Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

The result:

3 2/5 + 3 4/6 = 106/15 = 7 1/15 ≅ 7.0666667

The spelled result in words is one hundred six fifteenths (or seven and one fifteenth).

How do we solve fractions step by step?

Conversion a mixed number 3 2/5 to a improper fraction: 3 2/5 = 3 2/5 = 3 · 5 + 2/5 = 15 + 2/5 = 17/5

To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
c) Write a previous answer (new numerator 17) over the denominator 5.

Three and two fifths is seventeen fifths.
Conversion a mixed number 3 4/6 to a improper fraction: 3 4/6 = 3 4/6 = 3 · 6 + 4/6 = 18 + 4/6 = 22/6

To find a new numerator:
a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6
b) Add the answer from the previous step 18 to the numerator 4. New numerator is 18 + 4 = 22
c) Write a previous answer (new numerator 22) over the denominator 6.

Three and four sixths is twenty-two sixths.
Add: 17/5 + 22/6 = 17 · 6/5 · 6 + 22 · 5/6 · 5 = 102/30 + 110/30 = 102 + 110/30 = 212/30 = 2 · 106/2 · 15 = 106/15
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, 6) = 30. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 6 = 30. In the following intermediate step, cancel by a common factor of 2 gives 106/15.
In other words - seventeen fifths plus twenty-two sixths is one hundred six 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

Symbol	Symbol name	Symbol Meaning	Example
+	plus sign	addition	1/2 + 1/3
-	minus sign	subtraction	1 1/2 - 2/3
*	asterisk	multiplication	*2/3 3/4**
×	times sign	multiplication	2/3 × 5/6
:	division sign	division	1/2 : 3
/	division slash	division	1/3 / 5
:	colon	complex fraction	1/2 : 1/3
^	caret	exponentiation / power	1/4^3
()	parentheses	calculate 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.