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:

86 14/24 + 7 13/24 = 753/8 = 94 1/8 = 94.125

The result spelled out in words is seven hundred fifty-three eighths (or ninety-four and one eighth).

How do we solve fractions step by step?

Conversion a mixed number 86 14/24 to a improper fraction: 86 14/24 = 86 14/24 = 86 · 24 + 14/24 = 2064 + 14/24 = 2078/24

To find a new numerator:
a) Multiply the whole number 86 by the denominator 24. Whole number 86 equally 86 * 24/24 = 2064/24
b) Add the answer from the previous step 2064 to the numerator 14. New numerator is 2064 + 14 = 2078
c) Write a previous answer (new numerator 2078) over the denominator 24.

Eighty-six and fourteen twenty-fourths is two thousand seventy-eight twenty-fourths.
Conversion a mixed number 7 13/24 to a improper fraction: 7 13/24 = 7 13/24 = 7 · 24 + 13/24 = 168 + 13/24 = 181/24

To find a new numerator:
a) Multiply the whole number 7 by the denominator 24. Whole number 7 equally 7 * 24/24 = 168/24
b) Add the answer from the previous step 168 to the numerator 13. New numerator is 168 + 13 = 181
c) Write a previous answer (new numerator 181) over the denominator 24.

Seven and thirteen twenty-fourths is one hundred eighty-one twenty-fourths.
Add: 2078/24 + 181/24 = 2078 + 181/24 = 2259/24 = 3 · 753/3 · 8 = 753/8
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, cancel by a common factor of 3 gives 753/8.
In other words, two thousand seventy-eight twenty-fourths plus one hundred eighty-one twenty-fourths equals seven hundred fifty-three eighths.

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.