Problem 66 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ -(8+21) $$

Step-by-Step Solution

Answer

Answer: -29

Step 1: Evaluate the expression inside the parentheses

Add the numbers inside the parentheses. $$ 8 + 21 = 29 $$

Step 2: Apply the negative sign

Now that we have calculated the sum of the numbers inside the parentheses, we can apply the negative sign. $$ - (29)= -29 $$ The value of the given expression is -29.

Key Concepts

Evaluating expressions

Evaluating expressions is an essential skill in elementary algebra. To evaluate an expression means to calculate its value using a specific set of numbers. For example, in the exercise you provided, we start by figuring out what's happening inside the parentheses first.

• First, focus on any operations inside parentheses—these operations must be done first.
• Perform addition, subtraction, multiplication, or division as required.

Without correctly performing these steps, you might end up with the wrong value. It's also important to do operations systematically, moving from one calculation to the next. Practice makes perfect, so trying out different problems with varying difficulty levels will sharpen your skills over time.

Negative numbers

Negative numbers are numbers less than zero, and they have applications in various math and real-world scenarios such as temperature readings below zero or decreases in bank account balances. In our exercise, the result inside the parentheses was 29, onto which we then applied the negative sign.

• A negative sign before a number means we are dealing with the opposite of a positive number.
• For example, when we say \(-8\), we mean 8 units in the negative direction on a number line.
• Negative numbers combine with positive numbers in operations like addition and subtraction.

It's crucial to understand how negative numbers interact with various arithmetic operations. When you multiply or divide negative numbers, remember that multiplying or dividing two negatives will yield a positive result.

Parentheses in mathematics

Parentheses serve as indicators of priority in mathematical expressions, telling you what part of an expression to solve first. They organize calculations and denote which operations are to be performed earlier than others.

• Always resolve expressions within parentheses before moving on to other operations.
• In complex expressions, you may find nested parentheses—resolve the innermost first.
• The operations inside parentheses can be solely mathematical, or represent a group of numbers added together, like \((8 + 21)\).

Ignoring the order of operations can lead to incorrect answers, so parentheses are essential in guiding how an expression is calculated. Following the rules of parentheses ensures clarity in complicated calculations, reducing errors in your work.