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:

8 1/4 - 3 2/5 - (2 1/3 - 1/4) = 83/30 = 2 23/30 ≅ 2.7666667

The result spelled out in words is eighty-three thirtieths (or two and twenty-three thirtieths).

How do we solve fractions step by step?

Conversion a mixed number 8 1/4 to a improper fraction: 8 1/4 = 8 1/4 = 8 · 4 + 1/4 = 32 + 1/4 = 33/4

To find a new numerator:
a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/4 = 32/4
b) Add the answer from the previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 4.

Eight and one quarter is thirty-three quarters.
Conversion a mixed number 3 2/5 to a improper fraction: 3 2/5 = 3 2/5 = 3 · 5 + 2/5 = 15 + 2/5 = 17/5

To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
c) Write a previous answer (new numerator 17) over the denominator 5.

Three and two fifths is seventeen fifths.
Subtract: 33/4 - 17/5 = 33 · 5/4 · 5 - 17 · 4/5 · 4 = 165/20 - 68/20 = 165 - 68/20 = 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(4, 5) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-three quarters minus seventeen fifths equals ninety-seven twentieths.
Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds.
Subtract: 7/3 - 1/4 = 7 · 4/3 · 4 - 1 · 3/4 · 3 = 28/12 - 3/12 = 28 - 3/12 = 25/12
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(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, seven thirds minus one quarter equals twenty-five twelfths.
Subtract: the result of step No. 3 - the result of step No. 5 = 97/20 - 25/12 = 97 · 3/20 · 3 - 25 · 5/12 · 5 = 291/60 - 125/60 = 291 - 125/60 = 166/60 = 2 · 83/2 · 30 = 83/30
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(20, 12) = 60. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 12 = 240. In the following intermediate step, cancel by a common factor of 2 gives 83/30.
In other words, ninety-seven twentieths minus twenty-five twelfths equals eighty-three thirtieths.

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.