Introduction to Division Basics
In mathematics, division is one of the four fundamental arithmetic operations. The process involves splitting a number into equal parts. Here, we'll cover the essentials you need to understand division.
Key Terms in Division
 Dividend: The number you want to divide.
 Divisor: The number by which you want to divide the dividend.
 Quotient: The result of the division.
 Remainder: The part of the dividend that is left over, if it's not evenly divisible by the divisor.
Division Symbol
Division is often represented by the symbol $\div$ or a forward slash $/$.
Basic Division Formula
The general form of a division operation is:
$\text{Dividend} \div \text{Divisor} = \text{Quotient} + \text{Remainder}$
Understanding with an Example
For instance, consider $15 \div 4$:
Applying the division:
$15 \div 4 = 3 \text{ R } 3$
Here, 3 is the quotient and the remainder is also 3 because $4 \times 3 + 3 = 15$.
Long Division Method
To solve divisions manually, especially for larger numbers, you can use the long division method. Here's a stepbystep guide:
 Divide the dividend by the divisor.
 Multiply the divisor by the current quotient.
 Subtract the result from the current dividend.
 Bring down the next digit of the dividend (if any) and repeat the process.
Example of Long Division
Let’s perform $123 \div 4$ using long division:

Divide 12 by 4:
$12 \div 4 = 3$
The quotient is 3, with no remainder yet.

Multiply 3 by 4:
$3 \times 4 = 12$

Subtract 12 from 12:
$12  12 = 0$

Bring down the next digit, 3:
$\downarrow 3$

Divide 3 by 4:
$3 \div 4 = 0 \text{ R } 3$
The quotient here is 0, and the remainder is 3.
So, overall:
$123 \div 4 = 30 \text{ R } 3$
Important Points
 Division by zero is undefined. That is, you cannot divide any number by zero.
 Dividing zero by any nonzero number will always yield zero.
 Division is the inverse operation of multiplication.
Conclusion
Understanding the basics of division is crucial for working through more complex arithmetic and algebraic problems. The key is to grasp the relationship between the dividend, divisor, quotient, and remainder, and to practice with examples to build proficiency.