Problem 114 The Sign of a Quotient Is the qu... [FREE SOLUTION]

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Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 114

The Sign of a Quotient Is the quotient of 12 and $-4$ positive or negative? Explain.

Short Answer

Expert verified

The quotient of 12 and -4 is negative.

Step by step solution

Understand the numbers involved

In this problem, the two numbers involved are 12 (a positive number) and -4 (a negative number).

Apply the division operation

Divide the positive number (12) by the negative number (-4). Using the rule outlined in the problem analysis: a positive number divided by a negative number gives a negative result.

Verify the sign of the result

The result of the division is -3, which is a negative number. So, the quotient of 12 and -4 is negative.

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Key Concepts

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

Signs of Numbers

Understanding the signs of numbers helps in performing arithmetic operations accurately and determining the nature of the result. Numbers can either be positive or negative.

**Positive Numbers** are greater than zero, like 1, 2, 3, etc., and typically are written without a sign.
**Negative Numbers** are less than zero, like -1, -2, -3, and are indicated with a minus sign.

Without the correct understanding of these signs, calculating the results of operations like addition, subtraction, or division could be misleading. When two numbers with different signs are involved in an arithmetic operation, recognizing their signs is crucial.
For example, in multiplication and division, if the numbers have different signs, the result will be negative. This will help you predict outcomes without even performing the entire calculation.

Division Rules

Division is one of the fundamental arithmetic operations. When dividing numbers, understanding the rules concerning their signs ensures we get the correct outcome. These rules are simple but critical:

If you divide a **positive number** by a **positive number**, the result is **positive**.
If you divide a **negative number** by a **negative number**, the result is also **positive**.
If you divide a **positive number** by a **negative number**, the result is **negative**.
Conversely, if you divide a **negative number** by a **positive number**, the result is also **negative**.

These division rules are vital to remember when performing operations, especially with different signs. For instance, when dividing 12 by -4, you apply the rule that a positive divided by a negative results in a negative. Therefore, the outcome is -3, adhering to these division rules.

Negative Numbers

Negative numbers are a pivotal part of mathematics, especially in scenarios involving debt, temperatures below zero, and engineering concepts. Grasping how they function aids in numerous mathematical operations.
Negative numbers are represented with a minus sign (-), signifying values less than zero. In number lines, they appear to the left of zero.

When you add a negative number to another number, it's equivalent to subtracting the number.
When you multiply two negative numbers, the result is positive.
Dividing negative numbers might seem challenging, but the rules are straightforward: remember that a negative divided by a negative results in a positive.

Negative numbers often seem tricky, especially in complex operations like division, but once understood, they simplify the problem rather than complicate it. Embracing these concepts with confidence will ease your path through many mathematical challenges.

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91影视

The Sign of a Quotient Is the quotient of 12 and \(-4\) positive or negative? Explain.

Short Answer

Step by step solution

Understand the numbers involved

Apply the division operation

Verify the sign of the result

Key Concepts

Signs of Numbers

Division Rules

Negative Numbers

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