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Chapter 2: Problem 65

Find the sum of the given integers. \(6+(-1)+3+(-4)\)

Short Answer

Expert verified
The sum of the integers is 4.

Step by step solution

01

Identify the Numbers

First, list all the integers that are part of the sum: 6, -1, 3, and -4.
02

Group Positive and Negative Numbers

Separate the positive numbers and the negative numbers. Positive numbers: 6, 3. Negative numbers: -1, -4.
03

Sum the Positive Numbers

Add the positive numbers together: 6 + 3 = 9.
04

Sum the Negative Numbers

Add the negative numbers together: (-1) + (-4) = -5.
05

Add Positive and Negative Sums Together

Combine the sums obtained from Steps 3 and 4: 9 + (-5).
06

Compute the Final Sum

Calculate the final sum by performing the addition: 9 + (-5) = 4.

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Key Concepts

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

Positive Numbers
Positive numbers are numbers greater than zero. They have a "+" sign in front of them, although it is not always written down. For example, in the sum of integers problem, the numbers 6 and 3 are both positive numbers.

When adding positive numbers, you simply perform the usual addition. For example, adding 6 and 3:
  • Start by placing 6 in your mind or on paper.
  • Add 3 to 6, which gives you a total of 9.
Therefore, the sum of positive numbers 6 and 3 is 9. Positive numbers are straightforward as they follow the same rules you鈥檝e learned for adding whole numbers from an early age.
Negative Numbers
Negative numbers are numbers less than zero. They are represented with a "-" sign in front of them. In our exercise, -1 and -4 are examples of negative numbers.

When adding negative numbers together, think about them as debts or losses. If you owe $1 and then owe another $4, you have a total debt of $5. Adding -1 and -4:
  • Think of -1 as owing one dollar.
  • Add -4, which means you're owing another four dollars.
  • Your total debt becomes -5 dollars.
Thus, the sum of the negative numbers -1 and -4 is -5. Understanding negative numbers helps in visualizing scenarios involving loss or removal.
Sum of Integers
The sum of integers involves combining both positive and negative numbers. When we approach the problem 6+(-1)+3+(-4), simplifying involves considering each integer's sign.

First, we added the positive integers (6 + 3) to get 9. Then, we added the negative integers (-1 + -4) which gave us -5. Finally, to find the total sum:
  • Take the sum of the positive numbers: 9.
  • Add the sum of the negative numbers: -5.
  • Therefore, 9 + (-5) equals 4.
To visualize, think of the positive sum as money you have and the negative sum as money you owe. Combine them, and you have the total. In math, the sum of integers ensures every number's value contributes to a final, complete total.

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