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Chapter 1: Problem 5

In Exercises \(1-66,\) compute the value of each expression. $$-5+(+12)$$

Short Answer

Expert verified
7

Step by step solution

01

- Understand the operations inside the expression

Identify the numbers and operations in the expression (-5) + (+12). Here, we have -5 and +12.
02

- Compute the addition

Add the numbers together. Begin by visualizing the number line: starting at -5, move +12 steps forward. Therefore, -5 + 12 = 7.

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Key Concepts

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

Addition
Addition is one of the most basic operations in elementary algebra. It involves combining two or more numbers to get a sum. In our example, we need to compute the value of -5 + (+12). When you're adding, you can think of it as finding the total or combining quantities together.

When dealing with simple addition, remember to follow these steps:
  • Identify the numbers you need to add.
  • If you have positive or negative signs, keep them in mind.
Adding whole numbers is straightforward. But when negatives come into play, visualizing them on a number line can make it easier, which leads us to our next section.
Negative and Positive Numbers
Understanding negative and positive numbers is key in elementary algebra. Positive numbers are greater than zero, while negative numbers are less than zero. They are typically used to represent quantities in the opposite direction.

When adding negative and positive numbers:
  • Think of negative numbers as taking steps backward.
  • Think of positive numbers as taking steps forward.
In our example, -5 is a negative number and +12 is a positive number. Adding -5 to +12 means you're starting at -5 and moving forward by 12 steps 鈥� think of it like a number line.

To simplify, anytime you add a positive number to a negative number, you move in the positive direction if the positive number is greater, and vice versa.
Number Line
A number line is an excellent tool for visualizing addition, especially when dealing with negative and positive numbers. It helps by clearly showing the direction and distance you need to move.

Here's how it works:
  • Draw a horizontal line and mark it with numbers, zero being the center.
  • Negative numbers are to the left of zero and positive numbers are to the right.
In our example, to compute -5 + 12, you'd start at -5 on the number line. Then you'd count 12 steps to the right.

This movement lands you on 7. Therefore, -5 + 12 = 7. The number line thus makes it evident how we arrive from -5 to 7 by adding 12.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.02(28.6-13.5)$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{5 \cdot 2+3 \cdot 4+6 \cdot 3}{4 \cdot 5+2 \cdot 6+4 \cdot 2}$$

Factor the given number into its prime factors. If the number is prime, say so. $$3,024$$

Evaluate the given expression. Remember to follow the order of operations. $$(30-5)(4-2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$-6(3.7)$$
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