Problem 113 - Introductory Algebra for College Students

Question

Explain how to simplify a series of additions and subtractions. Provide an example with your explanation.

Step-by-Step Solution

Answer

The simplification of the series \(3 - 2 + 4 - 5 + 6\) is 20.

Step 1: Understanding the problem

Consider a series of additions and subtractions, say \(3 - 2 + 4 - 5 + 6\). The aim of this exercise is to simplify this series in a stepwise manner.

Step 2: Using the Commutative Property

The commutative property states that the order of numbers does not change the outcome in the case of addition or multiplication. Since this series has both additions and subtractions, first we need to separate additions from subtractions: \(3 + 4 + 6 - 2 - 5\).

Step 3: Simplifying the series

Now perform the additions and subtractions separately. Start by adding all the positive numbers: \(3 + 4 + 6 = 13\). Then subtract the negative numbers: \(-2 - 5 = -7\).

Step 4: Final subtraction

Subtract the calculated negative number from the calculated positive number to get the final result: \(13 - (-7) = 20\).