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:

17 1/5 - 2 5/8 = 583/40 = 14 23/40 = 14.575

The spelled result in words is five hundred eighty-three fortieths (or fourteen and twenty-three fortieths).

How do we solve fractions step by step?

Conversion a mixed number 17 1/5 to a improper fraction: 17 1/5 = 17 1/5 = 17 · 5 + 1/5 = 85 + 1/5 = 86/5

To find a new numerator:
a) Multiply the whole number 17 by the denominator 5. Whole number 17 equally 17 * 5/5 = 85/5
b) Add the answer from the previous step 85 to the numerator 1. New numerator is 85 + 1 = 86
c) Write a previous answer (new numerator 86) over the denominator 5.

Seventeen and one fifth is eighty-six fifths.
Conversion a mixed number 2 5/8 to a improper fraction: 2 5/8 = 2 5/8 = 2 · 8 + 5/8 = 16 + 5/8 = 21/8

To find a new numerator:
a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8
b) Add the answer from the previous step 16 to the numerator 5. New numerator is 16 + 5 = 21
c) Write a previous answer (new numerator 21) over the denominator 8.

Two and five eighths is twenty-one eighths.
Subtract: 86/5 - 21/8 = 86 · 8/5 · 8 - 21 · 5/8 · 5 = 688/40 - 105/40 = 688 - 105/40 = 583/40
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, 8) = 40. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eighty-six fifths minus twenty-one eighths is five hundred eighty-three fortieths.

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.