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:

-8 3/8 - 10 1/6 = -445/24 = -18 13/24 ≅ -18.5416667

Spelled out: minus four hundred forty-five twenty-fourths (or minus eighteen and thirteen twenty-fourths).

How do we solve fractions step by step?

Conversion a mixed number 8 3/8 to a improper fraction: 8 3/8 = 8 3/8 = 8 · 8 + 3/8 = 64 + 3/8 = 67/8

To find a new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from the previous step 64 to the numerator 3. New numerator is 64 + 3 = 67
c) Write a previous answer (new numerator 67) over the denominator 8.

Eight and three eighths is sixty-seven eighths.
Unary minus: -67/8 = -67/8
Conversion a mixed number 10 1/6 to a improper fraction: 10 1/6 = 10 1/6 = 10 · 6 + 1/6 = 60 + 1/6 = 61/6

To find a new numerator:
a) Multiply the whole number 10 by the denominator 6. Whole number 10 equally 10 * 6/6 = 60/6
b) Add the answer from the previous step 60 to the numerator 1. New numerator is 60 + 1 = 61
c) Write a previous answer (new numerator 61) over the denominator 6.

Ten and one sixth is sixty-one sixths.
Subtract: the result of step No. 2 - 61/6 = -67/8 - 61/6 = -67 · 3/8 · 3 - 61 · 4/6 · 4 = -201/24 - 244/24 = -201 - 244/24 = -445/24
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(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, minus sixty-seven eighths minus sixty-one sixths equals minus four hundred forty-five twenty-fourths.

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.