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Chapter 1: Problem 6

In Exercises \(1-72\), compute the value of each expression. $$5-(-7)$$

Short Answer

Expert verified
12

Step by step solution

01

- Identify the Operation

First, identify the operation within the expression. In this case, the operation is subtraction, and we have to subtract \( -7 \) from \( 5 \).
02

- Apply the Rule for Subtracting a Negative Number

When subtracting a negative number, it is equivalent to adding the positive version of that number. So, rewrite the expression \( 5 - (-7) \) as \( 5 + 7 \).
03

- Perform the Addition

Now, add the two numbers: \( 5 + 7 = 12 \).

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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 those that are less than zero. They are represented with a minus sign ( - ).
Commonly, you will find negative numbers in various real-life situations like temperatures below freezing, depths below sea level, and bank overdrafts.
Understanding negative numbers is crucial in performing operations like addition and subtraction accurately.
For instance, a number line helps illustrate this concept well. Numbers to the left of zero are negative, while numbers to the right are positive.
Whenever you deal with negative numbers in algebra, always pay close attention to the signs, as they can change the result of the operation significantly.
Subtraction Rules
Subtraction can be tricky when it involves negative numbers, so let's break it down.
Here are some key rules to remember:
  • Subtracting a positive: Subtracting a positive number from another number decreases its value. For example, \( 6 - 3 = 3 \).
  • Subtracting a negative: Subtracting a negative number is the same as adding its positive counterpart. For example, \( 6 - (-3) = 9 \).
When you come across an expression like \( 5 - (-7) \), apply the second rule.
Rewrite \( 5 - (-7) \) as \( 5 + 7 \). Now, it turns into an addition problem, which is much simpler to solve.
Addition
Addition is one of the basic operations in algebra and involves finding the total or sum of two or more numbers.
When adding positive numbers, the result is straightforward: the values are combined to create a larger number. For instance, \( 5 + 7 = 12 \).
Here's a brief rundown of addition properties:
  • Commutative Property: You can add numbers in any order. For example, \( a + b = b + a \).
  • Associative Property: Numbers can be grouped in any way when adding. For example, \( (a + b) + c = a + (b + c) \).
In our exercise, we converted the subtraction \( 5 - (-7) \) into \( 5 + 7 \). Then, we simply added the numbers to get the final result of 12.
Understanding addition and its properties is essential for mastering more complex algebraic concepts.

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Most popular questions from this chapter

In Exercises \(73-84\), evaluate the given expression. $$9-(5 \cdot 4-2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-8.4}{1.2}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-6}{1.5}+\frac{21.6}{-1.2}$$

Sketch the given set on a number line. $$\\{x | 3

Graph the given set on a number line. \(\\{x | x \text { is an even natural number less than } 10\\}\)
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