Fraction Calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, and division — and evaluates expressions with fractions. Each calculation includes detailed step-by-step explanations.

The result:

3 7/16 - 2 5/8 = 13/16 = 0.8125

Spelled out: thirteen sixteenths.

How do we solve fractions step by step?

Conversion a mixed number 3 7/16 to a improper fraction: 3 7/16 = 3 7/16 = 3 · 16 + 7/16 = 48 + 7/16 = 55/16

To find a new numerator:
a) Multiply the whole number 3 by the denominator 16. Whole number 3 equally 3 * 16/16 = 48/16
b) Add the answer from the previous step 48 to the numerator 7. New numerator is 48 + 7 = 55
c) Write a previous answer (new numerator 55) over the denominator 16.

Three and seven sixteenths is fifty-five sixteenths.
Conversion a mixed number 2 5/8 to a improper fraction: 2 5/8 = 2 5/8 = 2 · 8 + 5/8 = 16 + 5/8 = 21/8

To find a new numerator:
a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8
b) Add the answer from the previous step 16 to the numerator 5. New numerator is 16 + 5 = 21
c) Write a previous answer (new numerator 21) over the denominator 8.

Two and five eighths is twenty-one eighths.
Subtract: 55/16 - 21/8 = 55/16 - 21 · 2/8 · 2 = 55/16 - 42/16 = 55 - 42/16 = 13/16
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(16, 8) = 16. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 16 × 8 = 128. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, fifty-five sixteenths minus twenty-one eighths equals thirteen sixteenths.

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.