# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 71/2 + 31/7 = 149/14 = 10 9/14 ≅ 10.6428571

The spelled result in words is one hundred forty-nine fourteenths (or ten and nine fourteenths).

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

1. Conversion a mixed number 7 1/2 to a improper fraction: 7 1/2 = 7 1/2 = 7 · 2 + 1/2 = 14 + 1/2 = 15/2

To find a new numerator:
a) Multiply the whole number 7 by the denominator 2. Whole number 7 equally 7 * 2/2 = 14/2
b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 2.

Seven and one half is fifteen halfs.
2. Conversion a mixed number 3 1/7 to a improper fraction: 3 1/7 = 3 1/7 = 3 · 7 + 1/7 = 21 + 1/7 = 22/7

To find a new numerator:
a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7/7 = 21/7
b) Add the answer from the previous step 21 to the numerator 1. New numerator is 21 + 1 = 22
c) Write a previous answer (new numerator 22) over the denominator 7.

Three and one seventh is twenty-two sevenths.
3. Add: 15/2 + 22/7 = 15 · 7/2 · 7 + 22 · 2/7 · 2 = 105/14 + 44/14 = 105 + 44/14 = 149/14
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(2, 7) = 14. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - fifteen halfs plus twenty-two sevenths is one hundred forty-nine fourteenths.

### 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.