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Chapter 1: Problem 125

$$ \text { Add: }-3+(-4)+(-5)+4+3 $$

Short Answer

Expert verified
The sum is -5.

Step by step solution

01

Combine Negative Numbers

First, add all the negative numbers together. This will help us consolidate them. We have \[-3 + (-4) + (-5) = -12\] because adding negatives is like subtracting positives. You simply add their absolute values and keep the negative sign.
02

Sum Positive Numbers

Next, combine the positive numbers. Looking at the equation, the positive numbers are \[4 + 3 = 7\]. Sum them to consolidate our work with positive numbers.
03

Combine Results

Now, subtract the total sum of positive numbers from the sum of negative numbers:\[-12 + 7 = -5\]. This gives us the final answer, as we combine the total of the negative and positive calculations.

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Key Concepts

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

Negative Numbers
When we deal with negative numbers, it's like facing the opposite direction on a number line from zero. Think of it as moving backwards or facing a loss. For example, if you have \(-3\), it's three places to the left of zero on the number line. It's crucial to understand that negative numbers are not lesser in value, but they represent a different value orientation compared to positive numbers.

When adding negative numbers, the process might seem confusing, but it follows a straightforward logic:
  • Think of adding negatives as combining debts or losses.
  • If you add \(-3\) and \(-4\), you combine them to \(-7\), meaning one debt accrued more.
  • Remember: more negatives mean moving further left on the number line.
Positive Numbers
Positive numbers are like moving forward or gaining on a number line. They represent values or amounts. For example, when you look at a number like \(3\), it's three places to the right of zero on a number line.

Combining positive numbers is straightforward:
  • Add them together just as you would count items. \(4 + 3\) means you have a combined total of seven units or steps forward.
  • Think about gathering resources or units that add up in your favor.
This naturally leads to a larger number, meaning a greater gain or distance from zero.
Absolute Value
The absolute value of a number helps us understand how far a number is from zero, regardless of direction. Think of it as the magnitude or size of a number without worrying about its sign.

Here are a few key points about absolute value:
  • The absolute value of both \(-3\) and \(3\) is \(|3|\), because each is three units away from zero.
  • It's always non-negative, telling us only about the distance from zero.
Knowing absolute values helps simplify arithmetic with negative and positive numbers, especially when adding or subtracting them. The concept becomes useful when
  • calculating debts or gains,
  • measuring distances,
  • and balancing positive and negative outcomes.

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Most popular questions from this chapter

Simplify each expression, if possible. $$ -9.8 c+6.2 c $$

Find the prime factorization of \(30 .\)

U.S. Jobs. The table lists the three occupations that are predicted to have the largest job declines from 2008 to 2018 . Complete the column labeled "Change." $$ \begin{array}{|c|c|c|} \hline & {\text { Number of jobs }} \\ \hline \text { Occupation } & {2008} & {2018} & {\text { Change }} \\ \hline \text { Farmers/ranchers } & {985,900} & {906,700} \\ \hline \text { Sewing machine operators } & {212,400} & {140,900} \\ \hline \text { Order clerks } & {245,700} & {181,500} \\ \hline \end{array} $$

Simplify by combining like terms. $$ 10 y^{2}-8 y+y-7 $$

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