Problem 49 $\frac{-81}{-3}$... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 49

$\frac{-81}{-3}$

Short Answer

Expert verified

The simplified form of $\frac{-81}{-3}$ is 27.

Step by step solution

Identify the Numbers

The numbers present in this exercise are -81 and -3.

Perform the Division

Divide -81 by -3. When a negative number is divided by another negative number, it results in a positive quotient.

Write the Result

The result of $\frac{-81}{-3}$ is 27.

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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 values less than zero, represented with a minus sign (-). They often describe deficits, debts, or temperatures below freezing, among other real-world concepts. Mathematically, they are used to explore the opposite operations of addition and subtraction. For instance:

-81 is a negative number.
Negative numbers appear frequently in both division and multiplication exercises.
Understanding their properties is crucial for solving arithmetic operations involving negatives.

When working with negative numbers, it is important to understand that multiplying or dividing two negative numbers results in a positive outcome. This is because the two negative signs cancel each other out.

Positive Quotient

In arithmetic, a quotient is the result of division. A positive quotient means the result is greater than zero. When dividing integers, it's important to remember:

A negative number divided by another negative number yields a positive quotient.
This is because the two negative signs negate each other, similar to when two "no" responses are taken as a "yes."
For example, dividing -81 by -3 gives a positive result of 27.

Thus, when you see two negatives in a division problem, prepare your mind for a positive quotient.

Arithmetic Operations

Arithmetic operations are basic mathematical processes that include addition, subtraction, multiplication, and division. They form the foundation of mathematics and are used in more complex equations and real-world applications.

Division is one of the critical operations and can be thought of as repeated subtraction or distributing a total into equal parts.
The result of a division operation can be a whole number or a decimal, depending on the numbers involved.
When working with integer division, it鈥檚 important to correctly apply the rules of signs for positive and negative numbers.

Understanding these fundamental operations allows for more accurate and efficient problem-solving in mathematics. Division operations, like the one we are discussing, highlight how arithmetic rules apply to create meaningful results from numbers.

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91影视

\(\frac{-81}{-3}\)

Short Answer

Step by step solution

Identify the Numbers

Perform the Division

Write the Result

Key Concepts

Negative Numbers

Positive Quotient

Arithmetic Operations

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