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Chapter 1: Problem 71

Subtract. $$ -5-(-12) $$

Short Answer

Expert verified
7

Step by step solution

01

Understand the Problem

The goal is to perform the subtraction of two numbers, -5 and -12. This requires an understanding of how to handle the subtraction of negative numbers.
02

Apply the Rule of Subtracting Negatives

When subtracting a negative number, the operation can be converted to an addition. Therefore, oe{-5 - (-12)} can be rewritten as oe{-5 + 12}.
03

Perform the Addition

Now, simply add -5 and 12. Start by considering the number line or simple arithmetic: oe{-5 + 12 = 7}.

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Key Concepts

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

Integer Subtraction
Subtraction is one of the basic operations you perform on integers. When you subtract integers, you are finding the difference between them.
For example, in the problem -5 - (-12), you are asked to subtract -12 from -5.
This might look complicated, but if you understand the basics of integer subtraction, it becomes easier to solve.
One key thing to remember is that subtracting a number is the same as adding its opposite.
So, -5 - (-12) can be rewritten as -5 + 12.
This conversion makes the problem simpler.
Negative Numbers
Negative numbers are numbers less than zero.
They are represented with a minus sign (-) before the number.
For instance, in the problem -5 - (-12), both -5 and -12 are negative numbers.
When working with negative numbers, it's useful to remember a few basic rules:
1. Adding a negative number is the same as subtracting its positive counterpart (e.g., -5 + (-3) = -5 - 3).
2. Subtracting a negative number is the same as adding its positive counterpart (e.g., -5 - (-12) = -5 + 12).
Following these rules helps simplify complex-looking arithmetic problems.
Number Line
A number line is a visual tool used to understand the position of numbers relative to each other.
It can be very helpful in solving subtraction and addition problems involving negative numbers.
For example, to solve -5 -(-12) using a number line, start at -5.
When you subtract -12, it's the same as adding 12.
Therefore, you move 12 steps to the right on the number line, arriving at 7.
This visualization aids in confirming that -5 -(-12) equals 7.
Using a number line can make arithmetic operations more intuitive, particularly when dealing with negative numbers.

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Most popular questions from this chapter

To the student and the instructor: Synthesis exercises are designed to challenge students to extend the concepts or skills studied in each section. Many synthesis exercises require the assimilation of skills and concepts from several sections. On a quiz, Mia answers \(6 \in \mathbb{Z}\) while Giovanni writes \(\\{6\\} \in \mathbb{Z} .\) Giovanni's answer does not receive full credit while Mia's does. Why?

Solve and check. The symbol \(\sqsubseteq\) indicates an exercise designed to be solved with a calculator. $$ 6 x-\\{5 x-[7 x-(4 x-(3 x+1))]\\}=6 x+5 $$

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. $$ m^{2}-[2(m-n)]^{2}, \text { for } m=7 \text { and } n=5 $$

Write an equivalent expression using the distributive law. $$ 6(s-t) $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{H} \subseteq R $$
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