# 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:

### 356/34 - 51/2 = -29/34 ≅ -0.8529412

Spelled result in words is minus twenty-nine thirty-fourths.

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

1. Conversion a mixed number 3 56/34 to a improper fraction: 3 56/34 = 3 56/34 = 3 · 34 + 56/34 = 102 + 56/34 = 158/34

To find a new numerator:
a) Multiply the whole number 3 by the denominator 34. Whole number 3 equally 3 * 34/34 = 102/34
b) Add the answer from previous step 102 to the numerator 56. New numerator is 102 + 56 = 158
c) Write a previous answer (new numerator 158) over the denominator 34.

Three and fifty-six thirty-fourths is one hundred fifty-eight thirty-fourths
2. Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2

To find a new numerator:
a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2
b) Add the answer from previous step 10 to the numerator 1. New numerator is 10 + 1 = 11
c) Write a previous answer (new numerator 11) over the denominator 2.

Five and one half is eleven halfs
3. Subtract: 158/34 - 11/2 = 158/34 - 11 · 17/2 · 17 = 158/34 - 187/34 = 158 - 187/34 = -29/34
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(34, 2) = 34. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 34 × 2 = 68. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one hundred fifty-eight thirty-fourths minus eleven halfs is minus twenty-nine thirty-fourths.

#### 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 signs 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
+plus signaddition 1/2 + 1/3
-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 /) has the same priority and then must evaluate from left to right.