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:

12 5/8 ÷ 3 19/24 = 303/91 = 3 30/91 ≅ 3.3296703

The result spelled out in words is three hundred three ninety-firsts (or three and thirty ninety-firsts).

How do we solve fractions step by step?

Conversion a mixed number 12 5/8 to a improper fraction: 12 5/8 = 12 5/8 = 12 · 8 + 5/8 = 96 + 5/8 = 101/8

To find a new numerator:
a) Multiply the whole number 12 by the denominator 8. Whole number 12 equally 12 * 8/8 = 96/8
b) Add the answer from the previous step 96 to the numerator 5. New numerator is 96 + 5 = 101
c) Write a previous answer (new numerator 101) over the denominator 8.

Twelve and five eighths is one hundred one eighths.
Conversion a mixed number 3 19/24 to a improper fraction: 3 19/24 = 3 19/24 = 3 · 24 + 19/24 = 72 + 19/24 = 91/24

To find a new numerator:
a) Multiply the whole number 3 by the denominator 24. Whole number 3 equally 3 * 24/24 = 72/24
b) Add the answer from the previous step 72 to the numerator 19. New numerator is 72 + 19 = 91
c) Write a previous answer (new numerator 91) over the denominator 24.

Three and nineteen twenty-fourths is ninety-one twenty-fourths.
Divide: 101/8 : 91/24 = 101/8 · 24/91 = 101 · 24/8 · 91 = 2424/728 = 8 · 303 /8 · 91 = 303/91
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 91/24 is 24/91) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 8 gives 303/91.
In other words, one hundred one eighths divided by ninety-one twenty-fourths equals three hundred three ninety-firsts.

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.