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Chapter 4: Problem 44

Find the value of each expression. $$ 8+(-5) $$

Short Answer

Expert verified
The value of the expression is 3.

Step by step solution

01

Identify the Numbers

The expression given is \( 8 + (-5) \). Here, the numbers involved are 8 and \(-5\).
02

Understand the Mathematical Operation

The operation in the expression is addition. When adding a negative number, it is equivalent to subtracting its absolute value from the other number.
03

Convert Addition to Subtraction

Convert the expression from addition of a negative number to subtraction. Thus, \( 8 + (-5) \) becomes \( 8 - 5 \).
04

Perform the Calculation

Subtract 5 from 8. This is a straightforward subtraction: \( 8 - 5 = 3 \).
05

Verify Your Result

Double-check the calculation to ensure accuracy. Verify that \( 8 + (-5) \) simplifies correctly to \( 3 \), confirming our answer is correct.

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Key Concepts

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

Addition of Negative Numbers
When you add a negative number to another number, it can feel a bit confusing at first. Essentially, adding a negative number is similar to subtracting the absolute value of that number. For instance, in the equation \( 8 + (-5) \), adding \(-5\) means moving 5 units to the left on a number line from 8. In other words, you are subtracting 5 from 8. This concept helps in understanding why \( 8 + (-5) \) can be rewritten as \( 8 - 5 \).
  • Addition as Movement: Moving left means subtracting, and moving right means adding. So, when you add a negative, you're effectively moving in the opposite direction.
  • Common Misunderstanding: It鈥檚 important not to get confused by the word "addition". Just think of it as a direction on the number line: negatives go left.
Subtraction
Subtraction is a fundamental operation in arithmetic where you take one quantity away from another. In our expression, \( 8 + (-5) \), we effectively perform the subtraction \( 8 - 5 \). The subtraction process is crucial because it helps in simplifying expressions that involve negative numbers.
  • Simple Steps: Identify the larger number, subtract the smaller one, and retain the sign of the larger number if you're working with positives and negatives.
  • Practical Example: From 8, remove 5: you have 3 left. It's that simple.
  • Verification: Always take a moment to verify your solution. In our example, double-checking shows that taking away 5 from 8 indeed leaves you with 3.
Absolute Value
The absolute value of a number is its distance from zero on the number line, without considering which direction it's in. This is always non-negative. For negative numbers, the absolute value is the same number but positive. In the expression \( 8 + (-5) \), the absolute value of \(-5\) is 5.
  • Understanding Absolute Value: No matter if a number is positive or negative, absolute value discusses its magnitude or size.
  • Usefulness: By focusing only on the size and ignoring the sign, absolute value helps convert problems to simpler subtraction.
  • Visualizing on a Number Line: Imagine you are at zero, the absolute value tells you how far you need to step regardless of direction.

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Most popular questions from this chapter

The bottom of the Mariana Trench in the Pacific Ocean is 6.8 miles below sea level. Water pressure in the ocean is represented by the function \(f(x)=1.15 x\) , where \(x\) is the depth in miles and \(f(x)\) is the pressure in tons per square inch. Find the pressure in the Mariana Trench.

Find the inverse of each matrix, if it exists. \(\left[\begin{array}{ll}{4} & {4} \\ {2} & {3}\end{array}\right]\)

Find each product, if possible. \(\left[\begin{array}{rr}{5} & {-4} \\ {8} & {3}\end{array}\right] \cdot\left[\begin{array}{l}{5} \\ {1}\end{array}\right]\)

Solve each system of equations. $$ \begin{array}{l}{3 x-2 y=-2} \\ {4 x+7 y=65}\end{array} $$

Write a matrix equation for each system of equations. \(5 a-6 b=-47\) \(3 a+2 b=-17\)
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