Question

Evaluate the following expression. (-2.2) • (-2) • (-1/4) • (5)1: 882: 5 1/23: -884: -5 1/2

Answer 1

We will investigate how to evaluate expressions in their simplest form.

The expression that is given to us is as follows:

`(-2.2)\cdot(-2)\cdot(-(1)/(4))\cdot(5)`

There are two rules that must always be followed when we are simplifying or evaluating expressions. PEMDAS is the rule that determines the order in which each mathematical operation is to be performed. The sign rule allow us to determine the resulting sign of either a multiplication or a division operation highlighted:

`\begin{gathered} +\text{ x + = +} \\ -\text{ x + = -} \\ +\text{ x - = -} \\ -\text{ x - = +} \end{gathered}`

Since each parathesis in the given expression is multiplied by the subsequent parenthesis we dont have much to think over the PEMDAS rule. We will only be dealing with the multiplication operator.

We will multiply out a pair of parathesis in the expression and write down their result and their resultant signs as follows:

`\begin{gathered} (-2.2)\cdot(-2)\cdot(-(1)/(4))\cdot(5) \\ \\ (-(11)/(5))\cdot(-2)\cdot(-(1)/(4))\cdot(5) \\ \\ ((22)/(5))\cdot(-(5)/(4)) \end{gathered}`

Now we have solved two pairs of parentheis and now we are left with the last two. We will again apply the multiplication operation and keeping in mind the product of two signs rule.

`\begin{gathered} -(22\cdot5)/(5\cdot4) \\ \\ -(22)/(4) \\ \\ -(11)/(2) \\ \\ -5(1)/(2)\ldots\text{ Answer} \end{gathered}`