Divide — Definition, Formula & Examples
Divide is the arithmetic operation of splitting a number into a given number of equal parts, or finding how many times one number fits inside another.
Division is the operation that determines the quotient of two numbers: given a dividend and a nonzero divisor , dividing by yields the unique value such that .
Key Formula
Where:
- = The dividend — the number being divided
- = The divisor — the number you divide by (cannot be zero)
- = The quotient — the result of the division
How It Works
When you divide , you are asking: what number multiplied by gives ? The number is called the dividend, is the divisor, and the result is the quotient. If the dividend is not evenly split, you get a remainder. Division by zero is undefined because no number multiplied by zero can produce a nonzero result.
Worked Example
Problem: Divide 36 by 4.
Set up: Write the division expression.
Find the quotient: Ask: what number times 4 equals 36? Since , the quotient is 9.
Answer: 36 ÷ 4 = 9
Why It Matters
Division is used every time you share things equally, convert units, or calculate rates like speed (miles per hour). It is also the foundation for working with fractions, ratios, and proportional reasoning in later math courses.
Common Mistakes
Mistake: Dividing by zero and expecting a result.
Correction: Division by zero is undefined. There is no number that, when multiplied by zero, gives a nonzero dividend.