Problem 88 - Prealgebra and Introductory Algebra

Question

Divide. $$(-200) \div 8$$

Step-by-Step Solution

Answer

-25

Step 1: Identifying the Operation

Recognize the operation required by the exercise as division.

Step 2: Applying Rule of Signs

Apply the rule of signs. Here, a negative number (-200) is divided by a positive number (8). Thus, the result will be negative.

Step 3: Performing Division

Perform the division ignoring the negative sign for now: \( 200 \div 8 = 25 \). Then attach the negative sign to the result.

Key Concepts

Negative Numbers

Negative numbers are those that are less than zero. They are typically represented with a minus sign in front of them, like -200. Negative numbers are an essential concept in mathematics and can be found in various real-world applications like temperatures below freezing, financial debt, or depth below sea level.

When performing arithmetic operations with negative numbers, it's important to understand how they interact with positive numbers:

• Adding a negative number is like subtracting the absolute value of that number.
• Subtracting a negative number is like adding its absolute value instead.
• Multiplying or dividing negative numbers follows specific rules, which will be explained next.

Rule of Signs

The rule of signs is a fundamental guideline used in multiplication and division involving negative and positive numbers. When dividing or multiplying numbers, this rule helps us determine the sign of the result.

To apply the rule of signs:

• If both numbers you're dividing or multiplying have the same sign (both positive or both negative), the result is positive.
• If the numbers have different signs (one positive, one negative), the result is negative.

In the original exercise, we can use the rule of signs: a negative number (-200) divided by a positive number (8), yields a negative result. Therefore, \[(-200) \div 8 = -25\] Understanding this rule simplifies the process of determining the signs for your answers in arithmetic operations.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of most mathematical calculations and are critical for solving many types of problems.

Let's focus on division, which is splitting one number by another to get a result, called the quotient. In our example,\[(-200) \div 8\]the process involves a simple division where you find how many times the divisor (8) fits into the dividend (200). Ignoring the signs for a moment, \[200 \div 8 = 25\]After computing the quotient, consider the rule of signs to assign the correct sign to the result. Here, because 200 was negative and 8 was positive, the quotient is negative: \[-25\]. Understanding these steps facilitates performing division and other basic arithmetic operations involving negative numbers.