Fraction Calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, and division — and evaluates expressions with fractions. Each calculation includes detailed step-by-step explanations.

The result:

8 4/6 - 5 8/12 = 3/1 = 3

Spelled out: three.

How do we solve fractions step by step?

Conversion a mixed number 8 4/6 to a improper fraction: 8 4/6 = 8 4/6 = 8 · 6 + 4/6 = 48 + 4/6 = 52/6

To find a new numerator:
a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6
b) Add the answer from the previous step 48 to the numerator 4. New numerator is 48 + 4 = 52
c) Write a previous answer (new numerator 52) over the denominator 6.

Eight and four sixths is fifty-two sixths.
Conversion a mixed number 5 8/12 to a improper fraction: 5 8/12 = 5 8/12 = 5 · 12 + 8/12 = 60 + 8/12 = 68/12

To find a new numerator:
a) Multiply the whole number 5 by the denominator 12. Whole number 5 equally 5 * 12/12 = 60/12
b) Add the answer from the previous step 60 to the numerator 8. New numerator is 60 + 8 = 68
c) Write a previous answer (new numerator 68) over the denominator 12.

Five and eight twelfths is sixty-eight twelfths.
Subtract: 52/6 - 68/12 = 52 · 2/6 · 2 - 68/12 = 104/12 - 68/12 = 104 - 68/12 = 36/12 = 12 · 3/12 · 1 = 3
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(6, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 12 = 72. In the following intermediate step, cancel by a common factor of 12 gives 3/1.
In other words, fifty-two sixths minus sixty-eight twelfths equals three.

Rules for expressions with fractions:

Fractions - Use a forward slash to separate the numerator and denominator. For example, for five-hundredths, enter 5/100.

Mixed numbers Leave one space between the whole number and the fraction part, and use a forward slash for the fraction. For example, enter 1 2/3 . For negative mixed numbers, write the negative sign before the whole number, such as -5 1/2.

Division of fractions - Since the forward slash is used for both fraction lines and division, use a colon (:) to divide fractions. For example, to divide 1/2 by 1/3, enter 1/2 : 1/3.

Decimals Enter decimal numbers using a decimal point (.), and they will be automatically converted to fractions. For example, enter 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)

Order of Operations

Ever wondered why calculators don't just work left to right? This calculator follows the mathematical order of operations — a set of rules that ensures everyone solves expressions the same way, every time.

Popular Memory Tricks

Different regions use different mnemonics to remember this order:

* 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 (parentheses, brackets, braces: (){}), Exponents, Multiplication, Division, Addition, Subtraction

The Golden Rules

Rule 1: Multiplication and division always come before addition and subtraction. Think of them as the VIPs that skip to the front of the line!

Rule 2: When operations have equal priority (like × and ÷, or + and −), work from left to right—just like reading a book.

Rule 3: Parentheses change the natural order of evaluation of operations.