# 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:

### 145/10 - 129/10 = 8/5 = 1 3/5 = 1.6

Spelled result in words is eight fifths (or one and three fifths).

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

1. Conversion a mixed number 14 5/10 to a improper fraction: 14 5/10 = 14 5/10 = 14 · 10 + 5/10 = 140 + 5/10 = 145/10

To find a new numerator:
a) Multiply the whole number 14 by the denominator 10. Whole number 14 equally 14 * 10/10 = 140/10
b) Add the answer from the previous step 140 to the numerator 5. New numerator is 140 + 5 = 145
c) Write a previous answer (new numerator 145) over the denominator 10.

Fourteen and five tenths is one hundred forty-five tenths.
2. Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10

To find a new numerator:
a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10
b) Add the answer from the previous step 120 to the numerator 9. New numerator is 120 + 9 = 129
c) Write a previous answer (new numerator 129) over the denominator 10.

Twelve and nine tenths is one hundred twenty-nine tenths.
3. Subtract: 145/10 - 129/10 = 145 - 129/10 = 16/10 = 2 · 8/2 · 5 = 8/5
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(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 8/5.
In other words - one hundred forty-five tenths minus one hundred twenty-nine tenths is eight fifths.

#### 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.