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:

2 2/6 + 1 2/8 = 43/12 = 3 7/12 ≅ 3.5833333

Spelled out: forty-three twelfths (or three and seven twelfths).

How do we solve fractions step by step?

Conversion a mixed number 2 2/6 to a improper fraction: 2 2/6 = 2 2/6 = 2 · 6 + 2/6 = 12 + 2/6 = 14/6

To find a new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
b) Add the answer from the previous step 12 to the numerator 2. New numerator is 12 + 2 = 14
c) Write a previous answer (new numerator 14) over the denominator 6.

Two and two sixths is fourteen sixths.
Conversion a mixed number 1 2/8 to a improper fraction: 1 2/8 = 1 2/8 = 1 · 8 + 2/8 = 8 + 2/8 = 10/8

To find a new numerator:
a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8
b) Add the answer from the previous step 8 to the numerator 2. New numerator is 8 + 2 = 10
c) Write a previous answer (new numerator 10) over the denominator 8.

One and two eighths is ten eighths.
Add: 14/6 + 10/8 = 14 · 4/6 · 4 + 10 · 3/8 · 3 = 56/24 + 30/24 = 56 + 30/24 = 86/24 = 2 · 43/2 · 12 = 43/12
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(6, 8) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 8 = 48. In the following intermediate step, cancel by a common factor of 2 gives 43/12.
In other words, fourteen sixths plus ten eighths equals forty-three twelfths.

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)

Understanding 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.

Pro tip: MDAS is a simplified version focusing on the core concept: Multiplication and Division share the same priority level, as do Addition and Subtraction.