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Chapter 3: Problem 80

In the following exercises, simplify each expression. $$ -17+(-18)+6 $$

Short Answer

Expert verified
-29

Step by step solution

01

- Simplify the Negative Addition

Start by simplifying the addition of the two negative numbers. Combine \(-17\) and \(-18\).Adding \(-17\) and \(-18\) gives \(-17 + (-18) = -17 - 18 = -35\).
02

- Add the Remaining Number

Next, take the result from Step 1 and add the remaining positive number.So we have \(-35 + 6\).Adding \(-35\) and 6\ gives \(-35 + 6 = -29\).

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Key Concepts

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

negative numbers
In mathematics, a negative number is a number that is less than zero. Negative numbers are written with a minus sign in front, like -5, -12, -100. They represent quantities that are in the opposite direction or below a certain point. Think of temperatures below freezing or depths below sea level.
When dealing with negative numbers, it's important to remember:
  • Two negative numbers added together will result in a more negative number.
  • A positive number and a negative number added together will result in a number that is either positive or negative, depending on their absolute values.
For example, in our exercise, we had to add -17 and -18 together. Since both numbers are negative, their combination is even more negative: -17 + -18 = -35.
addition
Addition is one of the fundamental operations of arithmetic. It combines two or more numbers into a single number called the sum. Addition is usually the first operation learned in math, laid out in the form: $$a + b = c$$
When working with addition involving negative numbers, the rules slightly differ:
  • Adding two negative numbers together results in their further negative sum. For example, -3 + -4 = -7.
  • Adding a positive number to a negative number involves a subtraction process, such as 8 + -3, which is similar to 8 - 3, resulting in 5.
In the given exercise, we added -35 (a negative number) and 6 (a positive number). The result, -29, reflects the concept of 'larger quantity' remaining negative.
prealgebra
Pre-algebra introduces students to the basic concepts and operations that are foundational for algebra. The goal is to develop an understanding of arithmetic operations and the relationships between numbers. Key topics include:
  • Understanding variables and expressions
  • Simplifying expressions
  • Performing arithmetic operations with positive and negative numbers
In our exercise, we simplified a given expression. Such exercises in prealgebra help students gain confidence in handling more complex equations later on. Here is how we approached it:
We first added the two negative numbers -17 and -18 to get -35. Then, we added -35 to the positive number 6. These steps reinforce a strong comprehension of how to combine positive and negative values in calculations.

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Most popular questions from this chapter

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