Problem 22 - Elementary Algebra

Question

Determine the quotient of 26 and -13 .

Step-by-Step Solution

Answer

The quotient of 26 and -13 is -2.

Step 1: Understanding the Quotient

The quotient is the result of dividing one number by another. In this exercise, we need to find the quotient of 26 and -13.

Step 2: Determine the Division Setup

We need to divide 26 by -13. This can be set up as: \[\frac{26}{-13}\]

Step 3: Perform the Division

Now, calculate the division by dividing numerators and denominators: 1. Divide 26 by 13, which provides 2. 2. Since 26 is positive and -13 is negative, the quotient will be negative. 3. Therefore, the quotient is -2.

Key Concepts

Understanding Division

Division is one of the fundamental operations in mathematics. Imagine you have a group of objects and you want to split them into smaller, equal groups. The division operation helps you do just that.
In mathematical terms, when you divide one number, called the "dividend," by another number, called the "divisor," the result you get is called the "quotient." For example, dividing 10 by 2 means splitting 10 objects into 2 equal groups, which gives you 5 objects in each group. Thus, the quotient is 5.
Here's a simple way to remember it:

• Dividend: The number you are dividing up (e.g., 10 in 10 ÷ 2).
• Divisor: The number you divide by (e.g., 2 in 10 ÷ 2).
• Quotient: The result of the division (e.g., 5 in 10 ÷ 2).

Understanding division helps in various aspects of problem-solving, making it a vital skill for everyday math.

Working with Negative Numbers

Negative numbers are numbers that are less than zero. They are usually written with a minus sign (-) in front of them. In basic algebra, it's important to know how to handle these numbers, especially when performing operations like addition, subtraction, multiplication, or division.
When dividing numbers, the sign of the quotient can be affected. Here's a quick guide to remember the rules:

• If both the dividend and divisor are positive, the quotient is positive (e.g., 6 ÷ 2 = 3).
• If both are negative, the quotient is positive (e.g., -6 ÷ -2 = 3).
• If one number is positive and the other is negative, the quotient is negative (e.g., 6 ÷ -2 = -3).

The trickiest part is remembering how the signs influence each other. But once you practice, it becomes second nature!

Calculating the Quotient

Finding the quotient is the goal of a division operation. Let's look at a specific example involving both positive and negative numbers to see how it works.
Consider dividing 26 by -13. You start by setting up your division as \[ \frac{26}{-13} \].
Follow these steps to calculate the quotient:

• First, divide the absolute values: 26 ÷ 13 = 2.
• Determine the sign: Since one number is positive and the other is negative, the quotient must be negative.

Thus, the quotient of 26 divided by -13 is -2. A solid grasp of division and negative numbers ensures that you can handle these problems with ease.