# 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:

### 156/25 - 115/10 = 187/50 = 3 37/50 = 3.74

Spelled result in words is one hundred eighty-seven fiftieths (or three and thirty-seven fiftieths).

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

1. Conversion a mixed number 15 6/25 to a improper fraction: 15 6/25 = 15 6/25 = 15 · 25 + 6/25 = 375 + 6/25 = 381/25

To find a new numerator:
a) Multiply the whole number 15 by the denominator 25. Whole number 15 equally 15 * 25/25 = 375/25
b) Add the answer from the previous step 375 to the numerator 6. New numerator is 375 + 6 = 381
c) Write a previous answer (new numerator 381) over the denominator 25.

Fifteen and six twenty-fifths is three hundred eighty-one twenty-fifths.
2. Conversion a mixed number 11 5/10 to a improper fraction: 11 5/10 = 11 5/10 = 11 · 10 + 5/10 = 110 + 5/10 = 115/10

To find a new numerator:
a) Multiply the whole number 11 by the denominator 10. Whole number 11 equally 11 * 10/10 = 110/10
b) Add the answer from the previous step 110 to the numerator 5. New numerator is 110 + 5 = 115
c) Write a previous answer (new numerator 115) over the denominator 10.

Eleven and five tenths is one hundred fifteen tenths.
3. Subtract: 381/25 - 115/10 = 381 · 2/25 · 2 - 115 · 5/10 · 5 = 762/50 - 575/50 = 762 - 575/50 = 187/50
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(25, 10) = 50. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 25 × 10 = 250. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three hundred eighty-one twenty-fifths minus one hundred fifteen tenths is one hundred eighty-seven fiftieths.

#### 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.