# 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:

### 123/5 - 73/4 = 97/20 = 4 17/20 = 4.85

Spelled result in words is ninety-seven twentieths (or four and seventeen twentieths).

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

1. Conversion a mixed number 12 3/5 to a improper fraction: 12 3/5 = 12 3/5 = 12 · 5 + 3/5 = 60 + 3/5 = 63/5

To find a new numerator:
a) Multiply the whole number 12 by the denominator 5. Whole number 12 equally 12 * 5/5 = 60/5
b) Add the answer from the previous step 60 to the numerator 3. New numerator is 60 + 3 = 63
c) Write a previous answer (new numerator 63) over the denominator 5.

Twelve and three fifths is sixty-three fifths.
2. Conversion a mixed number 7 3/4 to a improper fraction: 7 3/4 = 7 3/4 = 7 · 4 + 3/4 = 28 + 3/4 = 31/4

To find a new numerator:
a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4
b) Add the answer from the previous step 28 to the numerator 3. New numerator is 28 + 3 = 31
c) Write a previous answer (new numerator 31) over the denominator 4.

Seven and three quarters is thirty-one quarters.
3. Subtract: 63/5 - 31/4 = 63 · 4/5 · 4 - 31 · 5/4 · 5 = 252/20 - 155/20 = 252 - 155/20 = 97/20
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(5, 4) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 4 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - sixty-three fifths minus thirty-one quarters is ninety-seven twentieths.

#### 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.