Special Division Rules: Dividing by 1, Itself, and 0

Core Concepts

Master the essential shortcuts for division. This stack covers the rules for dividing a number by 1, dividing a number by itself, and the special cases involving zero.

Special Division Rules: Dividing by 1, Itself, and 0

1 of 9

What is the result when you divide any number (except $0$) by itself? For example, $9 \div 9$.

The answer is always $1$. If you have $9$ items to share with $9$ people, each person gets $1$. $n \div n = 1$.

$$ 57 \div 57 = ? $$

$$ 1 $$

What is the result when you divide any number by $1$? For example, $14 \div 1$.

The answer is always the number itself. If you have $14$ items to put into $1$ big group, that group will have all $14$ items. $n \div 1 = n$.

$$ 250 \div 1 = ? $$

$$ 250 $$

What is the result when you divide $0$ by any non-zero number? For example, $0 \div 8$.

The answer is always $0$. If you have $0$ items to share among $8$ people, everyone gets $0$ items. $0 \div n = 0$ (for $n \neq 0$).

$$ 0 \div 42 = ? $$

$$ 0 $$

Why is dividing a number by $0$ not possible? For example, $5 \div 0$.

Dividing by zero is 'undefined'. You can't make groups of size zero and use up a non-zero amount. It's a question that has no logical answer in math.

True or False: $10 \div 10 = 1$.

True. Any non-zero number divided by itself is $1$.

True or False: $10 \div 1 = 10$.

True. Any number divided by $1$ is itself.

Special Division Rules: Dividing by 1, Itself, and 0

Confirm Action

Prompt