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:

3 3/5 x (-8 1/3) = -30/1 = -30

Spelled out: minus thirty.

How do we solve fractions step by step?

Conversion a mixed number 3 3/5 to a improper fraction: 3 3/5 = 3 3/5 = 3 · 5 + 3/5 = 15 + 3/5 = 18/5

To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 3. New numerator is 15 + 3 = 18
c) Write a previous answer (new numerator 18) over the denominator 5.

Three and three fifths is eighteen fifths.
Conversion a mixed number -8 1/3 to a improper fraction: -8 1/3 = -8 1/3 = -8 · 3 + (-1)/3 = -24 + (-1)/3 = -25/3

To find a new numerator:
a) Multiply the whole number -8 by the denominator 3. Whole number -8 equally -8 * 3/3 = -24/3
b) Add the answer from the previous step -24 to the numerator 1. New numerator is -24 + 1 = -23
c) Write a previous answer (new numerator -23) over the denominator 3.

Minus eight and one third is minus twenty-three thirds.
Multiply: 18/5 * (-25/3) = 18 · (-25)/5 · 3 = -450/15 = -30 · 15/1 · 15 = -30
Multiply both numerators and both denominators. Then simplify the resulting fraction to its lowest terms GCD(-450, 15) = 15.
In other words, eighteen fifths multiplied by minus twenty-five thirds equals minus thirty.

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.