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Chapter 2: Problem 92

Perform the indicated operation. $$-36 \div(-12)$$

Short Answer

Expert verified
3

Step by step solution

01

Identify the operation

First, identify the operation we need to perform. The exercise asks for division.
02

Set up the division

Set up the division problem as \(-36 \div (-12)\).
03

Divide the numbers

Divide the absolute values of the numbers: \(36 \div 12 = 3\).
04

Determine the sign

Since we are dividing two negative numbers, the result will be positive. Therefore, \(-36 \div (-12) = 3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

integer division
Integer division is the process of dividing one integer by another. In the exercise, we have \(-36 \div (-12)\). Here, the numbers we are working with are both integers. To complete the operation, we follow these steps: \
  • First, identify that we are performing a division operation.
  • Next, set up the problem visually as \(-36 \div (-12)\).
  • Divide the absolute values of the integers. The absolute value of \(-36\) is 36 and the absolute value of \(-12\) is 12. Dividing these, we get 3.

absolute value
In mathematics, the absolute value of a number refers to its distance from zero on the number line, without considering its direction. In our exercise, we need to find the absolute values of -36 and -12.
  • The absolute value of -36 is 36, because \[-(-36) = 36\].
  • Similarly, the absolute value of -12 is 12, because \[-(-12) = 12\].

Now that we know the absolute values, we can proceed with the division.
sign rules for division
When dealing with division, it is essential to apply the sign rules correctly to determine the sign of the resulting quotient. The rules are simple:
  • If you divide two positive integers, the result is positive (e.g., \(6 \div 2 = 3\)).
  • If you divide two negative integers, the result is also positive (e.g., \(-6 \div -2 = 3\)).
  • If one integer is positive and the other is negative, the result is negative (e.g., \(-6 \div 2 = -3\) or \(6 \div -2 = -3\)).

In our exercise, since we are dividing two negative integers (-36 and -12), the answer is positive. Hence, \-36 \div (-12) = 3\.

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