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:

8 1/5 - 4 2/5 = 19/5 = 3 4/5 = 3.8

Spelled out: nineteen fifths (or three and four fifths).

How do we solve fractions step by step?

Conversion a mixed number 8 1/5 to an improper fraction: 8 1/5 = 8 1/5 = 8 · 5 + 1/5 = 40 + 1/5 = 41/5

To find a new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equals 8 ·5/5 = 40/5
b) Add the answer from the previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
c) Write a previous answer (new numerator 41) over the denominator 5.

Eight and one fifth is forty-one fifths.
Conversion a mixed number 4 2/5 to an improper fraction: 4 2/5 = 4 2/5 = 4 · 5 + 2/5 = 20 + 2/5 = 22/5

To find a new numerator:
a) Multiply the whole number 4 by the denominator 5. Whole number 4 equals 4 ·5/5 = 20/5
b) Add the answer from the previous step 20 to the numerator 2. New numerator is 20 + 2 = 22
c) Write a previous answer (new numerator 22) over the denominator 5.

Four and two fifths is twenty-two fifths.
Subtract: 41/5 - 22/5 = 41 - 22/5 = 19/5
Both fractions have the same denominator, which is then the common denominator in the subtracting them. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, forty-one fifths minus twenty-two fifths equals nineteen fifths.

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.