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Chapter 2: Problem 38

Perform the indicated operations. See Sections 1.5 and 1.6 $$ -12-3 $$

Short Answer

Expert verified
-15

Step by step solution

01

Identify the Expression

The given exercise requires us to perform the operation \(-12 - 3\). This is a subtraction problem involving two negative numbers.
02

Simplify the Expression

To solve \(-12 - 3\), we consider the operation as subtracting 3 from -12. In the number line concept, moving left means subtracting values. So from -12, we move 3 units left, reaching -15.
03

Verify the Calculation

Verify by checking: Subtracting a positive number from a negative number results in a more negative number, hence \(-12 - 3 = -15\). This confirms our previous calculation.

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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 a fundamental concept in math, representing values less than zero. They are depicted with a minus sign (-) in front, such as -1, -5, or -12. These numbers are often encountered in various real-life scenarios, like temperatures dropping below freezing or a bank account overdraft. Understanding negative numbers is crucial, as they behave differently in arithmetic operations than positive numbers.
  • Negative numbers extend the number system below zero.
  • They are essential for expressing losses or deficits.
  • When adding two negative numbers, visualize moving further left on a number line.
Recognizing how negative numbers interact with other numbers, especially in subtraction, deepens our comprehension of arithmetic principles.
Number Line
A number line is a visual representation of numbers placed at equal intervals along a straight line. It is an incredibly useful tool for grasping the relationship between numbers, including positive, negative, and zero. On a number line, numbers increase as we move to the right and decrease as we move to the left.
  • This visualization helps understand adding and subtracting negative numbers.
  • For subtraction, move left; for addition, move right.
  • The number line is particularly helpful for comparing sizes of numbers and for seeing how large or small numbers are relative to each other.
When performing the operation \(-12 - 3\), use a number line to aid in visualization: start at -12 and move three steps left, landing at -15. This powerful tool simplifies complex operations by translating numerical operations into physical movement.
Arithmetic Operations
Arithmetic operations like addition and subtraction are the building blocks of mathematics. Understanding these operations helps solve complex math problems and real-life scenarios. When dealing with integers, especially negative numbers, it's important to know how they interact in these operations. Subtracting numbers, for instance, involves understanding how one number decreases in value relative to another.
  • Addition combines values, moving right on the number line when values are positive.
  • Subtraction removes values, moving left on the number line, particularly with negative numbers.
  • Understanding how arithmetic operations affect numbers enriches our problem-solving skills.
In the case of \(-12 - 3\), the operation involves subtracting a smaller number from a larger negative number, resulting in a more negative result, \(-15\). Recognizing these patterns ensures accuracy in both simple and complex calculations.

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