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:

9 3/5 - 7 7/15 = 32/15 = 2 2/15 ≅ 2.1333333

Spelled out: thirty-two fifteenths (or two and two fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 9 3/5 to an improper fraction: 9 3/5 = 9 3/5 = 9 · 5 + 3/5 = 45 + 3/5 = 48/5

To find a new numerator:
a) Multiply the whole number 9 by the denominator 5. Whole number 9 equals 9 ·5/5 = 45/5
b) Add the answer from the previous step 45 to the numerator 3. New numerator is 45 + 3 = 48
c) Write a previous answer (new numerator 48) over the denominator 5.

Nine and three fifths is forty-eight fifths.
Conversion a mixed number 7 7/15 to an improper fraction: 7 7/15 = 7 7/15 = 7 · 15 + 7/15 = 105 + 7/15 = 112/15

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 7. New numerator is 105 + 7 = 112
c) Write a previous answer (new numerator 112) over the denominator 15.

Seven and seven fifteenths is one hundred twelve fifteenths.
Subtract: 48/5 - 112/15 = 48 · 3/5 · 3 - 112/15 = 144/15 - 112/15 = 144 - 112/15 = 32/15
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 15) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 15 = 75. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, forty-eight fifths minus one hundred twelve fifteenths equals thirty-two 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.