# Dividing Integers

- - Pre-Algebra

The rules for dividing integers follow from the rules for multiplying integers since these two operations are reversed operations. After teaching these rules, dividing integers worksheets are essential tools to evaluate learning of students.

Before arriving at these rules, let us consider the following statements:

1. If $2\left (-3\right) =-6$, then $-6\div 2=-3$.
2. If $\left (-3\right) \times \left (-3\right) = 9$, then $9\div \left(-3\right)=-3$.
3. If $2\left (5\right) =10$, then $10\div 5=2$.
4. If $3\left (-4\right) =-12$, then $\left(-12\right) \div \left(-4\right)= 3$.
5. If $\left(-2 \right) \left (-5\right) =10$, then $10\div \left(-2\right)=-5$.

Based from the above examples, the following facts about division of integers can be established:

1. If a negative number is divided by a positive number, the result is negative.
2. If a positive number is divided by a negative number, the result is negative.
3. If a positive number is divided by another positive, the result is positive.

Summarizing the above three statements, the following rules are derived:

1. The quotient of any two integers with unlike sign is negative.
2. The quotient of any two integers with like signs is positive.

Examples:

1. $\left(-35\right) \div 7=-5$
2. $125 \div \left(-5\right)=-25$
3. $\left(-144\right) \div \left(-6\right)=24$
4. $18\div 2=9$
5. $\left(-100\right) \div 4=25$