answer from the previous step 54 to the numerator 2. New numerator is 54 + 2 = 56
c) Write a previous answer (new numerator 56) over the denominator 3.

Eighteen and two thirds is fifty-six thirds.
3. Subtract: 83/4 - 56/3 = 83 · 3/4 · 3 - 56 · 4/3 · 4 = 249/12 - 224/12 = 249 - 224/12 = 25/12
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(4, 3) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 3 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eighty-three quarters minus fifty-six thirds is twenty-five 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.