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:

3 2/3 × 2 1/7 = 55/7 = 7 6/7 ≅ 7.8571429

Spelled out: fifty-five sevenths (or seven and six sevenths).

How do we solve fractions step by step?

Conversion a mixed number 3 2/3 to a improper fraction: 3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3

To find a new numerator:
a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3
b) Add the answer from the previous step 9 to the numerator 2. New numerator is 9 + 2 = 11
c) Write a previous answer (new numerator 11) over the denominator 3.

Three and two thirds is eleven thirds.
Conversion a mixed number 2 1/7 to a improper fraction: 2 1/7 = 2 1/7 = 2 · 7 + 1/7 = 14 + 1/7 = 15/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 7.

Two and one seventh is fifteen sevenths.
Multiple: 11/3 * 15/7 = 11 · 15/3 · 7 = 165/21 = 55 · 3/7 · 3 = 55/7
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(165, 21) = 3. In the following intermediate step, cancel by a common factor of 3 gives 55/7.
In other words, eleven thirds multiplied by fifteen sevenths equals fifty-five sevenths.

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.