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Chapter 2: Problem 3

Find the value of \(-(-8)\) (a) \(-8\) (b) 0 (c) 8 \((d)-(+8)\)

Short Answer

Expert verified
The value is 8, which matches option (c).

Step by step solution

01

Identify the Expression

First, we need to identify the expression we need to evaluate: -(-8). The expression involves a double negative.
02

Understand Double Negatives

When dealing with double negatives in mathematics, such as -(-x), we understand it as taking the negative of a negative number. This is equivalent to the positive of that number, thus -(-x) = x.
03

Evaluate the Expression

Apply the understanding of Step 2 to evaluate -(-8), which gives us 8.
04

Select the Correct Option

After evaluating the expression as 8, compare it with the given options: (a) -8, (b) 0, (c) 8, (d) -(+8). Option (c), which is 8, matches the result.

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Key Concepts

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

Double Negatives
Dealing with double negatives can sometimes be confusing, but with a bit of understanding, you can master this concept easily! In mathematics, a double negative involves two negative signs affecting one another. This might sound a bit complicated, but it's simpler than you might think.
When you see
  • \(-(-x)\)
this essentially means you are reversing the reversal. Think of it as flipping over twice. If you start with a negative, and then flip it again, you end up with a positive. So, \(-(-x) = x\).
Applying this to \(-(-8)\) means the number becomes positive, turning the expression into just 8.
Evaluating Expressions
When you evaluate expressions, you need to understand what each part of the expression means. To evaluate an expression correctly, follow the steps to simplify the expression and understand its value.
For the expression \(-(-8)\), first recognize the double negative. As we just covered, a double negative makes the number positive. This changes \(-(-8)\) to 8.
  • Recognize each mathematical operation and symbol present.
  • Resolve complex signs step by step to avoid errors.
Once you simplify the expression by resolving double negatives, check if there are any further simplifications needed. In the expression \(-(-8)\), no further steps are required once the double negative is resolved.
Mathematical Signs
Understanding mathematical signs is crucial in correctly interpreting and solving mathematical problems. Mathematical signs represent the operations you perform on numbers.
Consider these common signs:
  • "+" for addition
  • "-" for subtraction
  • "脳" for multiplication
  • "梅" for division
When working with expressions involving signs, it's important to pay attention to details, such as the placement and type of each sign. In our example, \(-(-8)\), understanding the properties of negatives is key.
Always remember:
  • A positive sign before a number or variable usually does not change its value.
  • A negative sign reverses a number's or a variable's sign.

This understanding helps prevent common errors when evaluating mathematical expressions.

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Most popular questions from this chapter

Add \(-8+(-15)\) (a) 23 (b) \(-7\) (c) \(+7\) (d) \(-23\)

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Find \((-9)^{4}\) (a) \(-6561\) (b) 36 (c) 6561 (d) \(-36\)

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Simplify \(3 \times(6-2+1) \div 5\) (a) 3 (b) \(-5\) (c) 2 (d) 15
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