If you divide a negative number by another negative number, what type of number do you get?

When you divide a negative number by another negative number, the result is a positive number. This outcome is based on the rules of arithmetic regarding signs.

The division operation can be thought of as multiplying by the reciprocal. When you take a negative number and divide it by another negative number, you can rewrite the division as multiplication by the reciprocal. For example, if you have -a and -b (where both a and b are positive), the operation can be expressed as:

[

\frac{-a}{-b} = -a \times \left(\frac{1}{-b}\right) = a \times \left(\frac{1}{b}\right)

]

The negatives cancel out, and the multiplication of two positive values (a and the reciprocal of b) yields a positive result. This principle illustrates why the quotient of two negative numbers is positive, aligning with fundamental rules in mathematics concerning the signs of numbers.