Fraction Calculator

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

The result:

5 1/3 + 5 5/6 = 67/6 = 11 1/6 ≅ 11.1666667

Spelled out: sixty-seven sixths (or eleven and one sixth).

How do we solve fractions step by step?

Conversion a mixed number 5 1/3 to a improper fraction: 5 1/3 = 5 1/3 = 5 · 3 + 1/3 = 15 + 1/3 = 16/3

To find a new numerator:
a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3
b) Add the answer from the previous step 15 to the numerator 1. New numerator is 15 + 1 = 16
c) Write a previous answer (new numerator 16) over the denominator 3.

Five and one third is sixteen thirds.
Conversion a mixed number 5 5/6 to a improper fraction: 5 5/6 = 5 5/6 = 5 · 6 + 5/6 = 30 + 5/6 = 35/6

To find a new numerator:
a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6
b) Add the answer from the previous step 30 to the numerator 5. New numerator is 30 + 5 = 35
c) Write a previous answer (new numerator 35) over the denominator 6.

Five and five sixths is thirty-five sixths.
Add: 16/3 + 35/6 = 16 · 2/3 · 2 + 35/6 = 32/6 + 35/6 = 32 + 35/6 = 67/6
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 6) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 6 = 18. In the following intermediate step, the fraction cannot be simplified further by canceling.
In other words, sixteen thirds plus thirty-five sixths equals sixty-seven sixths.

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.