# 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:

### 91/4 - 45/6 = 53/12 = 4 5/12 ≅ 4.4166667

Spelled result in words is fifty-three twelfths (or four and five twelfths).

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

1. Conversion a mixed number 9 1/4 to a improper fraction: 9 1/4 = 9 1/4 = 9 · 4 + 1/4 = 36 + 1/4 = 37/4

To find a new numerator:
a) Multiply the whole number 9 by the denominator 4. Whole number 9 equally 9 * 4/4 = 36/4
b) Add the answer from the previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
c) Write a previous answer (new numerator 37) over the denominator 4.

Nine and one quarter is thirty-seven quarters.
2. Conversion a mixed number 4 5/6 to a improper fraction: 4 5/6 = 4 5/6 = 4 · 6 + 5/6 = 24 + 5/6 = 29/6

To find a new numerator:
a) Multiply the whole number 4 by the denominator 6. Whole number 4 equally 4 * 6/6 = 24/6
b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
c) Write a previous answer (new numerator 29) over the denominator 6.

Four and five sixths is twenty-nine sixths.
3. Subtract: 37/4 - 29/6 = 37 · 3/4 · 3 - 29 · 2/6 · 2 = 111/12 - 58/12 = 111 - 58/12 = 53/12
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, 6) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 6 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-seven quarters minus twenty-nine sixths is fifty-three 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 be evaluated from left to right.