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:

16 3/9 - 10 2/5 = 89/15 = 5 14/15 ≅ 5.9333333

The result spelled out in words is eighty-nine fifteenths (or five and fourteen fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 16 3/9 to a improper fraction: 16 3/9 = 16 3/9 = 16 · 9 + 3/9 = 144 + 3/9 = 147/9

To find a new numerator:
a) Multiply the whole number 16 by the denominator 9. Whole number 16 equally 16 * 9/9 = 144/9
b) Add the answer from the previous step 144 to the numerator 3. New numerator is 144 + 3 = 147
c) Write a previous answer (new numerator 147) over the denominator 9.

Sixteen and three ninths is one hundred forty-seven ninths.
Conversion a mixed number 10 2/5 to a improper fraction: 10 2/5 = 10 2/5 = 10 · 5 + 2/5 = 50 + 2/5 = 52/5

To find a new numerator:
a) Multiply the whole number 10 by the denominator 5. Whole number 10 equally 10 * 5/5 = 50/5
b) Add the answer from the previous step 50 to the numerator 2. New numerator is 50 + 2 = 52
c) Write a previous answer (new numerator 52) over the denominator 5.

Ten and two fifths is fifty-two fifths.
Subtract: 147/9 - 52/5 = 147 · 5/9 · 5 - 52 · 9/5 · 9 = 735/45 - 468/45 = 735 - 468/45 = 267/45 = 3 · 89/3 · 15 = 89/15
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(9, 5) = 45. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the following intermediate step, cancel by a common factor of 3 gives 89/15.
In other words, one hundred forty-seven ninths minus fifty-two fifths equals eighty-nine fifteenths.

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.