# 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 fraction value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## Result:

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

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

### How do you 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 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 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
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(9, 3) = 9. In practice, 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 = 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 are using mixed numbers, leave a space between the whole and fraction part.

Mixed numerals (mixed fractions or mixed numbers) 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 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.