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:

6 1/5 - 4 1/4 = 39/20 = 1 19/20 = 1.95

The result spelled out in words is thirty-nine twentieths (or one and nineteen twentieths).

How do we solve fractions step by step?

Conversion a mixed number 6 1/5 to a improper fraction: 6 1/5 = 6 1/5 = 6 · 5 + 1/5 = 30 + 1/5 = 31/5

To find a new numerator:
a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5
b) Add the answer from the previous step 30 to the numerator 1. New numerator is 30 + 1 = 31
c) Write a previous answer (new numerator 31) over the denominator 5.

Six and one fifth is thirty-one fifths.
Conversion a mixed number 4 1/4 to a improper fraction: 4 1/4 = 4 1/4 = 4 · 4 + 1/4 = 16 + 1/4 = 17/4

To find a new numerator:
a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/4 = 16/4
b) Add the answer from the previous step 16 to the numerator 1. New numerator is 16 + 1 = 17
c) Write a previous answer (new numerator 17) over the denominator 4.

Four and one quarter is seventeen quarters.
Subtract: 31/5 - 17/4 = 31 · 4/5 · 4 - 17 · 5/4 · 5 = 124/20 - 85/20 = 124 - 85/20 = 39/20
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, thirty-one fifths minus seventeen quarters equals thirty-nine 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.