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:

2 9/15 + 3 10/15 = 94/15 = 6 4/15 ≅ 6.2666667

Spelled out: ninety-four fifteenths (or six and four fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 2 9/15 to a improper fraction: 2 9/15 = 2 9/15 = 2 · 15 + 9/15 = 30 + 9/15 = 39/15

To find a new numerator:
a) Multiply the whole number 2 by the denominator 15. Whole number 2 equally 2 * 15/15 = 30/15
b) Add the answer from the previous step 30 to the numerator 9. New numerator is 30 + 9 = 39
c) Write a previous answer (new numerator 39) over the denominator 15.

Two and nine fifteenths is thirty-nine fifteenths.
Conversion a mixed number 3 10/15 to a improper fraction: 3 10/15 = 3 10/15 = 3 · 15 + 10/15 = 45 + 10/15 = 55/15

To find a new numerator:
a) Multiply the whole number 3 by the denominator 15. Whole number 3 equally 3 * 15/15 = 45/15
b) Add the answer from the previous step 45 to the numerator 10. New numerator is 45 + 10 = 55
c) Write a previous answer (new numerator 55) over the denominator 15.

Three and ten fifteenths is fifty-five fifteenths.
Add: 39/15 + 55/15 = 39 + 55/15 = 94/15
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, thirty-nine fifteenths plus fifty-five fifteenths equals ninety-four fifteenths.

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.