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Chapter 1: Problem 73

In Exercises \(67-74,\) evaluate the given expression. $$|-8|+(-8)$$

Short Answer

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Step by step solution

01

- Evaluate the Absolute Value

Determine the absolute value of ewline The absolute value of -8. . Absolute value measures distance from zero, disregarding the negative sign. ewline Absolute value of -8 is 8.
02

- Replace the Absolute Value

Replace |-8|with 8 in the expression: 8 + (-8).
03

- Simplify the Expression

Simplify the expression 8 + (-8) by adding negatives ewline The result is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Evaluating Expressions
When we evaluate expressions in math, we replace variables or simplify operations to find a single numerical value. In the given problem, we need to evaluate the expression \(|-8| + (-8)\).

Here's a step-by-step breakdown:
  • **Absolute Value**: First, find the absolute value of -8.
  • **Simplify**: Add this value to -8.
Remember that evaluating expressions often changes a complex expression into a simpler one. We make it as simple as possible until we get a single value.

This skill is crucial because it makes complex problems more manageable.
Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form. This means performing operations like addition, subtraction, multiplication, and division to condense the expression.

In our exercise, the expression \(|-8| + (-8)\) was simplified to 0.

Here鈥檚 how:
  • We first calculated the absolute value of -8, which is 8.
  • Next, we replaced |-8| with 8, making our expression 8 + (-8).
  • Finally, we combined 8 and -8, which sums to 0.

Simplifying expressions helps us understand the core components of a mathematical problem and solve it efficiently.
Integer Operations
Integer operations involve basic arithmetic (addition, subtraction, multiplication, and division) with whole numbers. Understanding these operations is essential when simplifying mathematical expressions or solving equations.

In our problem, we dealt with the operation of adding integers and understanding absolute value:
  • **Absolute Value**: Convert any negative number within the absolute value symbols to its positive form.
  • **Addition**: When adding a positive number and a negative number, you effectively subtract the smaller absolute value from the larger one and keep the sign of the larger value.

So, 8 + (-8) simplifies to 0 because we are adding a number and its negative counterpart.

Master the basics of integer operations to solve more complex problems with ease!

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Most popular questions from this chapter

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