Problem 33 - Algebra A Combined Function

Question

Divide. \(\frac{18}{-2}\)

Step-by-Step Solution

Answer

The result of \( \frac{18}{-2} \) is -9.

Step 1: Identify the Problem

We need to divide the number 18 by -2 and find the quotient.

Step 2: Apply Division Rule

The division rule states that when you divide a positive number by a negative number, your result will be negative. Here, we are dividing 18 by -2.

Step 3: Perform the Division

Divide 18 by 2. This equals 9.

Step 4: Determine the Sign

Since 18 is positive and -2 is negative, the result of the division will be negative, making the final result -9.

Key Concepts

Division of Integers

Division is one of the basic arithmetic operations, much like addition, subtraction, and multiplication. When we talk about dividing integers, we are referring to dividing whole numbers which can be either positive or negative. In simple terms, division can be described as determining how many times a number, known as the divisor, is contained within another number, the dividend. Let's break it down further:- **Dividend**: The number you are dividing up. In \(\frac{18}{-2}\), the dividend is 18.- **Divisor**: The number you are dividing by. In \(\frac{18}{-2}\), the divisor is -2.When you divide two integers, the outcome that you get is called the quotient. It's important to understand how to maintain the positive or negative nature of numbers when performing division, which leads us to exploring positive and negative numbers.

Positive and Negative Numbers

Positive and negative numbers are symbols used to represent values that are above or below zero in mathematics. These numbers form the foundation of arithmetic and algebra. - **Positive Numbers**: Any number greater than zero, expressed without a sign or with a "+" sign. Examples include 1, 2, and 100. - **Negative Numbers**: Numbers less than zero, expressed with a "-" sign. Examples include -3, -10, and -45. Understanding how these numbers interact under different operations is essential, particularly in division. In our case, 18 is positive while -2 is negative. When you engage in division, the sign of the numbers can affect the overall sign of your answer. This is where sign rules become very important.

Sign Rules in Math

In mathematical operations, sign rules determine the outcome when using positive and negative numbers. These rules are especially important when performing multiplication and division. Here are the basic sign rules you'll need to remember:

• **Positive "+" Positive**: The result is positive.
• **Negative "-" Negative**: The result is positive, because a negative times a negative gives a positive.
• **Positive "+" Negative**: The result is negative. A positive number divided by a negative number results in a negative quotient.
• **Negative "-" Positive**: The result is negative, due to the same reasoning as above.

When dividing 18 by -2, you apply the positive divided by negative rule, resulting in a negative quotient of -9. Remembering these rules helps in quickly determining the sign of your answers without confusion.