Question

Simplify the expression. $$58 z \div\left(-\frac{2}{5}\right)$$

Short answer

The simplified expression is \(-145z\).

Step-by-step solution

Understand the expression

The original expression is \(58z \div\left(-\frac{2}{5}\right)\), where the operation being performed is division. In mathematics, division by a fraction is equivalent to multiplication by its reciprocal.

Identify the reciprocal

The reciprocal of \(-\frac{2}{5}\) is \(-\frac{5}{2}\). So the next step is to convert the division operation to multiplication by using the reciprocal of \(-\frac{2}{5}\). This changes the expression to \(58z \cdot \left(-\frac{5}{2}\right)\)

Perform the multiplication

Multiplying \(58z\) by \(-\frac {5}{2}\) gives the final simplified expression as \(-145z\).