# 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:

### 163/9 - 102/5 = 89/15 = 5 14/15 ≅ 5.9333333

Spelled result in words is eighty-nine fifteenths (or five and fourteen fifteenths).

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

1. Conversion a mixed number 16 3/9 to a improper fraction: 16 3/9 = 16 3/9 = 16 · 9 + 3/9 = 144 + 3/9 = 147/9

To find a new numerator:
a) Multiply the whole number 16 by the denominator 9. Whole number 16 equally 16 * 9/9 = 144/9
b) Add the answer from the previous step 144 to the numerator 3. New numerator is 144 + 3 = 147
c) Write a previous answer (new numerator 147) over the denominator 9.

Sixteen and three ninths is one hundred forty-seven ninths.
2. Conversion a mixed number 10 2/5 to a improper fraction: 10 2/5 = 10 2/5 = 10 · 5 + 2/5 = 50 + 2/5 = 52/5

To find a new numerator:
a) Multiply the whole number 10 by the denominator 5. Whole number 10 equally 10 * 5/5 = 50/5
b) Add the answer from the previous step 50 to the numerator 2. New numerator is 50 + 2 = 52
c) Write a previous answer (new numerator 52) over the denominator 5.

Ten and two fifths is fifty-two fifths.
3. Subtract: 147/9 - 52/5 = 147 · 5/9 · 5 - 52 · 9/5 · 9 = 735/45 - 468/45 = 735 - 468/45 = 267/45 = 3 · 89/3 · 15 = 89/15
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(9, 5) = 45. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the following intermediate step, cancel by a common factor of 3 gives 89/15.
In other words - one hundred forty-seven ninths minus fifty-two fifths is eighty-nine fifteenths.

#### 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.