Problem 66 - Beginning and Intermediate Algebra

Question

Divide. $$ \frac{-18}{-6} $$

Step-by-Step Solution

Answer

The result is 3.

Step 1: Understand the Problem

We are given a fraction \( \frac{-18}{-6} \). This means we need to divide -18 by -6.

Step 2: Apply the Rule of Division for Negative Numbers

When dividing two negative numbers, the negative signs cancel each other out. This means \( \frac{-18}{-6} \) is equivalent to \( \frac{18}{6} \).

Step 3: Perform the Division

Now, divide 18 by 6. We know that 18 divided by 6 equals 3.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-). Understanding how negative numbers interact with each other is crucial in arithmetic. When you multiply or divide two negative numbers, the result is positive. This is because the negative signs cancel each other out.
For example, if we have \(-a \) and \(-b \), the product \(-a \times -b\) is \(+ab\). This same rule applies to division.

• If you divide \((-18)\) by \((-6)\), you are left with \( \frac{18}{6} \), which is a positive number.
• It's important to remember this rule because working with negative numbers can sometimes be confusing.

Knowing how to handle them makes mathematical operations much easier.

Mastering Division

Division is a basic arithmetic operation which is essentially the process of splitting a number into equal parts. It’s important to grasp the concept of division fully to solve fractions involving both positive and negative numbers.
For example, in the operation \( \frac{-18}{-6}\), division simplifies the expression by canceling negatives and reducing \( \frac{18}{6}\) to 3.

• Division allows us to determine how many times one number fits into another.
• It’s also crucial to understand the terminology. The dividend is the number being divided; in this case, -18. The divisor is the number you are dividing by, which is -6. The result you get after the division is called the quotient; here, it is 3.

Practicing division helps in developing a strong foundation in arithmetic skills.

Basic Arithmetic Simplified

Basic arithmetic involves the simpler mathematical operations of addition, subtraction, multiplication, and division. Learning these elementary operations is essential before tackling more complex equations.

• Addition is combining numbers together, while subtraction is finding the difference between them.
• Multiplication involves determining the product when one number is repeated a certain number of times, and division helps in understanding how these numbers can be evenly distributed.

In the exercise given, \( \frac{-18}{-6} \) involves basic arithmetic in the form of division. Understanding it can clear the pathway to solving more intricate math problems.
Enhancing your skills in basic arithmetic includes regular practice and understanding the logical steps needed to solve problems accurately.

Approaching Problem-Solving Comfortably

Problem-solving is an essential skill in mathematics and beyond. It involves understanding the problem, planning a way to solve it, and then executing that solution.

• Always begin by carefully analyzing the problem, like determining what is being asked.
• Next, gather all relevant information and decide which mathematical operations can help. In our exercise, we identified that dividing two negative numbers simplifies to dividing their positive counterparts.
• Try solving the problem step by step, ensuring each part of your solution makes sense logically.

Having a clear plan of action, as demonstrated in solving \( \frac{-18}{-6}\), is a significant part of every successful problem-solving strategy.
Practice these steps with regular examples to become comfortable with problem-solving.