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Chapter 1: Problem 60

In Exercises \(1-72\), compute the value of each expression. $$-16-23$$

Short Answer

Expert verified
-39

Step by step solution

01

Understand the Problem

Identify the operation that needs to be performed. In this case, it's subtraction of two negative integers: -16 - 23.
02

Set Up the Expression

Re-write the expression to reflect subtraction: -16 - 23.
03

Combine Like Terms

Combine the two terms by simply adding their absolute values and keeping the negative sign: -16 - 23 = -(16 + 23).
04

Perform the Addition

Add the absolute values of the integers: 16 + 23 = 39.
05

Apply the Negative Sign

Place the negative sign in front of the result from the addition: -(16 + 23) = -39.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. In mathematics, they are represented with a minus sign (鈭�) in front of them. For example, 鈭�5, 鈭�16, or 鈭�23 are all negative numbers. Negative numbers are used to represent a deficit, loss, or decrease. They can also represent temperatures below freezing. When dealing with negative numbers:
  • Remember to keep the minus sign attached to the number.
  • Negative numbers are to the left of zero on the number line.
  • The further left the number is, the smaller its value.
Working with negative numbers might seem tricky at first, but with practice, it becomes easier to manage their operations in mathematical problems.
Subtraction
Subtraction is the process of taking one quantity away from another. In the context of this exercise, we are subtracting two numbers: -16 and 23. The rules of subtraction are:
  • When you subtract a positive number, you move further to the left on the number line.
  • When you subtract a negative number, it's equivalent to adding its positive counterpart.
For this problem, we are subtracting 23 from -16. To set up this expression, we write it as -16 - 23. This means we are taking 23 away from -16, which involves moving further left on the number line, thus making the result a larger negative number.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It's always a positive number or zero. For example, the absolute value of both -5 and 5 is 5, denoted as \(|-5| = 5\). In subtraction involving negative numbers:
  • First find the absolute values of each number involved.
  • Combine these absolute values in the operation.
  • Apply any necessary negative signs according to the operation rules.
In our example, \(|-16| = 16\) and \(|-23| = 23\). Combining these values in subtraction implies \(-16 - 23 = -(16 + 23)\), which simplifies to -39. Understanding the role of absolute values can greatly help in handling negative number operations efficiently.

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Most popular questions from this chapter

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