Problem 68 - Beginning and Intermediate Algebra

Question

Divide. $$ \frac{-60}{5} $$

Step-by-Step Solution

Answer

The result of dividing \(-60\) by \(5\) is \(-12\).

Step 1: Understand the Problem

We are given a division problem where we need to divide \(-60\) by \(5\). Division is the process of determining how many times one number is contained within another. In this case, we want to find out how many times \(5\) is contained within \(-60\).

Step 2: Divide the Numerical Values

To divide \(-60\) by \(5\), first ignore the negative sign and perform the division for the absolute values. Thus, divide \(60\) by \(5\):\[ 60 \div 5 = 12 \]

Step 3: Apply the Sign of the Result

Since we are dividing a negative number by a positive number, the result will be negative. Therefore, the answer after applying the sign is \(-12\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are an essential part of mathematics and are used in various situations to represent loss, debt, or decrease. When a number is negative, it is typically written with a minus sign in front of it. For instance, \(-60\) is a negative number. Negative numbers can be tricky, especially when it comes to operations such as addition, subtraction, multiplication, and division.

• Negative numbers are found on the left side of a number line.
• They can represent things like temperature drop, debt, or decrease in value.
• Negative numbers interact differently with positive numbers during mathematical operations.

Understanding how negative numbers behave is crucial for mastering basic and advanced math concepts.

Division Process

The division process is about finding out how many times a divisor fits into a dividend. In our example, we need to determine how many times \(5\) can be drawn out of \(-60\).
The process of division typically involves:

• Identifying the dividend (the number to be divided) and the divisor (the number you divide by).
• Performing the calculation by dividing the absolute values.
• Obtaining a quotient, which is the result of the division.
• Applying any necessary rules, such as sign rules, to arrive at the final result.

While division might seem complex, breaking it into these steps makes it manageable. Practice and familiarity with the process can help solidify your understanding of division.

Sign Rules in Division

When dividing numbers, it is important to understand how the signs of the numbers affect the result. The sign rules in division help determine whether the final quotient is positive or negative.

• If both the dividend and divisor are positive, the quotient is positive.
• If both the dividend and divisor are negative, the quotient is positive.
• If one number is positive and the other is negative, the quotient is negative.

For instance, when dividing \(-60\) by \(5\), you first carry out the division ignoring the negative sign, arriving at \(12\). Then, applying the sign rules, you determine that the final result is negative, hence \(-12\). Understanding these rules ensures accuracy in division operations involving negative numbers.