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:

16 3/8 - 9 5/8 = 27/4 = 6 3/4 = 6.75

Spelled out: twenty-seven quarters (or six and three quarters).

How do we solve fractions step by step?

Conversion a mixed number 16 3/8 to an improper fraction: 16 3/8 = 16 3/8 = 16 · 8 + 3/8 = 128 + 3/8 = 131/8

To find a new numerator:
a) Multiply the whole number 16 by the denominator 8. Whole number 16 equals 16 ·8/8 = 128/8
b) Add the answer from the previous step 128 to the numerator 3. New numerator is 128 + 3 = 131
c) Write a previous answer (new numerator 131) over the denominator 8.

Sixteen and three eighths is one hundred thirty-one eighths.
Conversion a mixed number 9 5/8 to an improper fraction: 9 5/8 = 9 5/8 = 9 · 8 + 5/8 = 72 + 5/8 = 77/8

To find a new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equals 9 ·8/8 = 72/8
b) Add the answer from the previous step 72 to the numerator 5. New numerator is 72 + 5 = 77
c) Write a previous answer (new numerator 77) over the denominator 8.

Nine and five eighths is seventy-seven eighths.
Subtract: 131/8 - 77/8 = 131 - 77/8 = 54/8 = 2 · 27/2 · 4 = 27/4
Both fractions have the same denominator, which is then the common denominator in the subtracting them. In the following intermediate step, cancel by a common factor of 2 gives 27/4.
In other words, one hundred thirty-one eighths minus seventy-seven eighths equals twenty-seven quarters.

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.