Problem 46 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -9.4+[5.8+(-7.9)] $$

Step-by-Step Solution

Answer

-11.5

Step 1: Identify the Inner Parentheses

First, solve the expression inside the parentheses. Begin with the inner sum: $$5.8 + (-7.9).$$

Step 2: Solve the Inner Parentheses

To add 5.8 and -7.9, subtract 7.9 from 5.8: $$5.8 - 7.9 = -2.1.$$

Step 3: Substitute Back

Replace the original parentheses with the result from Step 2: $$-9.4 + (-2.1).$$

Step 4: Add the Results

Now, add -9.4 and -2.1: $$-9.4 + (-2.1) = -9.4 - 2.1 = -11.5.$$

Key Concepts

Order of Operations

When solving any mathematical problem, it's essential to follow the correct sequence of operations, often abbreviated as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This order determines how you solve complex expressions correctly. In the given exercise, we start by solving the expressions inside the parentheses first because they are at the top of the hierarchy. Without respecting the order of operations, you might end up with the wrong result, so always handle parentheses first.

Adding Negative Numbers

Working with negative numbers can be tricky at first, but it becomes easier once you understand the concept. When adding a negative number, it’s the same as subtracting its positive counterpart. For instance, in the exercise, when adding 5.8 and -7.9, it's equivalent to subtracting 7.9 from 5.8. This is why you see: $$5.8 + (-7.9) = 5.8 - 7.9.$$ Once you get the difference, you end up with a negative result because 7.9 is larger than 5.8.

Inner Parentheses

Parentheses in mathematical expressions indicate that the operations inside them should be performed first. In this exercise, we handle the operation inside the parentheses before anything else. The inner operation is: $$5.8 + (-7.9),$$ which simplifies to -2.1. After solving the inner parentheses, replace it with the result for easier calculations. You then proceed with the remaining expression $$-9.4 + (-2.1),$$ which gives you the final answer of -11.5. Removing the parentheses after computation simplifies subsequent steps.