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 3/5 - 7 3/4 = 97/20 = 4 17/20 = 4.85

The result spelled out in words is ninety-seven twentieths (or four and seventeen twentieths).

How do we solve fractions step by step?

Conversion a mixed number 12 3/5 to a improper fraction: 12 3/5 = 12 3/5 = 12 · 5 + 3/5 = 60 + 3/5 = 63/5

To find a new numerator:
a) Multiply the whole number 12 by the denominator 5. Whole number 12 equally 12 * 5/5 = 60/5
b) Add the answer from the previous step 60 to the numerator 3. New numerator is 60 + 3 = 63
c) Write a previous answer (new numerator 63) over the denominator 5.

Twelve and three fifths is sixty-three fifths.
Conversion a mixed number 7 3/4 to a improper fraction: 7 3/4 = 7 3/4 = 7 · 4 + 3/4 = 28 + 3/4 = 31/4

To find a new numerator:
a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4
b) Add the answer from the previous step 28 to the numerator 3. New numerator is 28 + 3 = 31
c) Write a previous answer (new numerator 31) over the denominator 4.

Seven and three quarters is thirty-one quarters.
Subtract: 63/5 - 31/4 = 63 · 4/5 · 4 - 31 · 5/4 · 5 = 252/20 - 155/20 = 252 - 155/20 = 97/20
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, 4) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 4 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, sixty-three fifths minus thirty-one quarters equals ninety-seven twentieths.

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.