# 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:

### 61/4 + 94/5 = 321/20 = 16 1/20 = 16.05

Spelled result in words is three hundred twenty-one twentieths (or sixteen and one twentieth).

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

1. Conversion a mixed number 6 1/4 to a improper fraction: 6 1/4 = 6 1/4 = 6 · 4 + 1/4 = 24 + 1/4 = 25/4

To find a new numerator:
a) Multiply the whole number 6 by the denominator 4. Whole number 6 equally 6 * 4/4 = 24/4
b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 4.

Six and one quarter is twenty-five quarters.
2. Conversion a mixed number 9 4/5 to a improper fraction: 9 4/5 = 9 4/5 = 9 · 5 + 4/5 = 45 + 4/5 = 49/5

To find a new numerator:
a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5
b) Add the answer from the previous step 45 to the numerator 4. New numerator is 45 + 4 = 49
c) Write a previous answer (new numerator 49) over the denominator 5.

Nine and four fifths is forty-nine fifths.
3. Add: 25/4 + 49/5 = 25 · 5/4 · 5 + 49 · 4/5 · 4 = 125/20 + 196/20 = 125 + 196/20 = 321/20
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(4, 5) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-five quarters plus forty-nine fifths is three hundred twenty-one 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 be evaluated from left to right.