Question

Divide \(-32 \div 8\) A. -2 B. 4 C. -4 D. 2

Short answer

C. -4

Step-by-step solution

- Understand the Problem

We need to divide anegative number ( -32) by a positive number( 8).

- Division Operation

Perform the division by taking the absolute values: 32 divided by 8 equals 4.

- Determine the Sign

Since one number is negative and the other is positive, the result will be negative. Thus, - 32 divided by 8 is -4.

- Choose the Correct Answer

From the given options, the correct answer is C. -4

Key concepts

negative numbers

Negative numbers are numbers that are less than zero. They are usually written with a minus sign (-) before them. For instance, -1, -5, and -32 are all examples of negative numbers.

When working with negative numbers in division, it is important to remember that the sign of the numbers involved will impact the result. If one number is negative and the other is positive, the outcome will be negative. However, if both numbers are negative or both are positive, the result will be positive. This follows from the basic rules of multiplying and dividing integers.

division rules

Division rules for integers are fairly straightforward. Here’s the main gist:

• When dividing a positive number by another positive number, the result is positive.

• When dividing a negative number by another negative number, the result is positive.

• When dividing a negative number by a positive number, or vice versa, the result is negative.

In the example of \(-32 \div 8\) from the problem, you determine that the result must be negative because you're dividing a negative by a positive. Doing the math with their absolute values \((\text{ignoring signs at first})\) gives you a positive integer, and applying the division rules, we know that the final answer must be negative.

absolute value

The absolute value of a number is its distance from zero on the number line, regardless of direction. This means it is always a non-negative number. It is represented by two vertical bars around the number, like this: |a|.

For example:

• \(|-32| = 32\)

• \(|8| = 8|\)

In our exercise division problem, to simplify, we first take the absolute values of the numbers (\text{ignoring the signs}).

So, dividing \(|-32|\) by \(|8|\) equals 4.

In the end, we apply the sign based on the division rules, knowing that one is positive and the other negative, making the result negative. Hence: \(-32 \div 8 = -4\).