Fraction calculator

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

The result:

17 1/5 - 2 5/8/1000 = 137579/8000 = 17 1579/8000 = 17.197375

The result spelled out in words is one hundred thirty-seven thousand five hundred seventy-nine over eight thousand (or seventeen and one thousand five hundred seventy-nine over eight thousand).

How do we solve fractions step by step?

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.
Divide: 21/8 : 1000 = 21/8 · 1/1000 = 21 · 1/8 · 1000 = 21/8000
The second operand is an integer. It is equivalent to the fraction 1000/1. Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1000/1 is 1/1000) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-one eighths divided by one thousand equals twenty-one over eight thousand.
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.
Subtract: 86/5 - the result of step No. 2 = 86/5 - 21/8000 = 86 · 1600/5 · 1600 - 21/8000 = 137600/8000 - 21/8000 = 137600 - 21/8000 = 137579/8000
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 8000) = 8000. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8000 = 40000. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eighty-six fifths minus twenty-one over eight thousand equals one hundred thirty-seven thousand five hundred seventy-nine over eight thousand.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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 are:

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
GEMDAS: Grouping symbols (brackets: `(){}`), Exponents, Multiplication, Division, Addition, Subtraction.
MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.

Important Notes:
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., `+` and `-`, or `*` and `/`) must be evaluated from left to right.