# 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:

### 92/3 - 26/7 = 143/21 = 6 17/21 ≅ 6.8095238

Spelled result in words is one hundred forty-three twenty-firsts (or six and seventeen twenty-firsts).

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

1. Conversion a mixed number 9 2/3 to a improper fraction: 9 2/3 = 9 2/3 = 9 · 3 + 2/3 = 27 + 2/3 = 29/3

To find a new numerator:
a) Multiply the whole number 9 by the denominator 3. Whole number 9 equally 9 * 3/3 = 27/3
b) Add the answer from the previous step 27 to the numerator 2. New numerator is 27 + 2 = 29
c) Write a previous answer (new numerator 29) over the denominator 3.

Nine and two thirds is twenty-nine thirds.
2. Conversion a mixed number 2 6/7 to a improper fraction: 2 6/7 = 2 6/7 = 2 · 7 + 6/7 = 14 + 6/7 = 20/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 6. New numerator is 14 + 6 = 20
c) Write a previous answer (new numerator 20) over the denominator 7.

Two and six sevenths is twenty sevenths.
3. Subtract: 29/3 - 20/7 = 29 · 7/3 · 7 - 20 · 3/7 · 3 = 203/21 - 60/21 = 203 - 60/21 = 143/21
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(3, 7) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-nine thirds minus twenty sevenths is one hundred forty-three twenty-firsts.

#### 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.