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:

7 3/15 + 9 12/15 = 17/1 = 17

Spelled out: seventeen.

How do we solve fractions step by step?

Conversion a mixed number 7 3/15 to an improper fraction: 7 3/15 = 7 3/15 = 7 · 15 + 3/15 = 105 + 3/15 = 108/15

To find a new numerator:
a) Multiply the whole number 7 by the denominator 15. Whole number 7 equals 7 ·15/15 = 105/15
b) Add the answer from the previous step 105 to the numerator 3. New numerator is 105 + 3 = 108
c) Write a previous answer (new numerator 108) over the denominator 15.

Seven and three fifteenths is one hundred eight fifteenths.
Conversion a mixed number 9 12/15 to an improper fraction: 9 12/15 = 9 12/15 = 9 · 15 + 12/15 = 135 + 12/15 = 147/15

To find a new numerator:
a) Multiply the whole number 9 by the denominator 15. Whole number 9 equals 9 ·15/15 = 135/15
b) Add the answer from the previous step 135 to the numerator 12. New numerator is 135 + 12 = 147
c) Write a previous answer (new numerator 147) over the denominator 15.

Nine and twelve fifteenths is one hundred forty-seven fifteenths.
Add: 108/15 + 147/15 = 108 + 147/15 = 255/15 = 15 · 17/15 · 1 = 17
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, cancel by a common factor of 15 gives 17/1.
In other words, one hundred eight fifteenths plus one hundred forty-seven fifteenths equals seventeen.

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.