# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 174/9 - 122/3 = 43/9 = 4 7/9 ≅ 4.7777778

The spelled result in words is forty-three ninths (or four and seven ninths).

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

1. Conversion a mixed number 17 4/9 to a improper fraction: 17 4/9 = 17 4/9 = 17 · 9 + 4/9 = 153 + 4/9 = 157/9

To find a new numerator:
a) Multiply the whole number 17 by the denominator 9. Whole number 17 equally 17 * 9/9 = 153/9
b) Add the answer from the previous step 153 to the numerator 4. New numerator is 153 + 4 = 157
c) Write a previous answer (new numerator 157) over the denominator 9.

Seventeen and four ninths is one hundred fifty-seven ninths.
2. Conversion a mixed number 12 2/3 to a improper fraction: 12 2/3 = 12 2/3 = 12 · 3 + 2/3 = 36 + 2/3 = 38/3

To find a new numerator:
a) Multiply the whole number 12 by the denominator 3. Whole number 12 equally 12 * 3/3 = 36/3
b) Add the answer from the previous step 36 to the numerator 2. New numerator is 36 + 2 = 38
c) Write a previous answer (new numerator 38) over the denominator 3.

Twelve and two thirds is thirty-eight thirds.
3. Subtract: 157/9 - 38/3 = 157/9 - 38 · 3/3 · 3 = 157/9 - 114/9 = 157 - 114/9 = 43/9
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, 3) = 9. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one hundred fifty-seven ninths minus thirty-eight thirds is forty-three 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.