# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 54/5 + 81/3 - 23/4 = 503/60 = 8 23/60 ≅ 8.3833333

The spelled result in words is five hundred three sixtieths (or eight and twenty-three sixtieths).

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

1. Conversion a mixed number 5 4/5 to a improper fraction: 5 4/5 = 5 4/5 = 5 · 5 + 4/5 = 25 + 4/5 = 29/5

To find a new numerator:
a) Multiply the whole number 5 by the denominator 5. Whole number 5 equally 5 * 5/5 = 25/5
b) Add the answer from the previous step 25 to the numerator 4. New numerator is 25 + 4 = 29
c) Write a previous answer (new numerator 29) over the denominator 5.

Five and four fifths is twenty-nine fifths.
2. Conversion a mixed number 8 1/3 to a improper fraction: 8 1/3 = 8 1/3 = 8 · 3 + 1/3 = 24 + 1/3 = 25/3

To find a new numerator:
a) Multiply the whole number 8 by the denominator 3. Whole number 8 equally 8 * 3/3 = 24/3
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 3.

Eight and one third is twenty-five thirds.
3. Add: 29/5 + 25/3 = 29 · 3/5 · 3 + 25 · 5/3 · 5 = 87/15 + 125/15 = 87 + 125/15 = 212/15
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(5, 3) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 3 = 15. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-nine fifths plus twenty-five thirds is two hundred twelve fifteenths.
4. Subtract: the result of step No. 3 - 23/4 = 212/15 - 23/4 = 212 · 4/15 · 4 - 23 · 15/4 · 15 = 848/60 - 345/60 = 848 - 345/60 = 503/60
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(15, 4) = 60. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 4 = 60. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two hundred twelve fifteenths minus twenty-three quarters is five hundred three sixtieths.

### 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.