# 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:

### -83/8 - 101/6 = -445/24 = -18 13/24 ≅ -18.5416667

Spelled result in words is minus four hundred forty-five twenty-fourths (or minus eighteen and thirteen twenty-fourths).

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

1. Conversion a mixed number 8 3/8 to a improper fraction: 8 3/8 = 8 3/8 = 8 · 8 + 3/8 = 64 + 3/8 = 67/8

To find a new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from the previous step 64 to the numerator 3. New numerator is 64 + 3 = 67
c) Write a previous answer (new numerator 67) over the denominator 8.

Eight and three eighths is sixty-seven eighths.
2. Unary minus: -67/8 = -67/8
3. Conversion a mixed number 10 1/6 to a improper fraction: 10 1/6 = 10 1/6 = 10 · 6 + 1/6 = 60 + 1/6 = 61/6

To find a new numerator:
a) Multiply the whole number 10 by the denominator 6. Whole number 10 equally 10 * 6/6 = 60/6
b) Add the answer from the previous step 60 to the numerator 1. New numerator is 60 + 1 = 61
c) Write a previous answer (new numerator 61) over the denominator 6.

Ten and one sixth is sixty-one sixths.
4. Subtract: the result of step No. 2 - 61/6 = -67/8 - 61/6 = -67 · 3/8 · 3 - 61 · 4/6 · 4 = -201/24 - 244/24 = -201 - 244/24 = -445/24
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(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus sixty-seven eighths minus sixty-one sixths is minus four hundred forty-five twenty-fourths.

#### 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.