Question

State the inverse operation. \(\text { Multiply by }-\frac{9}{4}\).

Short answer

The inverse operation of multiplying by \(-\frac{9}{4}\) is dividing by \(-\frac{9}{4}\).

Step-by-step solution

Identify Original Operation

The current operation is a multiplication by \(-\frac{9}{4}\). This operation will take any number \(x\), and multiply it by \(-\frac{9}{4}\). So if we start with \(x\), after the operation the result will be \(-\frac{9}{4}x\).

Understand Inverse Operations

An inverse operation is an operation that undoes the work of another. For multiplication, the inverse operation is division. For instance, if you multiply a number by 2, to undo this action, you would divide the result by 2. This removes the effect of the original operation.

Determine Inverse Operation

Using the understanding of inverse operations, for the given operation, multiplication by \(-\frac{9}{4}\), the inverse operation would be division by \(-\frac{9}{4}\). This operation would undo the effect of multiplying by \(-\frac{9}{4}\). So if we start with a number \(y = -\frac{9}{4}x\), dividing by \(-\frac{9}{4}\) will get us back to the original number \(y / -\frac{9}{4} = x\).