# 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:

### 29/15 + 310/15 = 94/15 = 6 4/15 ≅ 6.2666667

Spelled result in words is ninety-four fifteenths (or six and four fifteenths).

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

1. Conversion a mixed number 2 9/15 to a improper fraction: 2 9/15 = 2 9/15 = 2 · 15 + 9/15 = 30 + 9/15 = 39/15

To find a new numerator:
a) Multiply the whole number 2 by the denominator 15. Whole number 2 equally 2 * 15/15 = 30/15
b) Add the answer from the previous step 30 to the numerator 9. New numerator is 30 + 9 = 39
c) Write a previous answer (new numerator 39) over the denominator 15.

Two and nine fifteenths is thirty-nine fifteenths.
2. Conversion a mixed number 3 10/15 to a improper fraction: 3 10/15 = 3 10/15 = 3 · 15 + 10/15 = 45 + 10/15 = 55/15

To find a new numerator:
a) Multiply the whole number 3 by the denominator 15. Whole number 3 equally 3 * 15/15 = 45/15
b) Add the answer from the previous step 45 to the numerator 10. New numerator is 45 + 10 = 55
c) Write a previous answer (new numerator 55) over the denominator 15.

Three and ten fifteenths is fifty-five fifteenths.
3. Add: 39/15 + 55/15 = 39 + 55/15 = 94/15
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(15, 15) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 15 = 225. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-nine fifteenths plus fifty-five fifteenths is ninety-four fifteenths.

#### 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.