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Chapter 1: Problem 20

In Exercises \(1-66,\) compute the value of each expression. $$16+(-12)$$

Short Answer

Expert verified
The result is 4.

Step by step solution

01

Understand the Problem

You are asked to compute the value of the expression involving addition and a negative number: 16 + (-12).
02

Identify the Numbers

The numbers involved in the expression are 16 and -12.
03

Perform the Operation

When adding a positive number and a negative number, subtract the absolute value of the negative number from the positive number: 16 + (-12) = 16 - 12.
04

Calculate the Result

Subtract 12 from 16 to get the result: 16 - 12 = 4.
05

State the Final Answer

The final result of the expression 16 + (-12) is 4.

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Key Concepts

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

Addition of Integers
Adding integers might seem tricky at first, but with a little practice, it becomes quite simple. There are two main rules to remember:
  • If both integers are positive, simply add them as you would with natural numbers.
  • If one number is positive and the other is negative, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.
For instance, in the expression 16 + (-12), we identify that we are adding a positive integer (16) to a negative integer (-12). Following the rules, we subtract 12 from 16 (since 12 has a smaller absolute value) to get 4.
Absolute Value
The absolute value of a number refers to its distance from zero on the number line, regardless of its direction. In simpler terms, it's the non-negative value of a number. For example, the absolute value of both 12 and -12 is 12. When dealing with addition of integers, especially when one of them is negative, the concept of absolute value helps us determine the magnitude of each number. In the given expression 16 + (-12), we first find the absolute values: 16 and 12. We then proceed to the operation based on these absolute values.
Negative Numbers
Negative numbers can often throw people off, but they follow simple rules. A negative number is any number that is less than zero. When adding a negative number, think of it as subtracting its absolute value from the positive counterpart. In our example of 16 + (-12), we consider -12 as subtracting 12 from 16. This transforms the addition problem into a subtraction problem (16 - 12). Following this, we get the result 4. Understanding how negative numbers work greatly simplifies integer operations.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$\frac{18-3(4-1)}{2 \cdot 3+3}$$

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

Evaluate the given expression. Remember to follow the order of operations. $$6+(4 \cdot 3+2)$$

In Exercises \(1-72\), compute the value of each expression. $$225-56-97-115$$

In Exercises \(73-84\), evaluate the given expression. $$|2-6|-(2-6)$$
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