Question

Find the quotient. $$-90 \div\left(-\frac{2}{3}\right)$$

Short answer

The quotient of \(-90 \div\left(-\frac{2}{3}\right)\) is \(135\).

Step-by-step solution

Simplify the Fraction

First of all, to simplify the process of division, we should rewrite given fraction \(-\frac{2}{3}\) as a regular division operation. Rewriting it into division form, it becomes \(-2 \div 3 \).

Perform the Division

So, the initial problem is transformed to \(-90 \div (-2 \div 3)\), which then simplifies to \(-90 \times (3 \div -2) = -90 \times -1.5\) using the rule that division can be replaced by multiplication with the reciprocal.

Simplify the Result

Multiplication of two negative values results in a positive number, so \(-90 \times -1.5\) equals to \(135\).